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THESIS
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LIBRARY
Michigan State
University

 

 

 

This is to certify that the

dissertation entitled

Fentosecond Gas-Phase Molecular Dynamics:
Pulp—Probe and Pour-Have Mixing Experiments

presented by
Emily J . S . Brown

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Chemistry

115 I a
Con/UM—

Major professor

 

Date 8-2—0!

MS U is an Affirmative Action/Equal Opportunity Institution 0- 12771

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c:/ClRC/DateDue.p65-p.ts

 

 

 

FEMiOSECUXI
PiliP-PROBE i

 

 

FEMTOSECOND GAS-PHASE MOLECULAR DYNAMICS:
PUMP-PROBE AND F OUR-WAVE MIXING EXPERIMENTS

By

Emily J. S. Brown

A DISSERTATION

Submitted to
Michigan State University
in partial fitlfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Chemistry

2001

ETHOSECOXD 6*.

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ABSTRACT

FEMTOSECOND GAS-PHASE REACTION DYNAMICS: PUMP-PROBE
AND F OUR-WAVE MIXING EXPERIMENTS

By

Emily J. S. Brown

Time-resolved rotational anisotropy measurements can be used to obtain
rotational constants of molecules or information about the alignment and rotational
energy in chemical reactions. For some of the most common experimental configurations,
the well-known expression for obtaining the rotational anisotropy is not applicable;
unidirectional signal detection measurements can overestimate the parallel or
perpendicular components of the signal. New formulations that take into account
different unidirectional detection schemes and the f number of the collection optics are
given and demonstrated with femtosecond time-resolved anisotropy measurements on
iodine vapor. Fits to the calculated anisotropy are shown to provide quantitatively
accurate results. In addition, nonlinear saturation effects in ultrafast rotational anisotropy
measurements are observed as a function of increased pump laser intensity (ranging over
three orders of magnitude). These efl‘ects range fi'om a mild reduction in overall
anisotropy to the loss of anisotropy at time zero and the appearance of additional
photochemical processes. At the highest intensities, the rotational anisotropy
measurements show an unusual initial dip followed by a rise near time zero that is due to

excitation of a weaker perpendicular state. Experimental results on molecular iodine,

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chosen as a model system, fit with the conventional anisotropy formalism result in
erroneous rotational populations. Incorporating the observation of the perpendicular state

into a nonlinear rotational anisotropy model yields accurate rotational populations from

measurements with saturated transitions.

Time-resolved transient grating techniques (TG) arising from four-wave mixing
(FWM) processes are explored for the study of molecular dynamics in gas-phase systems
ranging fi'om single atoms to large polyatomic molecules with nonresonant pulses.
Atomic species Ar and Xe show a peak only at zero time delay. For diatomic 02 and N2

and linear triatomic CSz molecules, the TG signals exhibit ground state rotational
recurrences that can be analyzed to obtain accurate rotational constants. Both ground
state vibrational and rotational dynamics are observed in the heavier triatomic Hglz. TG
measurements on larger polyatomic molecules (CH2C12, CHzBl'z, benzene, and toluene)
show rotational dephasing. A theoretical formalism is developed and used successfully to
interpret and simulate the experimental transients. Four-wave mixing experiments with
resonant excitation allow us to select between measurements that monitor wave packet
dynamics, i. e. populations in the ground or excited states, or coherences between the two
electronic states. These cases are explored with the X—)B transition in 12. Control of the
population transfer between the ground and excited states is reported using three-pulse
four-wave mixing. The inherent vibrational dynamics of the system are utilized in timing
the pulse sequence that controls the excitation process. A slight alteration in the pulse

sequence timing causes a change in the observed signal from coherent vibration in the

ground state to coherent vibration in the excited state.

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ACKNOWLEDGMENTS

Many people have helped me along this journey— it is a diflicult task to name all
the individuals who have played a role during this portion of my life.

First, I would like to acknowledge all the support stafl‘ in the Chemistry
Department. Specifically, the people in the machine shop, glass shop, business otfice,
graduate office, and computer technology office were invaluable during my years at
MSU. I would like to personally thank Lisa Dillingham for helping to keep all the details
straight and Tom Atkinson and Paul Reed for their assistance with troublesome
computers.

I would also like to recognize the past and present members of the research group
for their assistance both professionally and personally. Specifically, Holly Bevsek,

Martha Gilchrest, Irene Grimberg, Peter Gross, Vadirn Lozovoy, Una Marvet, Igor
Pastirk, Kathy Walowicz, Mark Waner, and Qingguo Zhang — thank you for your
CXpertise in the lab (and classroom) and your advice out of the lab! To my advisor,
Marcos Dantus, thank you for the opportunities to learn and grow as a scientist and
team“- Thank you for your understanding and patience as family matters took me away
from Mi‘ihigan and I completed this degree “long-distance”.

I WOUId also like to thank my fiiends (especially those I made at MSU) and family

for their support, love, and encouragement (gentle nudges) over these years, especially
my parents 311d my husband Robert. Lastly, to my son Andrew, thank you for making me
Snfile every day!

 

1N OF TABLES

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LIST OF TABLES - x
LIST OF FIGURES, xi
1. INTRODUCTION 1
1.1. MOLECULAR DYNAMICS .................................................................................. 1
1.1.1. Wave Packet Motion .................................................................................... 3
1.1.2. Time-Resolved Spectroscopy ....................................................................... 6

1.2. PUMP-PROBE TECHNIQUE ................................................................................. 8
1.3. FOUR-WAVE MIXING TECHNIQUE .................................................................. 12
1.4. CONTROL OF MOLECULAR DYNAMICS ............................................................ 16

2. EXPERIMENTAL ' 19
2.1. LASER SETUP ................................................................................................. 19
2.1.1. Oscillator ................................................................................................... 19
2.1.2. Amplifier ................................................................................................... 25
2.1.3. Pulse Characteristics .................................................................................. 26
2.2. EXPERIMENTAL TECHNIQUES .......................................................................... 28
2.2.1. PumpProbe Technique .............................................................................. 28
2.2.1.1. Time Delay .......................................................................................... 28
2.2.1.2. Excitation Wavelengths ....................................................................... 29
2.2.1 .3 . Polarization ......................................................................................... 30
2.2.1.4. Intensity ............................................................................................... 32
2.2.1.5. Sample ................................................................................................. 32
2.2.2. Four-Wave Mixing/Transient Grating Technique ....................................... 32
2.2.2.1. Beam Arrangement .............................................................................. 33
2.2.2.2. Time Delay .......................................................................................... 34
2.2.2.3. Signal .................................................................................................. 35
2.2.2.4 Sample ................................................................................................. 36
23' SIGNAL COLLECTION ...................................................................................... 36

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3. ROTATIONAL ANISOTROPY MEASUREMENTS ON IODINE:

EXAMINING UNIDIRECTIONAL DETECTION AND LASER INTENSITY ...... 38
3.1. INTRODUCIION .............................................................................................. 38
3.2. THEORY ......................................................................................................... 41

3.2.1. Pump-Probe Technique for Studying Rotations (Rotational Anisotropy
Measurements) ........................................................................................................ 41
3.2.2. Iodine Sample ............................................................................................ 42
3.2.3. Rotational Anisotropy Formulation: All-Direction Detection ...................... 43
3.2.4. Rotational Anisotropy Formulation: Unidirectional Detection .................... 44
3.2.4.1. Large f number collection .................................................................... 45
3.2.4.2. f number dependence (small f number) ................................................. 48
3.2.5. Evolution ofthe coszaDistribution ............................................................. 49
3.2.6. Extracting Molecular Dynamics Information .............................................. 52
3.2.7. High Intensity Fields and Molecular Alignment ......................................... 53
3.2.8. Effects of Saturation ................................................................................... 55
3.3. EXPERIMENTAL .............................................................................................. 57
3.4. RESULTS AND DISCUSSION ............................................................................. 58
3.4.1. Unidirectional Detection at Weak Laser Intensities .................................... 58
3.4.2. Laser Intensity Effects ................................................................................ 63
3.4.2.1 . Ultrafast rotational anisotropy: Weak-field model ................................ 63
3.4.2.2. Ultrafast rotational anisotropy: Saturation effects ................................. 64
3.4.2.3. Ultrafast rotational anisotropy: Saturation and reactive pathway .......... 67
3.5. CONCLUSIONS ................................................................................................ 78

4. TRANSIENT GRATING AND THREE-PULSE FOUR-WAVE MIXING
TECHNIQUES FOR EXTRACTING AND CONTROLLING ROTATIONAL AND

 

VIBRATIONAL MOLECULAR DYNAMICS - 79
4.1. INTRODUCTION .............................................................................................. 79
4.2. THEORY ......................................................................................................... 83

4.2.1. General Considerations .............................................................................. 83
2.2.2. Feynman Diagrams .................................................................................... 85
4.2.3. Off-Resonant Excitation ............................................................................. 93
4.2.4. Resonant Excitation ................................................................................. 101
.2.5. Controlling Observation of Molecular Dynamics in Iodine ....................... 104
4-3- EXPERIMENTAL ............................................................................................ 106
4': 4 RESULTS AND DISCUSSION ........................................................................... 107
° '1' Off-Resonance Excitation ........................................................................ 107

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4.4.1.1. Atomic Response ............................................................................... 107

4.4.1.2. Rotational Contribution ..................................................................... 108
4.4.1.3. Vibrational Contribution .................................................................... 114
4.4.1.4. Early time response and comparison to liquid data ............................. 119
4.4.2. Resonant Excitation ................................................................................. 127
4.4.2.1. Rotational and Vibrational Response (Tab = 0) .................................... 127
4.4.2.2. Control of Molecular Dynamics (Tab at 0) ........................................... 134

4.5. CONCLUSIONS .............................................................................................. 144
5. APPENDICES 148

 

APPENDIX A. LABVIEWT" PROGRAM: TIME TRANSIENT DATA

ACQUISITION — TAKEFI'S4.VI (TAKE DATA) .................................................. 152
Al. fispgmvi (Main) ........................................................................................... 167
A2. paramfis4.vi (Setup Param) ........................................................................... 169

A.2.l. Errorfis.vi (Error ?) ................................................................................. 175
A3. Testfis.vi (Test file Setup) ............................................................................. 178
A4. Headerfts.vi (Header) .................................................................................... 182
A5. rediscrimfls.vi (Rediscr) ................................................................................ 184

A.5.l. SR 245_rediscr_fl52.vi (245 DISC) ......................................................... 185

A5. 1.1. refpower.vi (Power Ref) .................................................................... 188
A6. discrimdatafi82.vi (Discrirnin) ....................................................................... 189

A.6.l. discrimactwaitfis.vi (Discr Action) .......................................................... 194
A7. Savefis.vi (Save Data) ................................................................................... 197
A8. discrimactpercfis.vi (Discr Action) ................................................................ 199
A9. Finalfis.vi (Final Save) .................................................................................. 202
Am. viewfis.vi (View FTS) ................................................................................. 205

A10. 1 . opnnewfis2.vi (Open New) .................................................................... 209

A.10.2. Printfis.vi (Print) ................................................................................... 211

APPENDIX B. LABVIEwT" PROGRAM: WAVLENGTH SPECTRUM DATA
ACQUISITION — TAKESPEC2.VI (TAKE DATA) ............................................... 214
31- Specpgmvi (Main) ........................................................................................ 226
8.2. paramspec3.vi (Setup Param) ......................................................................... 228
3.2.1. Errorspec.vi (Error ?) ............................................................................... 234

3.3. TeStSpec.vi (Test file Setup) ........................................................................... 237

3.4. Headerspec.vi (Header) ................................................................................. 240
.5. rediscrimschi (Rediscr) ............................................................................... 243

B16351]. SR 245_rediscr_spc.vi (245 DISC) .......................................................... 244
- - discr' dataspc.vi (Discrirnin) ........................................................................ 247

B 21:1. discrimactwaitspc.vi (Discr Action) ......................................................... 252

3.8. :‘We.Spec.vi (Save Data) ................................................................................ 255

B. 9' d‘OSCI‘lmactpercspcyi (Discr Action) ............................................................... 257
. . FmaISPecNi (Final Save) ............................................................................... 260

viii

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1 RifiRENCES

B. 10. viewnewspec.vi (View New) ....................................................................... 263

B.10.1. opnnewspec.vi (Open New) ................................................................... 267
8.10.2. Printspec.vi (Print) ................................................................................. 269
APPENDIX C. LABVIEWN PROGRAM: INSTRUMENTAL CONTROL —
INSTRCON'I‘ROLVI (INSTR CONTROL) ............................................................ 272
APPENDIX D. COMMON LABVIEWT” VIS ........................................................ 274
DJ. fisglob.vi (Param) .......................................................................................... 274
D2. Actcontrol.vi (Actuator Control) .................................................................... 275
D.3. spexcontrol4.vi (Spex Control) ...................................................................... 278
DA. Moveact.vi (Move Act) ................................................................................. 285
D5. stddev_mean.vi (cs/p) .................................................................................... 288
D6 SR245_takedata.vi (245 DATA) .................................................................... 289
D7 cnclpaus.vi (Pause Stop) ................................................................................ 293
D8. Actconversionvi (Act Conv) ......................................................................... 294
D9. specglb.vi (Param) ......................................................................................... 295
D.10. actposforspexvi (Act Pos) ........................................................................... 296
DJ 1. Messages ..................................................................................................... 297
DJ 1.1. spexinitmess.vi (Message) ..................................................................... 297
DJ 1.2. spexparamess.vi (Message) ................................................................... 297
DJ 1.3. actmess.vi (Message) ............................................................................. 298
D.11.4. homemess.vi (Message) ......................................................................... 298
DJ 1.5. rediscrmess.vi (Message) ....................................................................... 299
APPENDIX E. FORTRAN PROGRAMS: ROTATIONAL ANISOTROPY FITTING
................................................................................................................................ 301
El. Unidirectional Detection with As and A i ....................................................... 301
E2. Unidirectional Detection with As and AM; ..................................................... 302
6- REFERENCES 304

 

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LIST OF TABLES

Table I. Semiclassical time-resolved anisotropy expressions for unidirectional
detection (parallel pump and probe transitions assumed) and large f number
collection. Corrections for multiphoton pump or probe measurements can be
made by using the formulae in Reference 9. ................................................ 47

Table II. Rotational temperatures (Ta) resulting from the fits based on Equation
(3.3) (A) without the saturation parameter and (B) with the saturation
parameter at different pump laser intensities. Note that parentheses around a
percentage indicate that the calculated temperature is below the actual
temperature ................................................................................................... 64

Table III. Rotational temperature fits (T3) at different pump laser intensities using
Equation (3.4) which includes both the saturation parameter (As) and the
reactive path parameter (A i). Parentheses around a percentage indicate that
the calculated temperature is below the actual temperature. ........................ 74

Table N. Rotational temperature fits (T3) at different pump laser intensities using
Equation (3.11) which includes the saturation parameter (As) and the fixed
ANB parameter (which is 0.49). Parentheses around a percentage indicate
that the calculated temperature is below the actual temperature. ................. 77

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LIST OF FIGURES

Figure 1.1. Obtaining vibrational information from the pump-probe technique. (a)
The pump pulse is resonant with the transition between V0 and V1. The wave
packet propagates on the V1 excited state. At the F ranck-Condon region, the
probe pulse excites the molecules to the V2 state where they emit
fluorescence which is detected. The ground (Va) and excited states (V1 and
V2) are all bound states in the case shown here. (b) The changes in the laser-
induced fluorescence as a function of the pump-probe time delay show the
time it takes for a full vibrational oscillation of the molecules in the V1 excited
state. Rotational effects were neglected here. .............................................. 10

Figure 1.2 Transient gratings formed in the forward-box configuration. (a) The
formation of the transient grating is due to interference by two interacting
electric fields. (b) The transient grating formed by fields E, and ED cause Ec to
be diffracted in the ks= k.- kb+ kc direction; this is the signal beam. (c) The
signal beam in this case is formed by field Ea diffracting off the grating formed
by Ec and Eb. (d) This is the pulse sequence that leads to the generation of
the transient grating signal (TG) shown in (b). The pulse sequence here, with
the scanned field coming before the fixed fields, corresponds to the reverse
transient-grating signal (RTG) shown in (c). Fields Ea and Eb are coincident in
time here. ...................................................................................................... 14

F Igure 2.1. Diagram of the colliding pulse mode-locked femtosecond laser
5Ystem used in these experiments. The femtosecond pulses are generated in
the CPM, then amplified and compressed to produce 60 fs, unchirped pulses
(average energy is about 300 pJ). The experimental setup shown here
(dOftEd boxed area) is for the pump-probe technique with two beam arms (d1
and 0'2, 622 nm and 311 nm) and fluorescence detected perpendicularly by
the monochromator. For the four-wave mixing technique (separate dotted
boxed area), two beam splitters are used to create three arms (one fixed (d3),

_ variable - manual (db) and automated M,» and the signal beam is
("reeled into the monochromator. ................................................................. 20

Figure 2.2. Example of a FROG trace with time increasing from left to right and
frequ?n<3y increasing .from bottom to top. (a) The dotted line represents a
peegatlvely chirped pulse where blue wavelengths (high frequencies) precede

Wavelengths (low frequencies). (b) Experimental FROG trace of an
““Ch'l’ped pulse where all the wavelengths arrive at the same time. (c) The

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dotted line represents a positively chirped pulse where red wavelengths
arrive before blue wavelengths. .................................................................... 27

Figure 2.3. Experimental setup for rotational anisotropy measurements with

unidirectional (X-axis) detection. The polarization of the probe beam remains
oriented along the Z—axis while the orientation of the polarization of the pump
beam can be rotated along either the X- (.L) or Z-axis (||). LIF is collected

perpendicular to the propagation of the laser beams. ................................... 31

Figure 2.4. Beam arrangement in the forward box configuration (see References

80 and 81). E6 and E, are overlapped and fixed in time. For positive time
delays, these fields set up a transient grating in the horizontal plane off which
Ec Bragg scatters to give the FWM signal. The time delay between E, and the
two other fields is varied to obtain the time-dependent dynamics of the
system. In our experiments, all beams were horizontally polarized. ............. 34

Figure 3.1. Relevant potential energy curves for lg. Molecules in the X state can
be excited to the B state (parallel transition) and the A state (perpendicular
transition) with 622 nm laser pulses. Excitation with 311 nm probe pulses will
induce a transition between the B and fstates (favored by parallel pump-
probe beams) and between the A and [3 states (favored by perpendicular
pump-probe beams). In both cases, LIF (f -> B, [3 -) A) at 340 nm is
detected. ....................................................................................................... 43

Figure 3.2. (3) Simulated rotational anisotropy graph at shorter time delays. The

distribution quickly changes from the initial alignment (A) to an isotropic
distribution (B) to a persistent alignment (C). Drawings of these distributions
as viewed from the X-Y plane are shown above the IU) graph. (b) Simulated
r(t) at longer time delays. After the persistent alignment, a half-recurrence (D)
develops. The drawing of this distribution is shown from a view out of the X-Y
plane so that the sin20 shape (rotated around the Z-axis) is evident. Each r(t)
is labeled with the distributions that occur as time evolves. .......................... 50

Figure 3.3. (a) I" and Ii transients for lg with 550/311(340). (b) I" and Ii transient

for 12 with 622/311(340). Vibrations are clear in both sets of transients.
Because different vibrational levels are reached on the anhannonic 8 state
by the two excitation wavelengths, (b) shows faster vibrational dynamics than
(a). For the same reason, the rotational constants are also different for the
two data sets resulting in a slight difference in the rotational dynamics. ....... 59

FiQure 3.4. URA measurements for 550l311(340) on l2. Rotational anisotropy

values calculated from normalized experimental data and Equation (3.5) are

slow as the scat
shown as he s: :
dismbutéon {1231
parameter. .

 

Ferrets Rotate-"a
Expe'fir‘le'13f data
is are shown wfi'
sat-ration pa'a":
measuemenc are.
ill respectively 1

59123.6. Rotationa
These URA meas.
tree saturafian r
lcezero and ye‘:

 

2:312:36
g .. .plase
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Dependicular tra."
Themaseis d1
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91-:- 3.8, $emiclass

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. ‘ u0e only be H
. weak laser infi
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Flangement leac‘

shown as the scattered points. Fits to these values using Equation (3.8) are
shown as the solid lines. The measurement is best fit by a thermal
distribution of 294 :t 12 K. Note that temperature is the only adjustable
parameter. .................................................................................................... 61

Figure 3.5. Rotational anisotropy of l2 in the low pump laser intensity regime.
Experimental data are shown by the square data points and the temperature
fits are shown with the lines. These URA measurements are fit without the
saturation parameter and accurately reflect the shape of the data. The
measurements are best fit by thermal distributions of 302 a: 22 K and 290 1
12K respectively. Note that temperature is the only adjustable parameter. ..62

Figure 3.6. Rotational anisotropy of I2 in the high pump laser intensity regime.
These URA measurements are fit with the saturation parameter, As. This
simple saturation model does not predict the observed dip in the data near
time zero and yields rotational temperatures with 6 - 22 % error. ................. 66

Figure 3.7. Parallel and perpendicular experimental transients obtained with
different pump laser intensities. As the laser intensity increases, there is a
significant increase in the LIF intensity of the first vibrational oscillation in the
perpendicular transients. The parallel transients do not show this pattern.
This increase is due to the contribution from the B-A-X excitation pathway at
high laser intensities when the polarization of the beams is perpendicular. ..69

Figure 3.8. Semiclassical calculations of the rotational component of parallel and
perpendicular transients and rotational anisotropy. (a) These calculations
include only the f-B-X excitation pathway (typical pump-probe experiment)
with weak laser intensity. (b) These calculations include both the f-B-X and [3-
A-X excitation pathways as is possible here with strong laser intensity. The
preferential probing of the A state in the perpendicular pump-probe
arrangement leads to an increase in the signal near time zero. This creates
the clip that is observed in the calculated rotational anisotropy. The thin r(t)
line was calculated assuming equal populations of A and B states; the thick
line assumed a larger B state population. ..................................................... 71

Figure 3.9. Rotational anisotropy of l2 in the high pump laser intensity regime.
The fits for these URA measurements include both the saturation effect, As,
and reactive state interaction, A L. The early time behavior is reflected well in
this model. The rotational temperatures for the data at the four laser
intensities shown are within 3.7 — 8.5 % of the laboratory temperature. ....... 73

xiii

591118310. RefiafiiO':
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197:294 1 3K :5
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isle 3.11. new;
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ll'le delay befweeF
fields E: and E. P
.'l$ a variable tima
elemental

 

 

100855“ Obseril'

 

Figure 3.10. Rotational temperatures, Tn, obtained from the three models used to
fit the experimental rotational anisotropy data. The laboratory temperature,
Tm = 294 :1: 3K is shown as the broad gray line. Error bars, corresponding to
one standard deviation, are shown for each fitted temperature. When
saturation is not included (squares), the model predicts only low intensity
regime temperatures well; the high intensity regime temperatures deviate far
above the actual temperature. When the model is based on the saturation of
the B<—X transition, the temperatures are too low. When both saturation of the
Be—X transition and the presence of the A state reactive path are included,
the fitted temperatures reflect the actual temperature (< 10% error) in the
high intensity regime. .................................................................................... 75

Figure 3.11. Dependence of the saturation (As) and perpendicular (A i)
parameters on the laser intensity. Both parameters show an exponential
trend with similar values for the saturation intensity, Io. ................................ 76

Figure 4.1. PS-l shown at the top for the three-pulse FWM process. 1,, is a fixed
time delay between fields E, and E, and ris a variable time delay between
fields E, and E, PS-ll shown at the bottom for the three-pulse FWM process.
ris a variable time delay between fields E, and E, and 2,, is a fixed time
delay between fields E, and E,. .................................................................... 82

Figure 4.2. Double-sided Feynman diagrams corresponding to four-wave mixing
processes observed for phase-matching condition k. = k, - k, + k,. In all
cases the signal, emission from the ket side, has been omitted for clarity.
Based on the experimental constraints of our measurements, beams E, and
E, are overlapped in time and beam E, can be delayed or advanced with
respect to these beams. The label for each diagram, for example abg,
indicates the two beams that form the transient grating and the state in which
the population is formed. (a) For positive time delays, E, and E, form the
grating and cause a transformation of pm)“, into pm“ or p‘2)gg'. When E,
scatters from this grating, at positive time, ground state dynamics are
obtained. (b) Here E, and E, form the grating and cause a transformation of

mg, into 2),, or 2),, When E, scatters from this grating, at positive time,
excited state dynamics are obtained. (c) These diagrams contain beam E,
between fields E, and E, which are overlapped in time. Therefore signal is
only observed only for times within the laser pulse duration. (d) For these
diagrams E, arrives first and, if resonant, forms a coherence between the
ground and excited states of the form p"),,. The coherence is allowed to
evolve for a time t. The coherence dynamics are probed by the arrival of field
E,, which forms the grating, and field E, that scatters from the grating ......... 86

xiv

 

rigire43 F111»! 55'

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‘igire 4.4. Expenr'e
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11; and 31 5.77 05
lie air tansienfi :
Simulated TG SlC'
{413) and are 5.;
Notefih lin the s;
the same recurre'
mammal Sig".

re’vll'llilloes are c
a’ltegnlfication of

Figure 4.3. FWM signal from xenon and argon samples at 1 atm pressure. The
data are represented by triangles for Xe and by circles for Ar. The black lines
show Gaussian fits to the data. FWM signal from Xe is 14 times greater than
from Ar because of the increase in polarizability of Xe over Ar. The width of
the Gaussian fits forAr is 131 fs and 139 fs for Xe. .................................... 108

Figure 4.4. Experimental (positive) and theoretical (negative) TG transients of air,
nitrogen, and oxygen. Full rotational recurrences are observed at 4.15 ps for
N2 and at 5.77 ps for 02. Half recurrences are also observed. The peaks in
the air transient directly correspond to recurrences in the N2 and 02 scans.
Simulated TG signals for these samples were calculated using Equation
(4.13) and are shown as the negative mirror image of the experimental data.
Note that in the simulations, the full and half recurrences are reproduced at
the same recurrence times and with the same intensity and shape as in the
experimental signal. .................................................................................... 110

Figure 4.5. TG transient of carbon disulfide. The half and full rotational

recurrences are observed at 38.2 and 76.4 ps respectively. The inset shows
a magnification of the first full rotational recurrence (circles) with the
simulation calculated using Equation (4.13) (solid line). Notice that the x-axis
is not continuous; there are 30 ps gaps between each recurrence and the tick
size is 822 is for each expanded region. The decrease in signal as a function
of time delay gives the overall rotational dephasing due to inelastic collisions
(see text). .................................................................................................... 1 12

Figure 4.6. Bottom: TG transient of mercury(ll) iodide. Ground state vibrations
and rotations can clearly be seen in the transient. Inset: The Fourier
transform of the experimental transient is shown as line (b). The top Fourier
transform (a) corresponds to the experimental transient with the coherence
spike subtracted. The symmetric stretch of Hglz has a frequency of 158.2 cm'
1. The cross term resulting from Equations (4.13) and (16) causes the Fourier
transform to have peaks corresponding to 2gp (19.7 i 0.1 cm“), a» - an
(148.4 i 0.2 cm“), and (a, + an, (167.9 i 0.2 cm“) as seen. The 2m, peak is
probably masked by the high frequencies from the experimental noise
because of the low signal to noise ratio. ..................................................... 115

Figure 4.7. Top: Experimental TG transient of Hglz. Middle: Transient resulting
from 1,,(t) equal to the sum of f“) and [(0. Bottom: Transient resulting
from 1,,(t) equal to the product of [(t) and 1"(t). Notice that the product
transient (bottom) is out-of-phase with the experimental data but the
summation transient (middle) is in-phase with the experimental data for all
times (see text). .......................................................................................... 117

XV

Home 4.8. T6 are
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irfiensities of the '

. I
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ellllléfilllenlal data

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Simulated usiqg El

one With the or:
signal for CS; ma;
lolooogeneous :e
dfiisional deohas
one used by Ne?
References 54 am

 

”11.31 We‘erlgfifii

 

Figure 4.8. TG transients of methylene chloride (upper) and methylene bromide
(lower). The experimental data are shown as circles and the simulations
calculated using Equation (4.13) are shown by the solid line. In both scans,
the time-zero coherence spike is observed and is more intense than the
rotational dephasing. As expected, the rotational recurrence is faster in
CH2CI2 than in CH2Br2. ............................................................................... 120

Figure 4.9. TG transients of benzene (upper) and toluene (lower). The
experimental data are shown as circles and the solid line shows the
simulations from Equation (4.13). The intensity of the rotational dephasing in
benzene is stronger than the time-zero spike. However, in toluene the
intensities of the rotational recurrence and the time-zero spike are about
equal. The rotational recurrence time is similar for both compounds as
expected from their rotational constants. .................................................... 122

Figure 4.10. Top: TG transient obtained for CS2 near time zero. The
experimental data (circles) contain a very small coherence coupling artifact
followed by a large rotational dephasing component. The data has been
simulated using Equation (4.13) as shown by the solid line. Bottom: The
curve with the circles corresponds to the simulation of our gas-phase TG
signal for CS2 multiplied by a fast decaying function which simulates
inhomogeneous dephasing and by a slow decay function which simulates
diffusional dephasing (see text). The smooth line corresponds to a simulation
curve used by Nelson and coworkers to fit the liquid-phase experiments (see
References 54 and 216). ............................................................................ 125

Figure 4.11. Bottom: TG and RTG transient of iodine. Vibrations can clearly be
seen at both negative (left) and positive (right) time delays. Lasers with
central wavelength of 622 nm are resonant with the X <—-) B electronic
transition. Left inset: Fourier transform of the data at negative delay times.
There is one main peak at 107.1 i 0.3 cm‘1 and another smaller peak at
209.9 1 0.3 cm". Right inset: Fourier transform of the data at positive delay
times. The frequencies of the three main peaks are 107.8 i 0.4, 210.8 i 0.1,
and 312.0 i 0.2 cm". Taking these values and accounting for the
combination frequencies that should be observed in each Fourier transform
because of the summation of cosines, values for the excited vibrational

frequency (105 cm“), ground vibrational frequency (208 cm"), and average
rotational frequency (3 cm“) can be obtained. ............................................ 128

Figure 4.12. Semiclassical simulation of the iodine signal for positive and
negative time delays (see text). The insets show the corresponding Fourier
transforms. The simulations agree well with the experimental results
presented in Figure 4.11. ............................................................................ 131

xvi

591194.13. E1295"
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the excited state
The power FFT -:
02 on" corresz.
iodine. ltreiecfis
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dephasing.

 

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Deareshowri) Tr
excited state of :21
PWFFT oftte
or" correspond "
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seal contributor
around 1.5 ps IS :

191164.15. Close-u:
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tie data show a p'
it uency of the e.
-.er a second ha'
lesion at low freq 3'
:Espond to the l

l r =
the; 514 is)

 

Figure 4.13. Experimental transient for PS—l (only the first 5 ps are shown) where
1,, = 460 fs corresponding to one and a half vibrational periods of iodine in
the excited state (3/2 1,). Observed vibrations have a period of about 307 fs.
The power FFT of the transient shows a predominant frequency of 107.7 1:
0.2 cm‘1 corresponding to vibrations of the excited B 311,, state of molecular
iodine. It reflects that the detected FWM signal is exclusively from the excited
state. The slow modulation with a dip near 1 ps is due to rotational
dephasing. .................................................................................................. 1 35

Figure 4.14. Experimental transient for PS-l where 1,, = 614 fs (only the first 5
ps are shown). This value of r,, is equivalent to two vibrational periods of the
excited state of iodine (2 1,). Observed vibrations have a period of 160 fs. The
power F FT of the transient shows a predominant frequency of 208.3 t 0.1
cm' corresponding to vibrations of the ground X 20., state of molecular
iodine. It depicts that the detected FWM signal IS predominately from the
ground state. There is a minor peak at 107. 1 i 0. 1 cm corresponding to a
small contribution from the excited state. Note that the slow dip in modulation
around 1.5 ps is due to rotational dephasing. ............................................. 136

Figure 4.15. Close—up of the power FFT for the transients shown in Figure 4.13
and Figure 4.14. When 1,, = 614 fs (gray line), the data show a small
contribution at 107 cm and a prominent peak at 208 cm ,corresponding to
the vibrational frequency of the ground state. When r,,- ‘460 fs (black line),
the data show a prominent peak at 108 cm co,rresponding to the vibrational
frequency of the excited state, and a minor peak at 218 cm which is most
likely a second harmonic of the 108 cm peak. The insert shows the enlarged
region at low frequencies with peaks at 16 :t 1 and 11 :I: 1 cm'1.These
correspond to the different rotational dephasing dynamics occurring in the X
state (7,, = 614 fs) and the B state (1,, = 460 fs), respectively. The difference
in the frequency is caused by the difference in the moment of inertia between
these two states. These data confirm the ability to select ground or excited
state dynamics based on the choice of 1,, in three-pulse FWM .................. 139

Figure 4.16. Experimental transient for PS—ll where 1,, = 460 is (only the first 5
ps are shown). Notice the well-resolved oscillations with a period of 307 fs.
The power F FT of this transient shows a predominant frequency of 108 cm
corresponding to vibrations of the excited state. A minor contribution at 218
cm‘1 is most probably a second harmonic of the 108 cm component. ...... 142

Figure 4.17. Experimental transient for PS-II where 1,, = 614 fs (only the first 5
ps are shown). The power F FT of this transient shows frequencies at both
108 cm'1 and 208 cm". Note that for this value of 7,, there is an increase in

xvii

the amount of 9':
(see Figure 4 1‘

 

 

the amount of ground state contribution as compared to the case 1,, = 0 fs
(see Figure 4.11) ......................................................................................... 143

xviii

 

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1 . INTRODUCTION

1 .1 . MOLECULAR DYNAMICS

Understanding chemical reactions — bond breakage and formation, orientation
and alignment conditions, time of reaction, mechanism, transition state and vibrations
rotations and torsion before and after the reaction —— is one of the fundamental areas of
hemistry For instance, the partition of energy among the products in a chemical reaction

can be used to learn about the forces involved during the formation and breakage of
chemical bonds.

In the late 1800’s, Arrhenius introduced his kinetic equation

k(T) = Ae‘Ea/kT (1.1)

\

Reproduced in part with permission from E. J. Brown, I. Pastirk, and M. Dantus, J.

Phys. Chem. A 103, 2912 (1999). Copyright 1999 American Chemical Society.
u'Reproduced 1n part with permission from E. J. Brown, I. Pastirk, and M. Dantus, J.

Plhys. Chem. A, In press. Unpublished work copyright 2001 American Chemical Society.
Reproduced in part with permission fiom E. J. Brown, Q. Zhang, and M. Dantus, J.

Chem. Phys. 110, 5772 (1999). Copyright 1999 American Institute of Physics.
«Reproduced in part with permission from E. J. Brown, I. Pastirk, B. I. Grimberg, V. V.

Lozovoy, and M. Dantus, J. Chem. Phys. 111, 3779 (1999). Copyright 1999 American
Institute of Physics.

I. Pastirk, E. J. Brown, B. I. Grimberg, V. V. Lozovoy, and M. Dantus, Faraday
Discuss. 113, 401 (1999)- Reproduced 111 part by permission of The Royal Society of
Chemistry.

 

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where k(T) is the temperature-dependent rate constant of the reaction, E, is the activation
energy (the minimum energy required to reach the transition state and allow the reaction
to go forward), k is the Boltzmann constant, and T is the temperature. The frequency of
collisions that lead to a reaction are included in the pre-exponential factor A; this was
later replaced by the expression z*P, where z is the number of collisions and P is the
probability of reaction (also called a steric or orientational factor). The probability is
usually less than 1 unless the reaction includes a catalyst or ionized species that have a
greater attraction for each other. This equation advanced our understanding of kinetics of
an ensemble and reactions in bulk matter, but it provided statistical information about a

thermal distribution of molecules rather than information about individual molecules.

In the early 1900's, London and Eyring and Polanyi worked on the development
0f potential energy surfaces (PBS) that would provide a path for molecules to follow in
Older to proceed from reactants to products. These PES eventually led to the calculation
0f reaction rates, translational and v1brational motion of molecules on these surfaces, and
aetivation energies and transition states. With the development of the molecular beam,
molecules would collide only once with a given energy in a particular angular
arrangement and the orientational dependence of the reaction could be studied. Rotational
information also aided in determining the lifetime of the intermediate species. Lasers
advanced this area of research even more by providing discrete amounts of energy to

deposit into a molecule and polarization to study orientational efiects. Energy level
spacings and the shape of the PES could be determined with fi'equency-resolved
Spectroscopy using continuous wave and nanosecond lasers. As the time duration of

lasers progressed from nanosecond to picosecond to femtosecond, the shorter pulse

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provided a method for studying molecular dynamics that were on the same time scale as
the pulse temporal width. Femtosecond transition state spectroscopy (FT S) is a technique
developed by Zewail and co-workers at Caltech to investigate the dynamics of the
transition state”; in 1987 they made the first real-time observation of a transition state in
a dissociation reaction.3 This technique can be utilized to gain information about the
transition state, time of reaction, vibrational and rotational dynamics of species involved
in the reaction, and potential energy surfaces. ‘14'6 This work has laid the conceptual
framework for the studies conducted by our group at Michigan State University,
including the concerted molecular photoelimination reactions of CHZIZ and the related
CXZYZ compounds (CXzYz '9 CXz + Y2) (bound-to-fi'ee transitions)7'12 as well as the

Photoassociation reaction to form Hg; (free-to-bound transition). '3'15

1 .1 .1. Wave Packet Motion

With resomnt excitation, a photon is absorbed by a molecular system in a ground
electronic state (V0). This absorption causes a vertical transition to an excited electronic
State (V 1). By the Uncertainty Principle, we know that a pulse that has a short temporal
duration will have a large spectral bandwidth; for most molecular systems and ultrafast
pluses, the frequency spread of the pulse is wider than the vibrational energy spacing.
Thus, a number of quantum states are populated on V. by the absorption of a short laser

pulse which produces a coherent superposition of states. The laser pulse is assumed to be

Gaussian, 80 exp[——t2 /a12]cos (cot) , where so is the amplitude of the field, a is equal to

213/112), 1' is the full width at halfmaximum (FWHM) ofthe temporal duration, and a) is

 

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the central fi‘equency of the pulse. The resulting wave function is a sum of all the possible

states p, in V. with amplitudes an,

T=Zan¢n. (1-2)

If only one a, at 0, then ‘1’ = a,¢,. and is a stationary state. If more than one a, 1: 0, then a
nonstationary state results that can evolve in time. These amplitudes, a,, can be calculated

by using first-order perturbation theory,16

 

an = C<¢n $010)) Iexp[—i(E,, - E0)t/h] cos(cot)exp[—t2 /a12]dt (1.3)
Where C is a constant that includes the amplitude of the electric field and the transition
dipole moment, $0101 is the ground state wave function, E, is the energy that corresponds

to the state ,0", and h is Planck constant divided by 211. Integrating this equation yields

 

an = C<tp,, ¢5°’)exp[—(m,, —a))2a12/4] (1.4)

where a)" = (En — Eo' )/ h and E0' is the energy corresponding to the ground state.

Notice that as the temporal duration increases (1 -) oo) in Equation (1.4),

an = C<¢n ¢0(°)>6(con —w). (1.5)

 

 

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The delta function in this equation ensures that only one a, at 0 when a) = 01,. Thus, there
will be only a single eigenstate (p, (stationary state) and no possibility for time
dependence or evolution with long pulses. Examining Equation (1.4) again for the case of

very short pulses (1 -) 0),

an =C<¢n

 

10“”) (1.6)

which correspond to the Franck-Condon factors. Therefore, the wave packet on V. is

‘I’=CZ<¢n

 

40010) )1)" (1.7)

and at t = O, the wave packet on V1 is a reproduction of the ground state wave function.
This wave packet can now evolve in time according to the time-dependent Schrodinger

equation

i 1659:1910). (1.8)

The general solution to this differential equation is

1]!” (t) = (pn exp [—iEnt / h]; (1.9)

therefore, the wave packet on V. is

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in:

t11(1) = 20,, exp[—iE,,t/h]¢,, . (1.10)

We can imagine this wave packet as a classical particle oscillating on the excited
potential energy curve showing the periodic nature of the molecular vibrations on this
curve. Classical and semiclassical descriptions of the temporal evolution of this wave
packet are available and can be applied to ultrafast spectroscopy, for example see
References 17-22 and a review in Reference 23. The laser induced fluorescence (LIF)
signal fi'om the excited V2 state corresponds to the dynamics (time evolution of the wave
packet) on the excited V1 state. In the case of non-resonant excitation with ultrashort laser
pulses, a coherent wave packet is produced in the ground electronic state due to
impulsive stimulated scattering24 and similar wave packet dynamics can be calculated

and discussed.

1.1.2. Time-Resolved Spectroscopy

High-resolution fi'equency-resolved spectroscopy can provide information about
the molecular dynamics of the system. However, under certain conditions such as high
temperatures, large polyatomic molecules, and mixtures, spectral congestion complicates
the spectroscopic analysis. Molecular dynamics can be obtained from frequency-resolved
spectra by taking the Fourier transform of the data; similarly, the Fourier transform of
time-resolved data yields the frequency information about the molecular system (vide
infra). Although frequency-resolved spectroscopy can be used to obtain the dynamics, it

seems more intuitive to consider these dynamics in the time-resolved domain where the

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dynamics can be observed directly ("srmpshots") by the femtosecond pulses. There are
other advantages of ultrafast time-resolved spectroscopy. The ease of nonlinear
processes, including multiphoton excitation due to high peak intensities allows for
additional reaction pathways that may not be seen otherwise. In time-integrated
(frequency-resolved) experiments, the short lifetimes of intermediate species lead to very
low spectral intensities for these species compared to the reactants and products. In time-
resolved experiments, the selection of the detection wavelength can discriminate against
other species and results in an increased signal-to-noise ratio for the intermediate species.
In gas-phase samples, collisions occur on a time scale much greater than the ultrafast
laser pulse; therefore, collisions do not affect these measurements. In addition, the
characteristics of the ultrafast laser pulse (such as phase, frequency components, and

chirp) can be manipulated (or "tailored") to control chemical reactions (vide infi'a).

The past decade has witnessed rapid grth of real-time molecular dynamics
investigation using ultrashort laser pulses. ”'6 Most ultrafast experiments on molecular
dynamics in the gas phase have been carried out using the pump-probe technique.
Various probing techniques have been exploited in this endeavor. More recently, third- or
higher-order nonlinear techniques have been employed increasingly for studying
molecular dynamics in the gas-phase environment; one of these nonlinear techniques is
four-wave mixing (FWM). The focus of this research is to examine the extraction of
rotational and vibrational information from pump-probe and four-wave mixing

experiments conducted with femtosecond pulses.

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1.2. PUMP-PROBE TECHNIQUE

Purnp—probe techniques, in which a process is initiated by a burst of light and is
monitored by a subsequent burst of light aimed at the sample some time later, have been
employed for over a hundred years. The advantage of this technique is that the time
resolution of the measurement depends only on the duration of the pulse and the degree
of control over the time delay, which can achieved by the use of a Mach-Zehnder
interferometer”,26 Around the middle of the twentieth century, pump-probe techniques

were used with microsecond pulsesZ7a28 and today can be used with pulses as short as 5 or

6 $29.30

Pump-probe spectroscopy using ultrafast lasers has advanced our understanding
of molecular dynamics and chemical reactions in real time. Studies have been done on
non-reactive systems where v1brational motion is observed as well as on reactive systems
where bond dissociation and formation take place.'t4t5t3| In the following studies we
concentrate on the angular motion of gas-phase molecules which reflects the rotations of
the parent and daughter species. Polarized lasers are used in these measurements to
follow the time evolution of the rotational alignment of the isolated molecules.”35 For
reactive systems, one learns about the rotational impulse during the chemical reaction as
well as the emergence of the final rotational populationfib33 which in some cases can aid
in the determination of a reaction mechanismfit9t15 Rotational anisotropy techniques are
well established for the study of molecular structure as in rotational coherence

spectroscopy.36v37 The measurements are relatively simple and can yield quantitative

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information on the molecular structure of the molecule studied in addition to information

on the overall rotational population.

In our pump-probe studies, a linearly polarized femtosecond pulse (91me) excites
a molecule from its (bound) ground electronic (V 0) state to an excited state (V 1) where a
wave packet is created (see Figure 1.13). In these experiments, a pump laser initiates the
dynamics of a system typically through a one-photon excitation process. In a few studies
multiphoton excitation by the pump laser has been utilized to access higher-lying
electronic or vibrational states-“3840 After a variable time delay, a second femtosecond
pulse (91m) then causes a transition to another excited state (V2) either higher or lower
in energy than the first excited state (V 1). If this excitation process causes the molecule to
break into fragments, the process is called photodissociation (reactive system). For the
probe process, various techniques have been used; examples include absorption,
emission, laser induced fluorescence (LIF), fluorescence up-conversion, coherent anti-
Stokes Raman scattering (CARS), and multiphoton excitation followed by
photoionization or photoelectron detection. I,4,5.23.4l We have generally measured LIF of
the excited molecule or one of its fi'agments, from either V. or V2, to monitor the

dynamics. In Figure 1.1a, LIF is detected from the second excited state.

 

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Figure 1.1. Obtaining vibrational information from the pump-probe technique. (a)
The pump pulse is resonant with the transition between V, and V1. The wave
packet propagates on the V1 excited state. At the F ranck-Condon region, the
probe pulse excites the molecules to the V2 state where they emit fluorescence
which is detected. The ground (Va) and excited states (V1 and V2) are all bound
states in the case shown here. (b) The changes in the laser-induced
fluorescence as a function of the pump-probe time delay show the time it takes
for a full vibrational oscillation of the molecules in the V1 excited state. Rotational

effects were neglected here.

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As the wave packet on V. propagates, the Franck-Condom factor of the transition
varies and the ability of the probe pulse to cause an excitation to V2 changes. Thus the
amount of LIF that can be detected oscillates with the pump-probe time delay. Thus in
Figure 1.1a, when the wave packet is at the inner turning point, the Franck-Condon
overlap is minimized resulting in a decrease in the LIF signal. Conversely at the outer
turning point, the Franck-Condon overlap is maximized resulting in an increase in the
signal. Thus, the vibration dynamics of the V. surface are measured as a function of the
pump-probe time delay and are equal to the summation of cosines.42 The vibrational
oscillations of the wave packet on the V. potential energy curve are shown in Figure

1.1b; from these oscillations, we can detemiine the excited state vibrational frequency

(all/ii) = 2n/ Tab)-

As the molecule vflnates, it also rotates in space. Thus, the ability of the probe
pulse to induce a transition is also affected by the relative alignment of the excited
species on V. with the polarization of the laser. When the dipole moment of the molecule
is well aligned with the probe laser polarization, the LIF signal is high. As the molecule
rotates, the overlap of the polarization of the probe and transition dipole of the molecule
decreases, resulting in a decrease in the LIF signal. So, underneath the fast vibrational
oscillations will be a slower undulation corresponding to rotations in the experimental
transients. Thus, as the fragment rotates, rotational anisotropy effects can be observed as
a function of the pump-probe time delay and will be discussed in detail in Chapter 3. In
addition, the separation of the rotational and vibrational dynamics in the data will be

discussed in Chapter 3. The formalisms for quantitative analysis of these measurements,

11

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have investigated recently how these formulae may change for unidirectional detection

and intense pump lasers“,45

1.3. FOUR-WAVE MIXING TECHNIQUE

Techniques similar to coherent transient birefiingence in vapor samples,
pioneered by Heritage et al. in the picosecond regime,46 were recognized by F ayer and
coworkers for their potential for probing gas-phase dynarnics.47'49 Although time-
resolved third-order nonlinear optical techniques have long been used in condensed
phases,24’50'66 only recently have these novel probes been applied to the study of
femtosecond dynamics in the gas phase.‘57'70 Hayden and Chandler used femtosecond
time-resolved CARS to study coherent rotational dephasing of large gas-phase
molecules.67 Zewail and coworkers used degenerate four-wave mixing (DFWM) for
probing real-time reaction dynamics.68 They demonstrated three types of arrangements:
DF WM, pump pulse followed by DFWM probing, and pump pulse followed by a control
pulse with the depletion dynamics probed by DFWM. Schmitt et a]. have studied iodine
vapor using time-resolved CARS and DFWM.69'72 By varying the time delay of one of
the incident pulses while maintaining the other two incident pulses fixed, they showed
that vibrational and rotational dynamics can be observed for both the ground and excited
electronic states. Here, the different types of dynamics that can be observed by time-
resolved transient-grating (TG) techniques, involving four-wave mixing (FWM)

nonlinear optical processes, are examined. The name “transient grating” is used here to

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highlight the fact that most of the information obtained in these experiments derives from
the time ordering of various ultrashort pulses and not fi'om high-resolution frequency
tuning. One of the goals of this work is to gain an increased level of understanding of the
quantitative analysis of ultrafast molecular dynamics measured by gas-phase transient

grating experiments arising from four-wave mixing nonlinear processes.

One of the most physically intuitive explanations of time-resolved four-wave
mixing techniques is based on the formation of transient gratings by the incident
lasers.47t73t74 Consider three incident light pulses with electric fields E,(t), E,(t) and E,(t)
interacting with a medium. From here on we will assume that the three fields are identical
in terms of pulse envelope and frequency components, 1'. e. , they are degenerate; however,
this is not to be considered as ‘a necessary condition. At the crossing of two beams, the
spatial modulation of their electric fields varies due to constructive and destructive
interference (see Figure 1.2a). The molecules in the interaction region experience varying
electric field intensities according to their position, and this leads to the formation of a
transient grating of polarized molecules in space. The transient grating formation can be
probed easily by the detection of Bragg scattering of a third laser beam.47t73t74 The
formation of the grating does not require that the two crossing beams coincide in time as
long as the coherence is maintained in the sample.75 This property has been exploited in
photon echo experiments where the time delay between the lasers is used to probe the

coherence dephasing tirne.75'81

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Figure 1.2 Transient gratings formed in the forward-box configuration. (a) The
formation of the transient grating is due to interference by two interacting electric
fields. (b) The transient grating formed by fields E, and E, cause E, to be
diffracted in the kg = k.- k,+ k, direction; this is the signal beam. (c) The signal
beam in this case is formed by field E, diffracting off the grating formed by E, and
E,. (d) This is the pulse sequence that leads to the generation of the transient
grating signal (TG) shown in (b). The pulse sequence here, with the scanned
field coming before the fixed fields, corresponds to the reverse transient-grating
signal (RTG) shown in (c). Fields E, and E, are coincident in time here.

14

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Experimentally, there are various configurations that can be used to observe the
FWM signal. For our studies, we have chosen the forward box arrangement as shown in
Figure 1.2 because it provides the best temporal resolution and phase matching between
the incident fields.82283 For all cases, the FWM sigml that is detected at the upper right
corner of the forward box, as shown in Figure 1.2, is defined by the wave vector ks = k, —
k, + kc, Note that other FWM signals are possible and they are observable in other
directions. In our studies we restricted our measurements such that within an
experimental scan Ea and E, are fixed in time and EC is scanned. When fields E, and E,

precede B, it is called positive time; negative time refers to field EC preceding E1, and Ea.

Based on the relative timing of the three fields, one can envision three types of
gratings being formed.73274284 The first one, shown in Figure 1.2b, involves E, and E1,
forming a grating in the horizontal plane from which EC scatters for positive delay times,
I. In this case (TG signal), fields E, and Eb are overlapped in time and arrive before E, as
shown in Figure 1.2d. The second arrangement, shown in Figure 1.2c, involves EC and E,
forming a grating in the vertical plane with subsequent scattering of Ea. More information
about this latter configuration, known as a reverse transient grating (RTG), will be given
later;85 here, fields E, and E, are coincident in time but arrive afier EC as shown in Figure
1.2e. The third grating is formed by E, and EC in a diagonal plane, but scattering of E,
takes place in the direction k, = k, — k + k1, which does not coincide spatially with k5 = k,
— k, + kc. The medium that constitutes the gratings discussed so far is composed of the
sample molecules that in the gas phase move fi'eely. Therefore, molecular dynamics
cause the decay and reformation of the transient grating. Our group has theoretically and

experimentally explored the ground and excited states vibrational and rotational

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populations and the coherence dynamics from gas-phase samples by these time-resolved
four-wave mixing techniques.36237 The theoretical considerations and experimental
demonstrations Of the quantitative extraction Of rotational and vibrational molecular

dynamics of various molecular systems fiom these experiments are shown in Chapter 4.

1.4. CONTROL OF MOLECULAR DYNAMICS

In the past decade, we have witnessed tremendous progress in the experimental
demonstration Of laser control Of chemical reactions. This area Of research has been
reviewed recently“89 and includes wide-ranging techniques such as "Coherent Control",

”Pump-Dump", "Mode-Selective Control", "Quantum Control", and "Optimal Control".

The probability Of excitation from the ground, |g>, to the excited state, |e>, in a

two-level system is expressed quantum mechanically as
|<<=III-E(t)|t>’>l2 =<elu-E(t)|g><g|v-E(t)'|e>, (1-11)

where u is the transition dipole moment and E(t) is the applied electric field. This
expression implies that two interactions with the electric field are required, one with E(t)
and one with E(t)', tO transfer part Of the population fiom one state to the other. The
excitation process, as measured in all linear spectroscopy methods, is a good example Of
this type Of population transfer. Although both interactions are with the same field for a

general excitation process, the two interactions do not imply that it is a two-photon

16

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process. Population inversion is not usually achieved because Of the competition between
the rates Of absorption and stimulated emission. The possibilities for influencing the
excitation process with a simple laser pulse are minimal. However, if one had individual
control over each Of the electric fields involved in the excitation, full control could be
achieved. Control Of the population transfer can be achieved if the two electric fields
involved in the transition probability in Equation (1.11) are different and are correlated in

time or in phase.

It has long been recognized that in order to Optimize the transfer Of population
between two states sophisticated electric fields are required.33290'92 One can create such
electric fields by a combination Of phase and amplitude masks,”9S or one can combine
phase-locked laser pulses to achieve the desired field. Scherer et 01.96 showed that when
two phase-locked laser pulses were combined in-phase, the excited state dynamics of
molecular iodine could be Observed as fluorescence enhancement; however, when they
were combined out-Of-phase, the signal is Observed as fluorescence depletion. Coherent
control Of chemical reactions depends on the relative phase Of two different laser pulses
that interact with the sample. The relative phase Of the pulses can be used to control the
population transfer from the ground state to two different excited states.97'99 A different
approach tO controlling population transfer100 and enhancing reaction yields1 12"" uses

chirped laser pulses.

Three-pulse four-wave mixing (F WM) is a nonlinear spectroscopic method that
combines the interaction Of three laser pulses in a phase-matched geometry with a well-

defined time sequence Of the pulses. The principles Of transient gratings apply here as

17

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well; the differences are that the molecular system being studied must have an electronic
transition that is resonant with the frequency of the laser pulses and fields E, and E, are
not overlapped in time. The signal from these measurements arises from a third-order
polarization resulting from the interaction Of the three electric fields and is itself a
coherent beam corresponding to a fourth electromagnetic wave. Three-pulse FWM is
similar tO the pump—probe technique in that a preparation step is followed, after some
variable time delay, by a probing step. ‘02 However, three-pulse FWM allows for a greater
degree Of control over the preparation and probing processes. Thus, the three-pulse FWM
technique allows individual manipulation Of the electric fields E(t) and E0). and can be
uxd to gain control over the transfer Of population between the ground and the excited
states. This technique allows one to combine three non-phase-locked electric fields in a
phase-matching geometry. The first two fields cause the population transfer and the third
field probes the system. The specific timing between the pulses can be used to achieve
near-unity or near-zero values Of diagonal (population) and Off-diagonal (to-vibrational
(mmmmfimmkdmmmoflmmmMMmflmfinnmflwMHMUwehmkmMs
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quantum mechanical processes involved in laser control Of chemical reactions.312103'109
Demonstrations Of this control involving two Of the possible pulse sequences are shown

in Ctmpter 4.

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2. EXPERIMENTAL

2.1 . LASER SETUP

A number Of different types Of femtosecond laser systems are available for
studying chemical reactions. At Michigan State University, there are two different laser
systems used by the Dantus research group — a titanium-sapphire laser (Ti-sapphire)
producing 13 fs pulses centered at 805 nm and a colliding pulse mode-locked laser
(CPM) producing 50 fs pulses centered at 622 um. All Of the experiments described here

were conducted using the CPM laser system; it is described in some detail below.

2.1.1. Oscillator

The laser system used for these experiments is a home-built colliding pulse mode-
locked dye laser‘lo'1 ‘2 (CPM), which is a ring cavity consisting Of 7 mirrors (M and SM),
4 prisms (P), and 2 dye jets (J). (See Figure 2.1.) A gain laser dye, rhodamine
tetrafluoroborate (R66), is dissolved in ethylene glycol (stock solution is 1.0 g / 100 ml
and is firrther diluted by a factor Of 10) and flows through one Of the dye jets (JG). The
514 nm line Of a continuous wave Coherent Argon ion laser (typically 4-6 W across all
lines) is used to pump the R66 dye Optically to an excited vibrational level in the first
excited singlet state. This wave packet then decays to the bottom Of the excited state and
then emits broad-band fluorescence centered around 590 nm due tO numerous transitions

to Vibrational levels in the ground state.

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The three mirrors (M) form a ring for the cavity while two Of the spherical mirrors
(SM) collimate the fluorescence generated by the R6G gain dye. Notice that this cavity
arrangement allows light tO travel in both clockwise and counter-clockwise directions;
thus, we can think Of two “arms” or oppositely propagating beams. Note that mirror at the
right edge Of the CPM cavity is only partially reflective; some light is allowed to escape
the cavity and light fiom one arm enters the amplifier and light from the other arm can be
used to monitor the pulse characteristics. With this laser cavity and gain dye, we Obtain a

continuous wave laser with wavelengths in the range of 580-630 nm.

The length Of a laser cavity defines the specific frequencies Of light that can exist
in that cavity. In the ring cavity, constructive interference Of the radiation is required tO
sustain the laser; the phase must be reproduced after each pass around the ring. These
Observations are described by the equation Vq = qc/L where Vq are the frequencies Of light
sustainable in the cavity, q is an integer, c is the speed of light, and L is the entire length
Of the cavity. The light in the laser cavity consists of a number Of different frequencies all
oscillating with unrelated phases (multimode). In this case, the laser is continuous wave
and there is not a series Of laser pulses. In order to produce pulses, the phase relationship
between all the different frequencies must be constant in time. When the initial phases Of
all the oscillations are equal, we Obtain Fourier transform-limited pulses and the laser is
"mode-locked". Equations (as well as figures) describing this change from a multimode
continuous wave laser tO a mode-locked pulsed laser can be found in Reference 41 in

addition to other advanced laser books and ultrafast laser articles.

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In order tO Obtain femtosecond pulses from the continuous wave laser (generated
by R66), we introduce a saturable absorber dye, 3,3 ’-diethyloxadicarbocyanine iodide
2,3 (DODCI) dissolved in ethylene glycol (stock solution is 0.50 g / 100 ml and is further
diluted by a factor of 10) in the other dye jet (ISA). The saturable absorber dye has an
intensity-dependent absorbance. When the light intensity is low, all the radiation is
absorbed and no light passes through the saturable absorber. If there is a higher intensity
Of light, e. g. a spike due tO a noise fluctuation in the laser, the spike saturates the
absorbance transition and allows partial passage Of light through the saturable absorber.
This signal passes through the gain dye and is amplified and then easily passes through
the saturable absorber on the next trip around the cavity. This pattern through the gain
and saturable absorber dyes repeats until the gain dye is saturated. As this alternating
process Of gain-saturable absorber occurs, the leading edge Of the pulse is absorbed by
the saturable absorber (because Of the low intensity) while the trailing edge is not
amplified by the gain dye (because Of saturation). Note that the maximum of the pulse is
not affected by the saturable absorber while it is increased by the gain dye. The
consequence Of these properties is that the time duration Of the pulse narrows and we
Obtain femtosecond pulses. The final shape Of the pulse is Obtained when the pulse does
not change as it propagates through the cavity. This steady state condition is Obtained
because the duration Of the pulse in time is inversely related to the spectral width
(uncertainty principle) and a point is reached where the time duration cannot decrease

any farther due to the spectral width limit.

Recall that we have two counter-propagating pulses; they must collide in time and

space at two points in the cavity. If they collide at the saturable absorber dye, there will

22

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cells? 31 the S34 d
tamer} time for th
e. ite m0 jets shot.
The clockwise pap.
58:11:: ahsorlm d}
is: characteristics
SELF-3T1 {II last 1335‘
'5 added to the .r-‘
Zl‘l'i'S from about 5‘4

i: .: ;.

 

m”Tor

. ' C
34:63: .

h 11hr“ .
. Q
Q;
. h as I

gT 011p ‘C‘ltg

be less loss Of the intensity Of the pulse than if they pass through the saturable absorber
individually; thus, colliding at the saturable absorber jet is the Optimal situation. If they
collide at the gain dye, each pulse will be amplified less than if they separately passed
through the gain; therefore, this is the worst situation. SO tO allow for the maximum
recovery time for the gain dye while having the pulses collide at the saturable absorber
jet, the two jets should be placed at a distance apart equal to ‘A Of the length Of the cavity.
The clockwise propagating pulse is used in the experiment because it last passed the
saturable absorber dye; the counter-clockwise propagating pulse is used tO monitor the
pulse characteristics in the CPM by difli'acting Ofi‘ a grating (G) and displaying the
spectrum (it last passed the gain dye and is broader in time). When the saturable absorber
dye is added tO the ring cavity, the central wavelength Of the radiation fiom the gain dye
moves fiom about 590 nm tO 622 nm with an increase in the bandwidth fi'om 0.2 nm to
10 nm. This change in the laser can be Observed while adding DODCI by Observing the
spectrum Off the diffraction grating. Note that there are other possible gain dye-saturable
absorber dye pairs to generate femtosecond pulses; others can be found in Reference 41

along with their corresponding wavelength range.

The four prisms (P) in the cavity are used tO compensate for temporal broadening
Of the pulses which is introduced by transparent media in the ring cavity, e. g. ethylene
glycol and mirror coatings. The indices Of refi‘action Of different materials vary
differently with respect to frequency (wavelength). The consequence Of this behavior is
known as group velocity dispersion (GVD); different wavelengths travel at different
velocities in a particular medium. This phenomenon is also referred tO as chirp. The

“bluer” wavelengths are slowed down by these transparent media more than the “redder”

23

male-321315 33' W
on can Q 1122:»:

223. Trim prism

tr naielenib ‘ i“
ar cared to Ctr-F
moors “hkh C“:

.rxi 4. "
gait“ ‘ XQLU-UITJ

From the LL'l
me that te broad ir.
(are. For Gaussian ‘

am (WIN 1 i

‘33 Egg-
- «.‘u the values tl

A

«gm pulSt‘s. the

uttfigmds [0 3 “id r

 

The output in

5332‘:
Wm of 20
3.2:}

 

 

wavelengths are, resulting in a temporal broadening Of the pulse. Equations that define
GVD can be found in advanced Optics or laser books, for example References 41 and
113. Various prism arrangements can correct for this “positive” GVD (or chirp) by
introducing “negative” GVD where the wavelengths towards the blue end Of the spectrum
travel a shorter pathlength than the ones toward the red end Of the spectrum allowing the
blue wavelengths to “catch-up" to the red ones. Here in the CPM cavity, the four prisms
are arranged tO correct for the GVD introduced in the cavity with two Of the prisms on
translators which can be adjusted to produce the shortest pulses (those which have the

broadest spectrum).

From the uncertainty principle (AtAa) 2 I/2), we know that pulses that are short in
time must be broad in frequency. The value Of this inequath depends on the shape Of the
pulses. For Gaussian shaped pulses, AtA v 2 0.441 where At and Av are full-width at half-
maxirnum (FWHM) values for time and fi'equency (cm'l), respectively.“ Reference 41
also lists the values that make this inequality true for non-Gaussian pulses. For 50-60 fs
Gaussian pulses, the frequency bandwidth is approximately 245-300 cm’1 , which

corresponds to a width Of 10-12 nm (F WHM) for pulses at 622 nm.

The output from the CPM is centered at 622 nm and is usually 50-60 fs with an
average power of 20 mW which translates to about 200 p] per pulse. The pulses are
produced at about 100 MHz in our ring cavity with length 3.3 m. In order tO conduct
experiments, we need larger pulse energies and must amplify the pulses from the CPM

(vide infra). The CPM oscillator is fairly stable and requires only minor mirror

24

fifli‘TmS on a ti;

mammal COTE:

thAmpMfin
For a more e
”\iCh group at .\T

11‘ Tea Klan et \A h.

rgxmonized with t}:
3‘"- l‘ -
A" m Flgure 2.1)
”LL34 039mb“ el'LQ;
be flUCI‘tL;
3731‘ PH and
‘ rhOda‘h-
FL“.
atm
. 0 .
the slum.

QE‘in l
.\. p
The Spont;

2.,
Can CallSe [EDI

>21.

Ivi

2376.712“

 

adjustments on a daily basis. Dye changes are needed every 4-8 weeks depending on the

environmental conditions in the laboratory and the amount Of time the laser was used.

2.1 .2. Amplifier

For a more complete description of the specific amplifier used by the Dantus
research group at Michigan State University, see the doctoral theses by Marcos Dantus
and Una Marvet who built our amplifier.‘ ”2' ‘5 The four-stage dye amplifier116 (Figure
2.1) consists Of four Bethune cells1 '7 (BC) which contain circulating gain dyes which are
transversely pumped by the frequency-doubled 532 nm output of a 30 Hz Nd:YAG laser
(typically 10.5 W or about 300 ml average energy per pulse). The Nd:YAG laser is
synchronized with the CPM by detecting femtosecond pulses with a photodiode (PD near
CPM in Figure 2.1) and using this electronic signal to trigger the NszAG. This
synchronization ensures that the femtosecond pulses are being amplified rather than
random noise fluctuations. The gain is achieved using kiton red dissolved in water in the
first cell and rhodamine 640 dissolved in water in the other three cells; the stimulated
emission fiom the excitation process Of these dyes is what amplifies the CPM beam In
addition to the stimulated emission Of these gain dyes, we also Obtain spontaneous
emission. The spontaneous emission is incoherent and on the nanosecond time scale;
thus, it can cause temporal and spectral distortion Of the output when it is amplified
preferentially over the femtosecond pulses from the CPM. Reduction Of the amplification
of spontaneous emission (ASE) is achieved through both spatial filtering (using diamond
pinholes, PH) and temporal filtering (using malachite green as a saturable absorber, J SA)

in the path Of the beam in the amplifier. Notice that the pulses have now traveled through

25

at appreciihle 3:32.
'-.:tdueing negro
ll 2 reeompresses
magma} Width F ‘i

as: late zero chit:

 

 

 

an appreciable amount Of water and glass in the amplifier and are broadened by GVD. By
introducing negative GVD, a double-pass prism pair alter the amplifier (shown in Figure
2.1) recompresses the pulses and removes the GVD. The resulting amplified 60 fs
(temporal width FWHM) pulses have an energy Of 0.35 mJ per pulse at a rate of 30 Hz

and have zero chirp.

2.1.3. Pulse Characteristics

The temporal width and the spectral profile across the time duration Of the pulse
can be measured by a frequency resolved Optical gating (FROG) setup.l 132‘ 19 We use a
commercial system, Clark-MXR FRG-l, for our measurements tO confirm that the pulses
have been recompressed correctly without any remaining chirp. Without the frequency
resolution, the setup would yield an autocorrelation of the pulses. The entering beam is
split into two arms, one Of which gates the other in time. Following this time resolution
(intensity autocorrelation), the beam then passes to a grating where the fre®ency
distribution with respect tO time is recorded. A FROG trace Of the pulse shows the
fi'equency (vertical) and time (horizontal) profile as seen in Figure 2.2. If all frequencies
arrive at the same time, the chirp is zero (1'. e. unchirped, see Figure 2.2b). When the
frequencies in the pulse change with respect tO time, the chirp is nonzero (see Figure 2.2a
and c). The dotted line in Figure 2.2a represents the trace that would be Obtained for a
negatively chirped pulse (higher (blue end) frequencies arriving before lower (red end)
frequencies); the line in Figure 2.2c represents a positively chirped pulse trace (higher

frequencies delayed compared tO lower frequencies). By using the FROG trace, we can

26

‘— _____.

 

frequency

—.-_————-_—-———_,
r ___—

2 129.79 2
then:
"Q‘Etve
“than.
3256 wt
in

..jci
”leim
!

adjust the position of one of the prisms in the pulse compression to yield pulses with the
chirp needed for our experiments. For all experiments described here, the pulses were
unchirped. Experiments in our group using chirped pulses (with both pump-probe and
four-wave mixing techniques) have been published elsewhere. ' 121052106

ll

frequency

 

 

time

Figure 2.2. Example Of a FROG trace with time increasing from left tO right and
frequency increasing from bottom to top. (a) The dotted line represents a
negatively chirped pulse where blue wavelengths (high frequencies) precede red
wavelengths (low frequencies). (b) Experimental FROG trace Of an unchirped
pulse where all the wavelengths arrive at the same time. (c) The dotted line
represents a positively chirped pulse where red wavelengths arrive before blue
wavelengths.

27

1!

F0. {Al ‘3 In}.
re ted to treat 2

the Lord hf?

 

resin: temmral .
3%. a. 1.1 3.“:

mt, .uion neck}.

 

2.2. EXPERIMENTAL TECHNIQUES

Following the generation Of the amplified femtosecond pulses, a number Of optics
are used tO create the laser beam arrangement needed for each type of experiment; for the
methods used here, either two or three femtosecond pulses must be used in their own
specific temporal and spatial arrangement. The description Of the laser beam setup for
each experimental technique is described in detail below. In addition, the sample

preparation specific to the experimental technique used is listed below.

2.2.1. Pump-Probe Technique

In the pump-probe experiments, two femtosecond pulses are required. One excites
(pumps) the system tO an excited state and then at some later time, t, the excited state is
probed with another pulse. This probing may excite the system tO another excited state or
de—excite the system. In order tO monitor the reaction, Often laser-induced fluorescence

(LIF) from one Of the excited states is measured.

2.2.1.1. Time Delay

A beam splitter (B8) was used tO divide the femtosecond beam from the
amplifier into two arms. These two beams followed separate paths with distances d1 and

d2, one having a fixed pathlength and the other having an adjustable pathlength. The time

28

tinveentlr "

tat-.2312. 4e

wheat?) rec

WE. the pol: '~

separated in ‘
‘Xegriie" tin
5353.? ll): pun

3pm ai'i'll:

rater “35 pl

Chad 02 pm

it.

__ — — — — -'

 

1 between these pulses must be well defined and controlled and was done so here with a
Mach-Zehnder interferometer (shown in Figure 2.1). These two beams were then
collinearly recombined before the sample cell using a dichrOic beam splitter (dBS). If d1
= d2, the pulses arrive at the sample at the same time. If d. i d2, then the pulses are
separated in time and this time delay can be calculated using the speed Of light.
“Negative” time delay refers to the arrangement when d. > d2 and the probe pulse arrives
before the pump pulse. “Positive” time delay refers to the arrangement when d; >d1 and
the pump arrives before the probe pulse. “Time zero” refers to the case when d1 = d2 and
the pulses are overlapped in time. TO change the length Of path d2, a computer-controlled
actuator was placed in the path. A mirror is mounted on this actuator; this mirror can be
moved 0.2 pm accurately resulting in a distance resolution of 0.4 pm which translates
into a temporal resolution Of 1.3 fs. Obviously, the actuator can make larger steps
(controlled with a LabVIEWT“ program, see Appendices) such that the data can be taken
at any time resolution between pump and probe pulses that is larger than 1.3 fs.
Sweeping the pump-probe time delay results in a time transient that shows how the
fluorescence, collected perpendicular to the propagation Of the beans, varies as a
function Of this time delay. Typical transients have 100 time delays and are averages of

10 scans.

2.2.1.2. Excitation Wavelengths

Variable wavelengths can be Obtained by frequency doubling the 622 nm with a

second harmonic generation crystal (SHG) to 311 nm or by creating a frequency

29

airman. 23.2.2.2
ll mm kDP Ct;
.11 for our ex
arms reg; .
itieiehgh “35 . I

.requetr} contin.

 

 

 

 

ratifies of the e\.

ACQCCQCD) b\ ‘
. I
mtd Wlih lht’
fink
*(‘f p
«$3315 were 6‘
If".

continuum from the 622 nm beam and filtering it to give the desired wavelength. Here a
0.1 mm KDP crystal was placed in the variable arm (pathlength = d2) to produce 311 nm
light for our experiments that require 311 nm as the probe. In addition, a few
experiments required the wavelength of the pump to be 550 nm rather than 622 nm. This
wavelength was obtained by focusing the 622 nm beam on a piece of quartz, creating a
fiequency continuum, and using the appropriate filter to pass 550 nm light. More

specifics of the excitation of the iodine sample are described in Chapter 3.

2.2.1.3. Polarization

The polarization of the 311 nm probe pulse was fixed perpendicular to the laser
table (Z-axis in Figure 2.3) while that of the 622 nm (550 nm) pump pulse was rotated to
be parallel or perpendicular relative to the probe pulse (Z- or X-axis in Figure 2.3
respectively) by a zeroth-order half-wavelength plate (HWP). Parallel transients are
obtained with the laser polarization vectors parallel; perpendicular transients are obtained
when the laser polarization vectors are perpendicular. The parallel and perpendicular
transients were examined to nuke sure that the time zero did not change when the

polarization of the pump beam was rotated.

30

 

  
  

Experimental

(622 or 550 nm) pump

  

(311 nm) probe

C0926
.91... . ‘ t . .45

 

 

 

 

Figure 2.3. Experimental setup for rotational anisotropy measurements with
unidirectional (X-axis) detection. The polarization of the probe beam remains
oriented along the Z-axis while the orientation of the polarization of the pump

beam can be rotated along either the X- (.L) or Z-axis (||). LIF is collected
perpendicular to the propagation of the laser beams.

Polarization measurements. were performed with well-polarized beams. We
measured polarimtion ratios (verticalzhorizontal) afier recombination of pump and probe
lasers by the dichroic beam splitter. The pump laser polarization ratio was enhanced with
a calcite polarizer (Pol) placed afier the half-wavelength plate. The polarization ratio of
the probe laser, at 311nm, was measured to be higher than 102:1. With this setup, the
polarization ratio of the pump beam was higher than we could experimentally determine
~104zl. Polarization ratios were also measured after the experimental cell to ascertain that

no polarization scrambling occurred in the cell windows.

31

22.1.4.

Saturei'h '
of lid-Tip and pr. '
i'r ml: of laser
used to attenua‘.

\

T33 “15 intrezh

 

 

 

3.“:
51;:“n
‘4‘ .
. as a V
‘1‘
s
3. _
‘x.:\‘ ‘Xk
k] ‘ .
I!“
1

2.2.1.4. Intensity

Saturation of spectroscopic transitions and detectors was prevented by attenuation
of pump and probe beams to energies below 1 it] per pulse. For experiments investigating
the role of laser intensity on the molecular dynamics, various neutral density filters were
used to attenuate the pump laser intensity. In some cases, the pulsewidth of the laser
pulse was increased from 50 fs to 120 fs in order to reduced the peak intensity and

minimize nonlinear effects.

2.2.1.5. Sample

A quartz cell containing iodine was prepared on a vacuum line and degassed to
less than 10'6 Torr before being permanently sealed. Experiments were conducted at

room temperature (21 i 3°C) where the vapor pressure of iodine is 0.25 Torr.

2.2.2. Four-Wave Mixingl'l’ransient Grating Technique

In four-wave mixing experiments, three fields must cross in a specific geometric
configuration. Two fields create a transient grating while the third one diffracts off the
grating as a signal beam. This signal beam contains molecular dynamics information
about the sample; the signal intensity depends on the time delay between the arrival of

the beams tint form the grating and the arrival of the beam that is thed.

32

2.2.2.1.

 

 

The ilVC'
has of comp-
ccnbimi at the
see Figure 2.4 ;.

lit l inch sides

 

2.2.2.1. Beam Arrangement

The laser from the amplifier was attenuated by a factor of two and split into three
beams of comparable intensity ~ 50 p] using two beam splitters. The three beams were
combined at the sample in the forward box geometry”,83 by a 0.5 m focal length lens
(see Figure 2.4). At the lens focus, the three beams occupied the three corners of a square
with 1 inch sides. Each pair of beams were crossed at an angle of 2.6° resulting in a

fiinge spacing of 14 pm. The beam size at the interaction region was 40-50 pm.

In order to optimize the initial alignment of the four-wave mixing setup, templates
of the beam arrangement were made and used to ascertain that all beams were parallel
before the focusing lens. A second harmonic generation crystal, KDP of 0.1 mm
thickness, was placed at the focus to optimize the spatial and temporal overlap of the
fixed beams. Once the third beam was overlapped in space, it was scanned in time until
the FWM signal beam appeared. When all three incident pulses were overlapped in time
andspace,amatrixofequallyspacedredandUVbearnscouldbeseenafterthecrystal.
These were the result of all combinations of second-, third-, and higher-order wave
mixing processes occurring at the crystal. After further optimization of spatial and

temporal overlap for the FWM signal, the crystal was removed fi‘om the beam path.

33

 

 

 

 

Figure 2.4. Beam arrangement in the forward box configuration (see References
82 and 83). E6 and Eb are overlapped and fixed in time. For positive time delays,
these fields set up a transient grating in the horizontal plane off which Ec Bragg
scatters to give the FWM signal. The time delay between Ec and the two other
fields is varied to obtain the time—dependent dynamics of the system. In our
experiments, all beams were horizontally polarized.

2.2.2.2. Time Delay

One of the fields (EC) had a variable pathlength (dc) and could be delayed by a
computer-controlled actuator. There was a manual translator in the pathlength of field E,
(db) while field Ea had a fixed pathlength (do). (See Figure 2.1.) Therefore within a

particular experimental scan, these fields E, and Eb were fixed in time - either overlapped

34

 

id; = J-l 0’

no fields 7
exgertnient.

defied as tl
seamed in-
12:33:: (d, =
m Mass.

2223? Lie or}

$.
\
\:.-- ~
11?; {Y e
» L53
is?‘
mu. [m
It
«s‘
‘-
4%

(da = db) or separated ((1,, #5 db) - while field EC was scanned in time with respect to these
two fields. The temporal relationship between fields E, and Eb will be specified in each
experiment. When E, and Eb are overlapped in time, time zero for these transients is
defined as the point at which all three fields are coincident in time. When E, and E1, are
separated in time, time zero is defined as the point when fields EC and Eb are overlapped
in time (dc = db) for the specific pulse sequences used here (vide infra). For "negative"
time delays, EC arrives before the other two fields. For "positive" time delays, EC arrives
after the other two fields. See Figure 1.2 for positive and negative time delays for the
experiments when E, and Eb are coincident in time. Diagrams of the pulse sequences

when these two fields are separated in time will be shown in Chapter 4.

2.2.2.3. Signal

The signal beam is generated at the fourth comer of the square defined by the
wave vector k5 = ltd - kb + Itc with a wavelength equal to the incident beam wavelength. It
is possible to collect the signal beam at other wavelengths;‘03"05 however, in all cases
discussed here, the data were collected at the central wavelength of the laser pulse, 622
nm. The sign] beam was collirnated and sent to the monochromator (see below).
Sweeping the time delay between the variable and the fixed fields yields transients that
reflect the temporal evolution of the dynamics. Typical transients contain data from 150
different time delays and are averages of 10 scans. Care was exercised to minimize

scattered light and to ensure that the collected signal was background free.

35

 

 

2.2.2.4

a. espt
5.3.5.1 samples
widened at it

‘ 1
ft and mercu.

3%»
“‘:‘W\

. ”01:? 6‘

‘ s

h.
u¥m*

;\\;E\. x

. d.- "'4

2.2.2.4. Sample

All experiments were performed on 30 to 760 Torr of gases or neat vapors (when
liquid samples were used) contained in static quartz cells. The experiments were
conducted at room temperature for the majority of these samples except for iodine (140

°C) and mercury iodide (280 °C).

2.3. SIGNAL COLLECTION

Following the experimental setup, the beams were focused on the sample cell and
the fluorescence (pump-probe) or signal beam (four-wave mixing) was collected and
collimated by lenses. The signal is directed to a 0.27 m monochromator (SPEX 270 M),
detected with a photomultiplier tube (PMT), averaged in a boxcar integrator, and then
transmitted to a Stanford Research 245 computer interface board for collection by the
computer. The monochromator and interface board were controlled with LabVIEWT“
computer programs. Two different LabVIEWTM computer programs were written by
Emily Brown (see Appendices) to obtain either wavelength spectra of the samples or to
obtain time transients. (Kathryn Walowicz has modified these programs for the Ti-
Sapphire system to incorporate the CCD detector in the programs.) At each wavelength
or time delay, the signal was collected for 10 laser shots. In all cases, the beam intensity
was monitored by a reflective scatter from an optic directed to a photodiode (311 nm for
pump-probe, 622 nm for four-wave mixing). Data points obtained when the laser pulse

intensity varied more than one standard deviation from the mean were discarded. Both

36

 

1h: numler of
IIIIIIIIEI of in"
(“Elfiff‘gih 9,

apple hem; m

the number of time delays (wavelengths) measured for a transient (spectrum) and the
number of individual transients (spectra) summed to obtain the final time transient

(wavelength spectrum) varied depending on the experimental technique and on the

sample being measured (vide supra).

37

 

 

3. R0

EX

Tht

.3555 are 1

3. ROTATIONAL ANISOTROPY MEASUREMENTS ON IODINE:
EXAMINING UNIDIRECTIONAL DETECTION AND LASER

INTENSITY

3.1. INTRODUCTION

The pump-probe technique has been described in Chapter 1. Two femtosecond
pulses are used to excite and then probe the molecular sample; these pulses are separated
in time by a variable delay. Rotational anisotropy measurements require the use of pump
and probe pulses that are polarized parallel and perpendicular to each other as explained

in Chapter 2.

Theories for time-resolved rotational anisotropy measurements of isolated
molecules have been developed using both quantum and classical rrrecharrics.2‘t33~'20“22
Given the multiple techniques available for ultrafast dynamics measurements such as
laser-induced fluorescence, multiphoton ionization and four-wave mixing, it is important
to realize that the rotational anisotropy theory applies differently in each case. As
discussed in recent papers fi'om our group,3’9t44t35a37»109 it is sometimes necessary to adapt
these well-known equations in order to extract accurate rotational constants and/or
rotational populations based on the experimental methods (e. g. pump-probe“,45 transient

grating,“’37 four-wave mixing,109 and multiphoton ionization”).

38

 

Rt‘lililt‘
pawl-on W.
I.) to tech 0'
armpit cont:
mimic co."
Whittier tr-
Elormpiicii) i:
If “Till?” as 1; iii

in?” the St

Cation noted the
it". 4 ' .
“If“ m Equalio

 

 

MW art'smroi

t'It‘ “ :~ .
mitten) 0ft

sag .
t .
he Wm

Rotational anisotropy is typically measured by obtaining transients with the
polarization vectors of the pump and probe beams oriented parallel (ll) or perpendicular
(.I.) to each other, In(t) and Ii(t) respectively. The difference, Iu(t) — Ii(t), contains
isotropic contributions in addition to the time-dependent anisotropy. ‘23 The pure
anisotropic component of the signal is obtained by subtraction of the parallel and
perpendicular transients and division by the purely isotropic component of the signal, [.30.
(For simplicity in the equations that follow, the parallel and perpendicular transients will
be written as In and I i.) Based on the work of Gordonm, the isotropic component can be
obtained by the sum

1,3,, =I”+21i. (3.1)

Gordon noted that dividing the difference by the isotropic component of the signal as
defined in Equation (3.1) leads to a measurement that is independent of isotropic
contributions and experimental parameters such as the relative signal intensity. Thus, the
rotational anisotropy could be obtained according to the formula33t123

I —I
r(t)=—-———Ill 21"" .
n+ i

(3.2)

The simplicity of this formula is misleading. In fact, it applies only to a subset of the
ultrafast dynamics detection techniques. Equation (3.2) is applicable only for
mmsurernents where Equation (3.1) is true. Among these are experiments where the
signal is the partial absorption of the probe, a common setup for liquid phase

experiments, or a measure of fluorescence depletion caused by the probe.

39

 

 

Ina

MIMIIOIE

$21331 ion
3?) UK I‘d:

In addition, the anisotropy formulae were originally derived assuming weak-field
interactions. 17-3 The peak intensities of femtosecond laser pulses can typically approach
1012 W/cm2 levels; therefore, it is important to consider the role of saturation and other
field-induced efiects on anisotropy measurements and how these nonlinear phenomena
must be included in the analysis to extract accurate information. In the case of severe
saturation, other photophysical and photochemical pathways become available. These
may include multiphoton excitation, ionization, and dissociation. From a theoretical
standpoint, the rotational anisotropy at time zero and time infinity are well defined for a
given experimentzh“4 We had observed that as the intensity of our pump laser increased,
the time-resolved measurements no longer reflected these theoretical values. In addition,
we observed a number of examples in the literature where these theoretical values were
not reproduced experimentally. This shortcoming implies that quantitative information
derived from ultrafast rotational anisotropy (URA) measurements rmy not truthfully
reflect the rotational populations and dynamics of the system when the laser intensity is

high.

In this study we explore the applicability of the typical rotatioml anisotropy
formula (Equation (3.2)) to ultrafast measurements where the signal arises from probe
laser induced fluorescence (LIF). In particular we explore the effect of unidirectional
detection of the fluorescence signal taking into account the f-number of the collection
optics. This experimental configuration is one of the most common in time-resolved gas-
phase measurements. We also present experimental URA data for gas-phase iodine using
a pump laser that is adjusted over three orders of magnitude in intensity, from no

saturation to highly nonlinear saturation of the Be—X transition. We develop a correction

40

 

[0 hit {11'de 9%
MOW ‘it‘m’l‘
we“ W
jasmine Ills“
error. Here V~
mam! cor
gpficébie l0
hfififi‘d. IF

STE-TIES. til:

321. Pur

Am

i

.1?

.\\I'~ 4'

E “Q

.g “ _‘
"U I‘d-t

5,. ._

c3 .. ‘
‘Qk‘iebe

; ...

‘43s“-

to the model based on saturation and other nonlinear effects and demonstrate that all data
become quantitatively correct. Ultrafast rotational anisotropy measurements are not
typically meant to provide highly accurate temperatures; they are usually used to
determine the temperature of products from chemical reactions within a 10% margin of
error. Here we show that this wide margin cannot be achieved if saturation occurs. Our
treatment concerns the first picoseconds of the URA measurements; however, they are
applicable to all time domains where rotational quantum recurrences or revivals are

observed. Implications of these measurements to the characterization of rotational

dynamics, distributions, and temperatures are discussed.

3.2. THEORY

3.2.1. Pump-Probe Technique for Studying Rotations (Rotational

Anisotropy Measurements)

The pump-probe technique has been described earlier. The time evolution of the
rotational alignment is measured with linearly polarized lasers. Excitation by the pump
pulse selects an initial population distribution described by c0320 where 6 is the angle
between the transition dipole and the pump laser polarization vector.124 (See Figure 2.3.)
As the distribution dephases due to rotations of the molecules, the probe pulse (polarized
either parallel or perpendicular to the excitation pulse) is unable to excite all the
molecules to another state, resulting in a decrease in the fluorescence fiom that state. This

fluorescence is monitored as a function of time delay between pump and probe pulses.

41

 

 

ll: time-rest

 

m and p.713}

iih'r's case. an;

3.22. Iodine

.‘slolccx
“hid met
a17"???)6'1115 r,
Hitachi“ me

Q

Li t

5,-

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2;» hm Inc

‘5'.

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U?

The time-resolved data for each polarization arrangement (1;. and 1;, where [I (parallel)
and J. (perpendicular) refer to the relative orientation of the polarization vectors of the

pump and probe pulses) contain an isotropic component, reflecting molecular vibrations

in this case, and an anisotropic component, reflecting rotational dephasing.

3.2.2. Iodine Sample

Molecular iodine is one of the most extensively studied molecules by time-
resolved methods. (See References 34,100,125-129 and 107 for example.) The
experiments measure the initial alignment and subsequent rotational dephasing of iodine
molecules that absorb a photon in a parallel transition fi'om the ground X ('ng) state‘30
to the excited B (3110)...) state.'3' The probe laser excites molecules in the B state to the E
(0+3) and f (0+3) ion pair states.132“3S The signal for the measurements presented here is
the laser induced fluorescence (LIF) from the f ion pair state to the B state at 340
nm‘34t‘35 unless otherwise noted. The potential energy curves for these states are shown
in Figure 3.1. As will be discussed in detail later, the A (3111,.) and B (18) states are also

accessible with the pump and probe lasers and are also shown in Figure 3.1.

42

 

 

 

“We 31.
iterated
Fashion) \
“0.139 a If;
liens; anc
Deans}. In ;

 

 

60000 '

 

40000

 

 

20000

 

 

 

 

Potential Energy (cm‘l)

 

 

 

 

 

3 4
R(A)

 

Figure 3.1. Relevant potential energy curves for lg. Molecules in the X state can
be excited to the B state (parallel transition) and the A state (perpendicular
transition) with 622 nm laser pulses. Excitation with 311 nm probe pulses will
induce a transition between the B and fstates (favored by parallel pump-probe
beams) and between the A and [3 states (favored by perpendicular pump-probe
beams). In both cases, LIF (f -) B, B -) A) at 340 nm is detected.

3.2.3. Rotational Anisotropy Formulation: All-Direction Detection

The dependence of URA measurements on the polarization of the pump-probe
transitions has been discussed by Baskin and Zewail.” For the case when the
fluorescence collection is proportional to the whole distribution (1'. e. all-direction
detection), one can consider the experimental signal for parallel and perpendicular pump-

probe configurations to be of the form,21

43

 

 

 

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“Milka

I” = C - A(t)-(1 + 20052 wt) and (3.3a)

1i = CtA(t)-(2—cosz cot) (3.3b)

where A(t) represents the time-dependent absorption probability of the probe beams (all
isotropic), C is a proportionality constant that takes into account experimental conditions
such as collection efficiency and spectroscopic parameters, and coszat represents the
semiclassical time-dependent rotational dynamics where a) = 41tBefli and Beg is the
effective rotational constant of the molecule. (For linear molecules, Beg equals B.)
Substitution of Equations (3.3a) and (3.3b) into Equation (3.1) yields an expression in
which the semiclassical time-dependent rotational dynamics terms (cos2 at) cancel
leaving I,” proportional to C-A(t). These terms cancel in Equation (3.2). Thus r(t)

depends only on the rotational population and the rotational constants of the molecule.

3.2.4. Rotational Anisotropy Formulation: Unidirectional Detection

A central aspect for the above analysis is that the experimental setup must satisfy
Equation (3.1), namely that the denominator must be truly isotropic. This is the case for
experiments where absorption of the probe laser is measured, as in most time-resolved
condensed-phase experiments. We need to consider one of the most common
experimental setups used for gas-phase measurements, unidirectional detection of probe
induced LIF, and determine whether or not Equation (3.1) is firlfilled. While the effects

of collection geometry have been noted before,” the implications have not been

 

 

explored. B;
of’J'r OPEIC

DIEM CC L“;

324.1.

For
him either
priprniora‘;
LII a: a rig

It shim a:

explored. Below, we first assume a large f number collection (f number is the focal length
of the optic divided by the diameter of the optic); then we examine differences for small f

number collection.

3.2.4.1. Large f number collection

For unidirectional detection experiments, fluorescence collection favors signals
from either parallel or perpendicular probing configurations; thus, the signal is not
proportional to the whole distribution. A common example is collecting probe induced
LIF at a right angle to the laser (e. g. X-direction) as shown in Figure 2.3. This point can

be shown analytically using the equations for the signals as given in Reference 21

SHX =5”, =%(1+20082wt), (3.4a)
C 2
SIIZ =3—5(l+2cos (at), (3.4b)
S ——C—(3—eos2ax) and (3 4c)
” 105 ’ '
C 2
SIX =Srz =El—6(ll—6cos (at). (3.4d)

For these expressions, the polarization vector of the probe is fixed along the Z-axis; the

polarization vector of the pump is oriented along the Z- or X-axes for parallel or

45

termini
the polar:
its signal
raihtion c.
milkecthis
Willlcul.‘
detection d,
mm! Ct
and l. for .\
méihlkm (
J‘li‘CUIaI on,
mills are

l
‘M

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_=L_

perpendicular measurements respectively. The LIF signal arises from the components of
the polarization dipole along each of the lab-fixed axes. For example, Sx corresponds to
the signal that is radiated by a dipole that is oriented along the X-axis. Note that this
radiation can not be observed along the X-axis itself. This is one of the reasons why
unidirectional detection can over- or under-estimate the ratio between parallel and
perpendicular signals. Equations (3.4a)-(3.4d) are used to calculate Ia and I; for different
detection directions. These expressions are shown in Table I in addition to other
important equations and values in anisotropic measurements. Clearly the addition of In
and I r for X-detection (I = Sy + 52) according to Equation (3.1) does not lead to the
cancellation of the rotational term. Because the goal is to render the sum independent of
molecular orientation, one can easily deduce the correct expression by substitution; these
formulae are shown in Table I. As shown in the table, the experimental r(t) for X-

detection can be calculated fiom the data using

(3.5)

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3.2.4.2. 1' number dependence (small 1' number)

So far the discussion has been limited to large f number collection, where f
number is defined as the focal length divided by the diameter of the collection optic.
However, it is important to recognize that most experirnentalists maximize the collection
efliciency by reducing the f number of the collection optics. We calculated the relative
contributions of Equations (3.4a)-(3.4d) as a firnction of f and again determined the
proper expression for the r(t) denominator by substitution. In the generalized rotational

anisotropy formula

r(t) — —i——— (3.6)

the resulting coefficients C(/) as a firnction of f for X-, Y-, and Z-detection are

5 7
C =————————-, 3.7
x03 2 2(5+16f2) ( a)
5 7
Cr(f)-§+Wiand (3-7b)
Cz (f) = 2 . (3.7c)

48

 

From Equal"
reglgltle. Ex'en for It
and 7% forf= 3 and
such :5 optical rrrourrts.
=1 collection dltfrcul'.

treeasar) for the um;

325. Evolution of tt

In Figure 3.3 I

orientation lnlllall) c

&

05‘

 

M as (A) initial
mm alignment and
but: .

44110

ml WPUlatlon Can I

From Equations (3.7a)-(3.7c), it is clear that for f 2 3 the second term is
negligible. Even for low f values, the deviation caused by the second term is small, 2%
and 7% for f = 2 and f = 1 respectively for X-detection. In general physical constraints
such as optical mounts, spatial filters, and spherical and chromatic aberrations make true f
= l collection difficult. Therefore, for most URA measurements, no f number correction

is necessary for the unidirectional equations in Table 1.

3.2.5. Evolution of the eos’o Distribution

In Figure 3.2 we have shown snapshots of the distribution of molecular
orientations, initially c0520, at certain characteristic points on the r(t) graph These can be
defined as (A) initial alignment or full-recurrence, (B) isotropic distribution, (C)
persistent alignment and (D) half-recurrence. The time-dependent evolution has been
simulated using semiclassical methods and a visualization of the evolution for a thermal

rotational population can be found at Reference 136.

49

Figure 3.2. (a) Simulated rotational anisotropy graph at shorter time delays. The
distribution quickly changes from the initial alignment (A) to an isotropic
distribution (B) to a persistent alignment (C). Drawings of these distributions as
viewed from the X-Y plane are shown above the r(t) graph. (b) Simulated r(t) at
longer time delays. After the persistent alignment, a half-recurrence (D)
develops. The drawing of this distribution is shown from a view out of the X-Y
plane so that the sin26l shape (rotated around the Z-axis) is evident. Each r(t) is
labeled with the distributions that occur as time evolves.

50

04

r(t)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

OAI r

03

10

6

Time Delay (ps)

4

 

fir

 

 

 

 

 

 

 

 

 

 

1000 1500

Time Delay (ps)

500

 

 

 

2000

Figure 3.2

51

In
when“
worm

detection
as one e'
liq-Lids. 1

=79: . merit

 

tie differ:
rest LR

“with:

3.2%. ‘

St

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if ”Uzi

In the absence of collisions, dilute gases for example, molecules exhibit a
persistent alignment (C) that favors parallel over perpendicular probing (parallel
transitions assumed). As a consequence fluorescence emission is anisotropic and the
detection configuration influences the measurement. The loss of this persistent alignment
as one enters the condensed phase is the subject of a paper fiom Zewail’s group.'37 In
liquids, the anisotropy values range fi‘om 0.4 at r(0) to 0.0 at r(oo) because rotational
alignment is relaxed by collisions. Table I shows the expected values at time zero and at
time infinity for each detection direction for gas-phase experiments. Differences among
the different detection geometries are significant and well above signal to noise ratios of
most URA measurements. Having identified the type of collection in the experiment, one

can make quantitative URA measurements.

3.2.6. Extracting Molecular Dynamics Information

Semiclassically, the rotational anisotropy, r(t), can be written as a weighted sum

of the individual rotational state anisotropies, r(i,t),2‘t33

ZPtj)r(j.t)
, ___ ,-
'() ZPo')
j

 

(3.8)

where P0) is the product state distribution, for example a Boltzmann or Gaussian

distribution The equations defining r(t) are adapted to the specific experimental method

52

1155“
the d
@351.

te“

in.»
.

3.2.7.

Tr
nnreson
Hershlah
hinted dl;
m to an
faucet 3
Emilio:
(’2' a? 1'40 .

t

J Ldj [O

used for the measurerrients.9t21t44s87 Fits of the experimental r(t) to Equation (3.8) lead to
the determination of the experimental rotational distributions. For the room temperature
measurements presented here, a Maxwell-Boltzmann distribution is assumed and a

temperature is extracted to quantitate accuracy of the measurement (vide infra).

3.2.7. High Intensity Fields and Molecular Alignment

The observation of molecular alignment stemming fi'om high intensity
nonresonant laser excitation has been explored theoretically by Friedrich and
Hershbach. 138439 In the laser-induced alignment method, the intense laser field causes an
induced dipole in polarizable molecules, which suppresses the rotational motion and
leads to aligned pendular states. 133,139 Friedrich and Herschbach developed this laser-
induced alignment theory based on earlier observations of dissociative multiphoton
ionization experiments on C0 and 12 with intense infi’ared lasers conducted by Normand
et aI. ‘40 and Dietrich et al.,'41 respectively. In these cases, either the parent molecule was
forced to align along the polarization vector of the laser before dissociation140 or a torque
was imparted on the molecule thereby causing a gain of angular momentum. 14‘
Demonstrations of the laser-induced alignment technique have been conducted by Kim
and Felker on large nonpolar moleculesmtI43 and by Stapelfeldt and coworkers on
smaller nonpolar molecules.144t”5 Corkum and coworkers have combined intense off-
resonance chirped circularly-polarized fields to induce rotational acceleration, thus
constructing a molecular centrifuge.I46 Fujimura’s group is currently exploring the

deformation of molecules in the presence of strong-fields.I47 Experimental findings from

53

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area: .

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353.17nt IS
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our group indicate that CS2 molecules bend in the presence of strong off-resonance fields.
Those experiments were carried out by measuring the field-free rotational recurrence

observed ~76 ps after strong-field excitation in a transient grating experiments-“43

In the laser-induced alignment method, increased alignment results from
increased laser intensity and decreased initial rotational temperature. In addition to being
intense and nonresonant, the pulses need to be relatively long (compared to the rotational
period of the molecules). The experimental demonstrations have shown that the
alignment is more successful if the initial rotational energy is reduced (< 10K).'44t145 It is
also important to turn on the field adiabatically where the rise time is much longer that
the rotational period of the molecule being aligned.'44 In the Corkum group’s
experiment, they noted that, with the use of intense femtosecond lasers, the I2 molecules
were frozen on the rotational time scale and the field only imparted a torque on the
molecules to gain some angular momentum; however, the 12 molecules would eventually
align with the intense field if it lasted picoseconds.I41 Furthermore, Posthumus et al. have
examined the multiphoton dissociative ionization of H2, N2 and 12 with 50 fs pulses and

found that only H2 and N2 show alignment characteristics. '49

Alignment with resonant intense laser fields has been examined theoretically by
Tamar Seideman. When on-resonance fields are used, the intensity does not have to be as
strong as in off-resonance experiments to generate alignment.”0 She noted that for
heavier molecules (which would correspond to greater rotational periods), a longer laser
pulse duration is required to align the molecules; in addition, she also noted that

nonresonant experiments may be more advantageous for these larger molecules under

54

kept/ifs
corrlasion
matted b
While. a]
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tilting r(

low initial rotational temperature conditions. I 50 Finally in these experiments, the
alignment survives and recurs at specific times after the field is turned off. Similarly,
Ortigoso et al. have calculated the conditions (laser pulse and rotational constant of the
molecule) for which recurrences of the laser-induced alignment can be expected with

nonresonant short pulses.'5‘

The experimental work presented here involves moderately intense femtosecond
laser pulses that are resonant with the electronic transitions of I2. Based on the results and
conclusions of the above on- and off-resonance studies, adiabatic alignment is not
expected because of the short duration of the laser pulses, the mass of the iodine
molecule, and the warm initial rotational temperature of the molecules (294 K). The goal
of this work is to explore how nonlinear processes brought about by resonant fields

influence rotational anisotropy measurements.

3.2.8. Effects of Saturation

As we discussed above, we do not expect laser-induced alignment from these
experiments. Another possibility is that the intense laser field will create a reduction in
the measured URA. The goal is to explore how the intensity of the pump laser affects
URA measurements because of saturation in the Bt—X transition. The initial population
impulsively excited by the pump pulse has a coszfldistribution. (See Figure 2.3.) As the
intensity of the pump pulse increases, the population in the B state increases and the

probability for stimulated emission increases as well. Hence saturation occurs. Those

55

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gmfiiifl
tar-.1". al
the me

aritrtrt'

“Ilt’l’f fol/h
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“an h

Klimt
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molecules which are well aligned with the laser will be more susceptible to stimulated
emission. Molecules with a smaller 0 are more likely to experience saturation than those
with a larger (9. Therefore the cos2 9 distribution broadens. The end result is a reduction in
the overall anisotropy. For these cases, we propose a modification of the state-resolved

anisotropy equation (in the X-direction)44 by including a saturation factor, A s, to obtain

’As out) = (1- As)ro(j,t) = (1— {49125-0 + 2cos<2axii , (3.9)

where ro(i,t) is the unperturbed rotational anisotropy, a) = 41tBjc, B is the rotational
constant of the molecule, and c is the speed of light. The saturation parameter can vary
between 0 and 1 (no saturation to severe saturation, respectively). As the pump laser
intensity increases, A 5 increases to take into account the reduction in the overall

anisotropy.

56

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3.3. EXPERIMENTAL

For more specific experimental details of the pump-probe method, see Chapter 2.
Experiments were carried out on gas-phase iodine with 622 nm pump — 311 nm probe
and 340 nm fluorescence detection (622/311(340)) or with 550 nm pump — 311 nm probe
— 340 nm detection (550/311(340)). The 622 nm (or 550 nm) pump excites 12 to the B
state; the 311 nm probe causes an excitation to the f state from which laser induced
fluorescence (LIF) was collected at 340 nm (see Figure 3.1). For the results presented
here, the pump and probe excitations are one-photon parallel transitions and the
unpolarized LIF is collected perpendicular to the propagation of the lasers. The signal

collection was restricted to f = 3.

The polarization of the pump and probe beams was ensured as described in
Chapter 2. Neutral density filters were used to attenuate the pump laser intensity in order
to explore the role of laser intensity on the molecular dynamics. For experiments where
the laser intensity was 0.056 x 1012 and 0.27 x IO'ZW/cmz, the pulsewidth of the laser
pulse was increased from 50 fs to 120 fs. This broadening reduced the peak intensity,
thereby reducing nonlinear effects even further. A quartz cell containing iodine was
prepared on a vacuum line and degassed to less than 1045 Torr. The vapor pressure of 12 is

0.25 Torr at the laboratory room temperature (T RT = 294 :I: 3 K).

57

3.4.1.

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tit-h weal p

its-m

E1

4

J

if

M
1,)

.I‘
~12 moi},

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1

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KIM
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34‘:

we:
“fit for the

'Isilh
3m f0r I) '

 

3.4. RESULTS AND DISCUSSION

3.4.1. Unidirectional Detection at Weak Laser Intensities

In gas-pimse molecular iodine, the B 6- X and f é-B excitations resulting from
the weak intensity pump and probe beams are one photon, parallel transitions. Only
signal propagating at a right angle (X-direction) to the lasers is collected. The formulae
applicable for this case are shown in column B of Table I. In Figure 3.3 we present 12
time-resolved measurements (In and 12) for 550/311(340) and for 622/311(340) obtained
with weak pump and probe laser beams. At negative time delays, the probe pulse arrives
before the pump (311 nm before 622 (550) nm); this sequence of pulses does not
correspond to an excitation pathway that would produce 340 nm fluorescence (refer to
Figure 3.1). Thus, no signal is observed. At positive time delays (or time zero), the pump
and probe pulses arrive in the correct order (or at the same time) for excitation through
the f (- B (- X pathway resulting in LIF at 340 nm as noted above. As the time delay
between the pump and probe pulses changes, the LIF varies due to vibrations and
rotations of the I2 molecules in the B state. In these transients, the oscillations in the LIF
correspond to the vibrations of iodine molecules (about 300 fs). Notice that these
vibrational oscillations are similar in the parallel and perpendicular transients. In
addition, underneath the vibrational oscillations is a more slowly changing signal that
corresponds to the rotations of the iodine molecules. Notice that this rotational signal is
different for the parallel and perpendicular transients as indicated by the theoretical

equations for In and I 2 in Table I.

58

 

I -11“ lnternsity

 

 

 

 

 

 

 

I ' I ' I ' I r 1 i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I (a) h 550/311(340) ‘
I 'I
In
I ‘ l I
_ I_L .
E”
U)
C:
3 - ..
.5 4- Jr : : : : t : + : :
E: *(b) 622/311040)-
..i , h _
l
.. I .
L I u
I _L .
_ I .
-l 0 1 2 3 4 5

Time Delay (ps)

Figure 3.3. (a) I" and 12 transients for l2 with 550l311(340). (b) I" and I 2 transient
for l2 with 622/311(340). Vibrations are clear in both sets of transients. Because
different vibrational levels are reached on the anhannonic B state by the two
excitation wavelengths, (b) shows faster vibrational dynamics than (a). For the
same reason, the rotational constants are also different for the two data sets
resulting in a slight difference in the rotational dynamics.

59

 

 

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heist ”5“ W
Saturation 659515 or
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The transients used for these URA measurements were obtained with low
intensity laser beams to minimize saturation effects on the anisotropy measurement.
Saturation effects on anisotropy measurements are discussed below. Experimental URA
measurements are presented in Figure 3.4 and Figure 3.5 (scattered points). The time-
resolved transients, I. and 12, have been normalized such that the intensity at negative
pump-probe time delays is 0 and the intensity at 6 ps (approaching time infinity) equals 2
for parallel transients and 1.3 for perpendicular transients before calculating r(t) using
Equation (3.5). (These values are obtained by examining the theoretical equations for I“
and I 2 as the time delay approaches infinity. See Table I for the relevant equations.) We
observed that using normalized versus unnormalized data in the anisotropy calculation
and fitting routine changes the results only slightly (33% for the rotational population
temperature). Equation (3.8) is used in the fitting program (see Appendices) with B
constants obtained from Reference 34. The fits to the normalized data sets, with
temperature as the only adjustable parameter, are shown in Figure 3.4 and Figure 3.5
(solid lines). The experimental URA data are devoid of vibrational oscillations, which are
isotropic. The data at these lower intensities reproduce the theoretical values for r(0) and
r(oo) with great accuracy. The higher intensity URA measurement (0.27 x 1012 W/cmz)
does show a slight decrease from the theoretical r(0) value of 0.4 as saturation begins to
play a role in the excitation process (vide infia). In addition, the fits reflect thermal
populations of 294 i 12 K with 550 nm pump; 302 i 22 K with 622 nm pump, laser
intensity = 0.056 x 1012 W/cmz; and 290 i 12 K with 622 nm pump, laser intensity = 0.27
x 10'2 W/cmz. These temperature fits agree with the temperature in the laboratory, 294

i 3 K. The deviation observed in the weaker intensity transient is probably caused by the

60

much lo

ohaned

00111066

I'(I)

Ol-

00 -

 

litre 3.4
lilies Calt
SEW as t

much lower sigml-to-noise ratio of the data. Thus, accurate rotational temperatures are
obtained when using the appropriate equations in Table I to evaluate URA measurements

obtained from probe induced LIF with a particular detection geometry.

 

 

 

 

 

550/31 1(340)

0.4 4

- CI

0.3 " "
C 0.2 "
Y I
0.1 r-
0.0 "

0 4 6

Time Delay (ps)

Figure 3.4. URA measurements for 550/311(340) on l2. Rotational anisotropy
values calculated from normalized experimental data and Equation (3.5) are
shown as the scattered points. Fits to these values using Equation (3.8) are
shown as the solid lines. The measurement is best fit by a thermal distribution of
294 d: 12 K. Note that temperature is the only adjustable parameter.

61

 

03

 

0:-

or.

 

 

622/311(340) *
I=0.056 x 1012 W/om2

.1

 

 

d

1:027 x1012 W/em2 l

 

 

 

 

0.0 4 J A L - l -
o 2 4 6 8
Time Delay (ps)

Figure 3.5. Rotational anisotropy of l2 in the low pump laser intensity regime.
Experimental data are shown by the square data points and the temperature fits
are shown with the lines. These URA measurements are fit without the saturation
parameter and accurately reflect the shape of the data. The measurements are
best fit by thermal distributions of 302 :I: 22 K and 290 1: 12K respectively. Note
that temperature is the only adjustable parameter.

62

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£1333“ 13.8) Where .
u "3131 The haekgroh
h Em Ill IO 1}}: ex;

salute the Quality 0 I

3.4.2. Laser Intensity Effects

One of the goals of this study was to determine how the accuracy in determining
rotational distributions or rotational temperatures is compromised by saturation and other
strong-field effects. To this end, all the laser intensity dependence measurements were
carried out at room temperature, TRT. The rotational temperature obtained fiom fitting
each URA measurement, T12, was compared with TRT. Each fit was found by calculating
the experimental rotational anisotropy from the experimental transients using Equation
(3.5), conducting a linear squares regression on the experimental r(t), fitting it to
Equation (3.8) where r(i,t) is defined in Equation (3.9), and allowing the temperature, rm,
to vary. The background and the saturation parameter, A s, were also optimized to obtain
the best fit to the experimental data. The agreement between Tfi, and TRT was used to

evaluate the quality of the model.

3.4.2.1. Ultrafast rotational anisotropy: Weak-field model

Parallel and perpendicular transients were measured over a range of pump laser
intensities from 0.056 x 10‘2 W/cm2 to 62 x 1012 W/cmz. The URA measurement
corresponding to each intensity was fit as described above, keeping the saturation factor
at zero and varying only the temperature and background. As can be seen in Table IIA, at
the two lowest laser intensities, the agreement with theory is very good with 1.4 to 2.7 %
deviation between T,;, and TRT. However, the URA measurements obtained with higher

pump laser intensities do not fit the conventional theory (up to 58 % deviation) because

63

of saturation effects. These two lowest laser intensity URA measurements are shown in

Figure 3.5 (data and fits) and are discussed in detail in the above section.

Table II. Rotational temperatures (Ta) resulting from the fits based on Equation
(3.3) (A) without the saturation parameter and (B) with the saturation parameter
at different pump laser intensities. Note that parentheses around a percentage

indicate that the calculated temperature is below the actual temperature.

 

 

 

 

 

 

 

 

 

 

 

A. No Saturation B. Saturation Parameter
Parameter
(Ae=1-0)
Intensity
(10‘2WIcm2) h (K) % Error A. rj (K) % Error

0.056 302 1 22 2.7% -- -- ~—

0.27 290 1 12 (1.4%) -- -- --
1.4 379 1 23 29% 0.23 325 1 22 11%
8.5 325 1 22 11% 0.36 243 1 15 (1799
19 433 1 34 47% 0.46 276 1 17 (6.1%)
37 446 1 47 52% 0.59 243 1 22 (17%)
62 464 1 55 58% 0.65 228 1 30 (22%)

 

 

 

 

3.4.2.2. Ultrafast rotational anisotropy: Saturation effects

The experimental URA data (squares) for strong-field excitation are shown in
Figure 3.6. Notice the overall reduction in anisotropy and the appearance of a dip around
time zero, t < 500 fs. In these cases, the saturation parameter, As, in addition to T1), and
the background were allowed to vary in the fitting procedure as described above. The
results from these fits are shown in Table IIB. The fits give temperatures that do not
correspond to Tm (6.1 — 22 % deviation) but are more accurate than the temperatures
obtained without the saturation parameter (see above). From Figure 3.6, it is evident that

the rotational temperature fits (lines) do not model the early time behavior properly

tense of the a
the lit at the hon
rnodel the data it
simple saturation
Imperatures. Th

anisotmp) for iihi

because of the appearance of a dip in the experimental URA measurement. In addition,
the fit at the bottom of the rotational anisotropy curve (near t = 2 ps) does not appear to
model the data very well. The depletion feature near time zero cannot be addressed by the
simple saturation model, leading to improper fits and resulting in inaccurate rotational
temperatures. Therefore, a different process is responsible for these changes in the

anisotropy for which the simple saturation model cannot account.

65

0.4

0.3

0.2 .

01

0.3 '.

 

01 '

 

 

 

 

0.4T‘F'1rl'I'l'l'l

I=8.5 x1012 W/om2 .. 1:37 x 1012 Warez.

 

 

 

 

 

 

 

 

 

0'0 0 2 4 6 0 2 4 6
Time Delay (ps)

Figure 3.6. Rotational anisotropy of l2 in the high pump laser intensity regime.
These URA measurements are fit with the saturation parameter, As. This simple
saturation model does not predict the observed dip in the data near time zero
and yields rotational temperatures with 6 - 22 % error.

66

 

3.4.2.3.

In the
Emission hut a}:
other States et
mail 51316 IS ;
lied Rate Pat‘l
leer. this is a p
H B ”31151110
Wes At hig,
will} repuls
lho‘efore, as 11
L‘l‘Liitlon hem
Mariam“ 0
m“ the B St.
late '5 Plotted

ml‘l‘robe arm

“mks hide it

We hate
(in. ,_ .
.hIkiIIOD heart“

5??
am“ .

panic“

3.4.2.3. Ultrafast rotational anisotropy: Saturation and reactive

pathway

In the case of iodine, high pump laser intensities allow not only stimulated
emission but also the possibility of other pathways, e. g. multiphoton excitation, access to
other states, etc. At the excitation wavelength of 622 nm, the repulsive wall of the A
(3111,.) state is accessible through the A (- X perpendicular transition”;153 The short-
lived wave packet on the A state can be excited to the [3 (13) state by the 311 nm probe
laser; this is a parallel transition. Interestingly, the 13 -) A fluorescence coincides with the
f -) B transition at 340 nrrr.'54"56 Refer to Figure 3.1 for the relevant potential energy
surfaces. At high intensities, the B state saturates; however, the A state, being reached at
a steeply repulsive region, has a short-lived transition state and is not easily saturated.
Therefore, as the B state becomes saturated at higher intensities, the weaker A state
transition begins to play an important role in the excitation process. Based on the
characteristics of the transitions (parallel or perpendicular), with parallel pump-probe
beams, the B state is primarily observed; with perpendicular pump-probe beams, the A
state is probed preferentially. The short-lived signal, arising fi'om the perpendicular
pump-probe arrangement, explains the dip in the URA observed near I = 0 fs at higher

intensities (vide infra).

We have observed in our measured data (In and 12) that the first vibrational
oscillation (nearest to t = 0) in the 12 transients is more intense than the oscillations that

follow it, particularly for the highest pump laser intensities. These perpendicular

67

trarsients at ditt‘ert
left-side shows thr
time.) The I, tra
he first irhratiorn
predicted based on

(SI 1 mol1 cm'IH
Ill“ dissociation en:
WWII.) emissit
SI: and I39 A at

mutter that depr
‘5 F A F X \‘erst
Saturation While 1.

mm in 15” PCTPCI
If”lmlfrtttm 01E:
”ll be ohm ed at

MOO-300 Is In

Qimhllss
It

: 0
for per-pend)“

ht
outs largm “it

t- . .
L (hill) of ”he first

transients at different pump laser intensities are shown on the right-side of Figure 3.7; the
left-side shows the parallel transients. (These transients were normalized as described
above.) The I" transients do not exhibit a similar significant increase in the intensity of
the first Vibrational oscillation as compared to the subsequent ones. This effect can be
predicted based on the extinction coefficients of the A-X (23.9 L mol'l cm") and the B-X
(51 L mol'l cm'l) transitions153 and the short lifetime of the wave packet excited above
the dissociation energy of the A state. The Einstein coefficients are similar for the two
spontaneous emission processes following the probe pulse: f 9 B at 341 nm is 712 x 105
s'I and B 9 A at 341 nm is 745 x 105 5".156 These values allow us to calculate a
parameter that depends on the ratio of the probability for probing these two pathways
(13 (— A <— X versus f <— B <— X), A“) = 0.49. At high intensities, 1" decreases fiom
saturation while 12 increases from the contribution fiom the A state that is preferentially
probed in the perpendicular configuration near t = 0. Therefore, the expression (In - I 2) in
the numerator of Equation (3.5) becomes much smaller and r(t) decreases. This effect can
only be observed at short time delays because molecules reaching the A state dissociate
in 200-3 00 fs (as measured by Zewail and coworkers who studied 12 in solvent
:ages).‘579158 Therefore, the additional signal (a fast decaying, almost delta function) at t
= 0 for perpendicular transients causes the dip in the URA measurements. This dip
)ecomes larger with higher pump intensities and can be predicted by examining the
ntensity of the first oscillation in the perpendicular transients as a firnction of pump laser

ntensity.

68

 

 

 

 

LIF Intensi

I=8.5 x 1012 W/cmz

e
b
q
i
D
p
1 h 1
p
l

I I=1.4x10'2W/cm2 J

 

 

 

 

 

Time Delay (ps)

Figure 3.7. Parallel and perpendicular experimental transients obtained with
different pump laser intensities. As the laser intensity increases, there is a
significant increase in the LIF intensity of the first vibrational oscillation in the
perpendicular transients. The parallel transients do not show this pattern. This
increase is due to the contribution from the B—A—X excitation pathway at high laser
intensities when the polarization of the beams is perpendicular.

69

Th'rs patt
account equatior
:' res to [and I
rate. In Figure
shonn for unidir
contribution ml;
and B states as .
tome signiliea
not affected as
“:an per]
neon due to a
Obsmid when tl.
Wgrmde of thi
WWW of thr
Q-l‘Ulathn that &
Ills [1311116 of r]
llI‘lllllillQn OI IIIC

.1qu

This pattern can also be examined with semiclassical calculations that take into
account equations for I. and 12 as defined in Table I, the contributions from the A and B
states to In and I 2, the Einstein coefficients for the two states, and the lifetime of the A
state. In Figure 3.8a, the typical 1“ and I2 transients (rotational contribution) and r(t) are
shown for unidirectional X-detection, with a one photon parallel transition (i. e. B state
contribution only). Then In and I 2 can be calculated by including the contribution of the A
and B states as described above and are shown in Figure 3.8b. Notice that I2 transients
increase significantly near time zero due to the A state preferential probing; whereas, I" is
not affected as much These theoretical calculations support the observations in the
experimental perpendicular transients (Figure 3.7) where the first oscillation is higher in
intensity due to a change in the rotational contribution to the signal. Therefore, the dip is
observed when the rotational anisotropy is calculated fi'om these rotational transients. The
magnitude of this dip is influence by the intensity of the laser as well as the relative
populations of the A and B states. The thin line in the r(t) plot in Figure 3.8b shows the
calculation that assumes A and B have the same populations, which does not reflect the
true nature of the system; the thick line shows the calculation assuming that the
population of the A state is equal to one-third of the population of the B state, more

reflective of the experimental system.

70

 

"I

l€()ruti0nul Intensity

1,)

'L/ _' ””“TTI

___. I“)

O

y ‘“ “r _- “'"v \._-

to
J.-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) f-B-X b) f-B-X and B-A-X

3
E9 l t
m
it 22 In
.5
76‘ I
.5 ’ ‘ i
iii
8 l/ 1
a:

I.

0 - r - t 4 i - i : lee

52’
t
0'00 2 4 6 0 I 2 L 4 A 6 s
Time Delay (ps)

Figure 3.8. Semiclassical calculations of the rotational component of parallel and
perpendicular transients and rotational anisotropy. (a) These calculations include
only the f-B—X excitation pathway (typical pump-probe experiment) with weak
laser intensity. (b) These calculations include both the f-B-X and B-A-X excitation
pathways as is possible here with strong laser intensity. The preferential probing
of the A state in the perpendicular pump-probe arrangement leads to an increase
in the signal near time zero. This creates the dip that is observed in the
calculated rotational anisotropy. The thin r(t) line was calculated assuming equal
populations of A and B states; the thick line assumed a larger B state population.

71

 

T0 accouri

 

for the stale-resolx

“hm the ill‘Sl Icy
ME B—X “Emil
imrs caused in l}
”million in the

“m0“. OfIhe pi!

To account for the additional state interaction, we propose the following model

for the state-resolved rotational anisotropy,
- _ - -(I/ r)2
rAS,_L(Jat)—(l-AS)r0(Jat)‘Aie (3.10)

where the first term describes the reduction in the overall anisotropy caused by saturation
of the B-X transition as in Equation (3.9) and the second term describes the dip at early
times caused by the interaction of the repulsive A perpendicular state. A i accounts for the
population in the A state and the Gaussian function accounts for the Gaussian spectral

window of the probe and the temporal convolution of the laser pulses.

The experimental URA data (squares) obtained with high pump laser intensities
are shown in Figure 3.9. In this case, the fits were obtained using Equation (3.8), where
r(i,t) is defined by Equation (3.10), and allowing As, A i, TM and the background to vary.
In Equation (3.10), r was set equal to 180 fs which corresponds to the fast dissociation
convoluted with the cross correlation of our laser system for these measurements. The fits
(lines) yield thermal populations that accurately reflect the laboratory temperature for all
URA measurements at higher laser intensities (3.7 — 8.5 % deviation for the strongest
intensities; 14 % for a moderate intensity, where Equation (3.9) yielded more accurate
results). See Table III for the temperatures obtained with the fits. The dip and subsequent
rise near time zero in the data for each intensity is modeled well and the entire fit of the
curve reflects the data more accurately as compared to the fits that do not include A i

(compare Figure 3.6 and Figure 3.9).

72

 

 

’(f)

c:

5::
‘7

0.3. L,

 

0.2

0,1 .

 

 

0.4

 

'I'I'I'T'Tfr'I

I=8.5 x1012 W/cmz

 

 

1:37 x 1012 W/cm2

.1
r1

.-

 

0.0

r( t)

 

 

1p
.-

1=19 x1012 W/cm2 “

 

 

 

1:62 x 1012 W/cm2

l

 

 

0.0 A l A l A l A 1 A J A l A L A l 4 l A l A I A I A l A
0 2 4 6 0 2 4 6
Time Delay (ps)

Figure 3.9. Rotational anisotropy of I2 in the high pump laser intensity regime.

The fits for these URA measurements include both the saturation effect, As, and

reactive state interaction, A L. The early time behavior is reflected well in this
model. The rotational temperatures for the data at the four laser intensities
shown are within 3.7 - 8.5 % of the laboratory temperature.

73

Table III. R01
Equation (3.4
path parame
calculated te

 

. Intensity
no ZW/cmz)

1.4
8.5

\1

V

ii

_A
(o

 

The Ircr
W m} line
M gm) Squz
tam field; 1
close; 10 the lab
1‘21 incorporates

My Million (l

Table III. Rotational temperature fits (Ta) at different pump laser intensities using
Equation (3.4) which includes both the saturation parameter (As) and the reactive
path parameter (A i). Parentheses around a percentage indicate that the
calculated temperature is below the actual temperature.

 

 

 

 

 

 

 

Saturation + Pemndicular Parameter
Intensity
(10‘2W/cm2) As A i Tm (K) % Error
1.4 0.18 0.042 336 t 23 14%
8.5 0.24 0.14 269 1 11 (8.5%)
19 0.34 0.12 309 112 5.1%
37 0.45 0.15 283 :l: 13 (3.7%)
62 0.49 0.17 273 t 18 (7.1%)

 

 

 

 

 

 

The trends in T,;, obtained with the three models are displayed in Figure 3.10; the
broad gray line is Tm (294 :l: 3 K). As has been noted above, the no saturation model
(dark gray squares) yields T,;, values that are much higher than the TRT for the most
intense fields. The simple saturation model (light gray triangles) leads to temperatures
closer to the laboratory temperature but are too low at the highest intensities. The model
that incorporates both the saturation of the B-X transition and the reactive path from the

A-X transition (black circles) results in temperatures closest to the actual temperature.

74

Tm (K)

5a.:

450

 

 

 

 

 

 

 

 

 

 

 

I I ITIIIII I r I rrnTT r T 1 IIIII' fl 1 1721371
500 l- — Laboratory Temperature _F '1
, ...... No Saturation Model ,
--A--— Saturation Model 1? /i
450 F . -
..- Saturation and A State Model —/
400 “ ~- -L- ‘
52
v 350 " -
H
[3" . .
I _L l
300 ’
V
i J- / \ \
250 '" \4/ ‘\ _a
200 b L J lLlJLli 1 I l Lillll I J I llllll J l l lilll
1E10 1E1] 1E12 1E13 1E14

Pump Laser Intensity (W/cmz)

Figure 3.10. Rotational temperatures, Ta, obtained from the three models used to
fit the experimental rotational anisotropy data. The laboratory temperature, Tm =
294 :1: 3K is shown as the broad gray line. Error bars, corresponding to one
standard deviation, are shown for each fitted temperature. When saturation is not
included (squares), the model predicts only low intensity regime temperatures
well; the high intensity regime temperatures deviate far above the actual
temperature. When the model is based on the saturation of the Bt—X transition,
the temperatures are too low. When both saturation of the Be—X transition and the
presence of the A state reactive path are included, the fitted temperatures reflect
the actual temperature (< 10% error) in the high intensity regime.

75

Base
parameter v:
pammer (.-.
mama 1
follow an ex
mmn“
ramble I(

lilacs for lht

Saturation Factor

Pcrpcn dic ular Factor
:9

0.1

 

Based on the modified rotational anisotropy equation (Equation (3.10)) and the
parameter values in Table III, as the intensity of the field increases, both the saturation
parameter (A s) and the perpendicular state parameter (A i) increase. We have empirically
determined the relationship between these parameters and the pump laser intensity. Both
follow an exponential model as shown in Figure 3.11. (For the A i trend line, the second
data point was not used in the fit because of its deviation fiom the rest of the data.) It is
reasonable to expect a simple relationship between the two parameters. Notice that the

values for the saturation intensity (10) are similar for these two trends.

 

   
 
   
 

 

 

 

 

 

 

 

 

 

 

 

 

0.5 l- a
h r
3
g 0.4 r -
in
a r
.3, Ax = Y0 ' A*exp(-I/Io)
:5 0.3 — -
3 yo 0.54 £0.04
a A 0.39 £0.03
0.2 _ 10 28.4 i6.7 ,
0.2:::::=:<:;:~:e
I-
O
t:
a
in
I-
.9.
.§ "'1 * Ai=yo-A*exp(-I/Io> -
'5
8 y, 0.18 i001
E" A 0.14 i001
I() 20.9 :l:1.8
0.0 l . L g l . l A 1 A l A I A
0 10 20 30 40 50 60 70

Laser Intensity (1012 W/cmz)

Figure 3.11. Dependence of the saturation (As) and perpendicular (A 1)
parameters on the laser intensity. Both parameters show an exponential trend
with similar values for the saturation intensity, lo.

76

A unifying equation for modeling the rotational anisotropy can be obtained if we
assume that the ratio of the probabilities for probing the two pathways (Be—Ae—X and

fe—Be—X) is fixed and corresponds to A A”; as discussed earlier. Under this assumption, we

obtain the following expression for the rotational anisotropy,

... T 2
rAS,AA/B(jat)=r0(j9t)_AS (70(j,1)+AA/Be (H ) ) (3-11)

where the saturation reduces the observed B-X anisotropy and, at the same time,
increases the ability to see the A-X transition. Using Equation (3.11) in place of Equation
(3.9) (or Equation (3.10)) in the fitting procedure described above, we have fit the data by
varying AS, Tfig, and the background and keeping the value of A M; equal to 0.49. We have
found satisfactory agreement between T,» and TRT with 1.7 — 16 % deviation (see Table
IV).

Table N. Rotational temperature fits (T5,) at different pump laser intensities using
Equation (3.11) which includes the saturation parameter (As) and the fixed AM;
parameter (which is 0.49). Parentheses around a percentage indicate that the
calculated temperature is below the actual temperature.

 

 

 

 

 

 

 

 

_S_aJ_uration + Perpendicular Parameter
(AM; = 0.490)
Intensity

(1 012W/cm2) Aa Tm (K) % Error
1.4 0.13 346 1:20 16%
8.5 0.26 265 :l: 10 (11%)
19 0.30 321 :t 11 8.1%
37 0.38 302 :1: 12 1.7%
62 0.43 290 :t 16 (2.4%)

 

 

 

 

 

77

 

 

l'lrrafasr
rotational charm
ltiibl} obtain q
from exrerimcm,
for Ullldlret‘llnm
100510 prom];
gown" St‘mm
Mines contim
50KB 01'1th m:
for midliona] anis
Wimp} earned

ci'nfbmnds 10 a r:

3.5. CONCLUSIONS

Ultrafast rotational anisotropy measurements are important for determining the
rotational characteristics of non-reactive and reactive systems. Therefore, being able to
reliably obtain quantitative rotational temperatures or rotational population distributions
from experimental data is essential. First, our results quantitatively reproduce the theory
for unidirectional signal detection (X-direction). The equations in Table I provide the
tools to properly analyze URA measurements given a particular experimental detection
geometry. Second, as the availability of femtosecond laser systems with very high peak
intensities continues to increase, it is important to understand how strong fields affect
some of these measurements. Here we explore the effect of high pump laser intensities
for rotational anisotropy measurements and give a formulation that includes the loss of
anisotropy caused by saturation as well as an additional parameter that, in the case of 12,

corresponds to a reactive pathway.

We have shown here how experimental detection geometry, saturation efi‘ects,
and competing reactive pathways can be taken into account in order to fit rotational
anisotropy data spanning three orders of magnitude in laser intensities and obtain
accurate quantitative measurements. This modified rotational anisotropy model can be
expanded to other systems, including reactive systems, to obtain quantitative rotational

distributions and temperatures when using intense laser fields.

78

 

4. TRAI
MleNG l

ROTAT

1M1
e$311113] asp£
“ample; lhi
'lr mlficulc
hmmn.
j$303k”):

exilli‘lined in

4. TRANSIENT GRATING AND THREE-PULSE FOUR-WAVE
MIXING TECHNIQUES FOR EXTRACTING AND CONTROLLING

ROTATIONAL AND VIBRATIONAL MOLECULAR DYNAMICS

4.1 . INTRODUCTION

The four-wave mixing (F WM) technique has been described in Chapter 1. The
essential aspect of this technique is that two fields interact to create a transient grating in
a sample; this transient grating decays and reforms based on the molecular dynamics of
the molecules in the sample. When a third field scatters off that grating, information
about the molecular dynamics of the sample can be obtained. In all our experiments
described here, we collect signal defined by the wave vector k5 = k, — k1, + kC as

explained in Chapter 1.

The time resolution of four-wave mixing measurements depends on two different
parameters. The first is related to the time duration of the laser pulses interrogating the
sample. The second is related to the coherence time of the laser pulses, i. e. the Fourier
transform of the spectral width of the laser pulse.78 The observation of femtosecond
vibrational dynamics can be achieved with nanosecond laser pulses provided they have a
broad spectral bandwidth.159 Experiments using nanosecond sources obtain purely the
information that is contained in the steady-state absorption spectrum, which is Fourier
transformed and convolved by the coherence length of the light source. The easy

availability of broad-band light sources with extremely short coherence lengths make

79

 

those kinds
spectroscopy.
experiments 0
interrogation o
lariotts depha
morements.
lire-ah- Obscrt'c
chenic fields at
"131156 of the r
Chili’s can be u
“lit the 53mph
nation states.

gated \lilh ultra

Many P05

mm“ The si.

me l’eqm lg :

those kinds of measurements, which are similar to Fourier transform infrared
spectroscopy, very attractive. ‘59 However, it is worth noting the advantages of
experiments obtained with femto second pulses. For these experiments, the laser
interrogation of the sample is complete within a time-scale that is short compared to
various dephasing mechanisms. Therefore, by using femtosecond pulses in FWM
measurements, (a) the onset of electronic vibrational and rotational dephasing can be
directly observed,81 (b) there is a possibility to control the temporal ordering of the three
electric fields and their relative phases,'°3a'04"°7 (c) four-wave mixing is easily achieved
because of the nonlinear dependence of these techniques on laser intensity, ((1) frequency
chirps can be used to control the wave packet that is launched by each laser interaction
with the sample,105’106 and (e) for chemical reactions one is able to interrogate the
transition states, 1'. e. observe as the reactants become products. The additional sensitivity

gained with ultrashort pulses makes off-resonant measurements easily accessible.

Many possible FWM signals can be formed in the forward box configuration;
however, each one has a unique wave vector determined by the phase-matching
geometry. The signal detected at the upper right corner of the box is identified by the
wave vector k5 = ka - k), + k, and is the one we collect. (See Figure 1.2 and Figure 2.4.)
For most of our measurements, two of the fields (Ea and Eb) are coincident in time (Tab =
0). When fields E, and E, precede EC, we refer to that as a positive time delay; this is also
known as a transient grating (TG) measurement. When field E, arrives before E, and Eb,
that is referred to as negative time delay; this is also known as a reverse transient grating
(RTG) measurement. A TG measurement can be taken for each of our samples, whether

the excitation is resonant or off-resonant. A RTG measurement can only be taken with

80

resonant exci
excitation of
orerlapred it
ital lime de
neasuremertt
M58 Sequett
5; precedes ,
that the desig
Oi mgalit'e 1i
@Uitakm T.
if firs: time
lime dab} (r
Eimtedes E
also of ch,
“filled 01h?

i" .
Modes,

resonant excitation of a sample. For some of the measurements involving the resonant
excitation of iodine, in addition to the TG and RTG measurements where E0 and E1, are
overlapped in time, we also make measurements with E, and Eb being separated by a
fixed time delay (ragJ ¢ 0) while B, is scanned in time (1). Furthermore with these resonant
measurements on iodine with rag, i 0, we have explored two different pulse sequences. In
Pulse Sequence I (PS-I), fields E, and Eb precede EC; in Pulse Sequence II (PS-II), field
E, precedes E1, and Ea. (See Figure 4.1 for schematics of the pulse sequences.) Notice
that the designations of PS-I and PS-H when Tab at 0 are similar to the notation of positive
or negative time delays when rag, = O. In the forward box geometry, fields E, and E, are
equivalent. This implies that the only difference between PS-I and PS-H is that for PS-I
the first time delay (Tab) is fixed and the second one (I) is variable. For PS-II, the first
time delay (I) is variable and the second one (Tab) is fixed. Also notice that in PS-I, field
E, precedes Eb for Tab > 0; in PS-II, field Eb precedes E, for Tab > 0. Here we explore the
effect of changing Tab on the molecular dynamics observed in the sample. We have

explored other pulse sequences in resonant three-pulse FWM measurements; results fiom

these studies are published elsewhere.'°3,106’107,'09,160

81

 

 

Powell. 93,1

We delay Dem
W EC. PS-l‘.

:

Pulse Sequence 1
a b 6 Signal
1., = t2- t,
’é

¢/ 1 = t3- t,
M 53%”.--
Pulse Sequence [1

it ll

7 a time

   
   

a Signal

r=g-g

  

Ta = t3- t2

  

Figure 4.1. PS—l shown at the top for the three-pulse FWM process. Tab is a fixed
time delay between fields E, and E, and r is a variable time delay between fields
E, and EC. PS-ll shown at the bottom for the three-pulse FWM process. I is a
variable time delay between fields EC and E, and tab is a fixed time delay
between fields E, and E...

Here we report a systematic study of femtosecond time-resolved transient-grating

experiments on atomic, diatomic, triatomic and larger molecular systems. Our goal is to

demonstrate the various types of molecular dynamics accessible and to provide a simple

formalism to extract quantitative information from T6 and related FWM nonlinear

optical signals. A theoretical fiamework is included that takes into account the different

third-order nonlinear processes that contribute to the observed signals. From this analysis

formulae are derived to analyze the Vibrational and rotational dynamics observed in the

experimental transients for both resonant and off-resonant excitation. We also

demonstrate on molecular iodine that pulse sequences in resonant three-pulse FWM can

be designed to control the transition probability between two electronic states of a

82

 

The

inthe literal

Ill. Gen

like lnciden:

4.2. THEORY

Theoretical treatments of time-dependent four-wave mixing signals are abundant

in the 1iterature.78’15' Here, a review of the results relevant to this study will be presented.

4.2.1. General Considerations

The FWM signal intensity, 1rwm( 1), resulting from the interaction between the

three incident laser pulses and the sample medium, can be evaluated using78s‘5'9‘62

[FWM(r)= ?IP(3)(kS,t)|2dt (4.1)

—00

where P‘3)(k,,t) represents the time-dependent third-order polarization for a given phase-
matching condition. This equation is applicable for homodyne detection. For TG
measurements with k,= k,,-- k), + kc, P‘3)(k,,t) can be expressed as"8

P13) (k5,!) = 452 (t) [[510 —z ')|2 1‘” (t ')dt' (4.2)
0

where 1(3)“) is the third-order susceptibility associated with the molecular system. In
order to determine what type of information should be included in the molecular
susceptibility term, it is important to first analyze the different interactions that are
possible between the laser fields and the sample.

Calculation of the FWM signal polarization P‘3)(k,,t) and associated susceptibility

tensor requires knowledge of the third-order density operator p‘3)(t).78"6‘ The explicit

83

form of d l.
nitration tha‘
trident elet
denied ties
the density 1
90m elect
919W State
5910C field
“CM (6) st
lllturred. ll
{5% Equatio
's’l'lk’ral an 0

“£th

form of p‘3)(t) follows from a perturbative solution of the quantum mechanical Liouville
equation that describes the temporal evolution of the system under the influence of the
incident electromagnetic fields and the intrinsic relaxation processes”,161 A more
detailed description of this density matrix theory is published elsewhere. 1039163 Initially,
the density matrix, pm), corresponds to the population of the vibrational levels in the
ground electronic state (upper diagonal block). In our calculation, we assume that the
ground state vibrational levels are equally populated. After the first interaction with the
electric field, the density matrix evolves into a coherence between the ground (g) and
excited (e) states where all the diagonal terms are zero and no net population transfer has
occurred. The interaction with a second electric field completes the population transfer
(see Equation (1.11)) without electronic coherence between the |g> and |e> states. In
general, an odd-number of interactions with the electric fields will produce a coherence,
which is also a time-dependent polarization of the molecules. An even number of
interactions will produce a population state that is characterized by the population of the
vibrational levels in each electronic state (the diagonal terms in the diagonal blocks) and
the ro-vibrational coherence within each electronic state (the off-diagonal terms in the
diagonal blocks). The changes in the density nuttrix after each interaction with an electric
field involve difierent processes that can be followed using double-sided Feynman
diagrams”,161 For further information about these diagrams and their applications to
four-wave mixing processes, the reader is referred to References 78,86,161,164 and 103.
Simpler diagrams that alternate up and down transitions between two states fail to

describe differences between populations and coherences.

84

 

‘ 2.1 Feynmal

First We ‘
hel system ll“
of th denslI) n
electric fieldfi. ll
1mg; ion the r
lotom to the 101
male. Those 0
naming left cor
mnestmndence t
eoniugate prefacl
D«‘t-Ier of the di
lotion mission.
tnloth Thus. it
all one side (

ostrption or en

4.2.2. Feynman Diagrams

First we consider the case in which the three laser fields are resonant with a two-
level system. The diagrams shown in Figure 4.2 are representations of the time evolution
of the density matrix operator p and its transformations by the interaction with the
electric fields. The operator is denoted by the two parallel arrows which correspond to the
bra <gl (on the right) and the ket |g> (on the left) of the matrix. Time increases from the
bottom to the top. Wavy arrows represent the interaction of each of the fields E,- with the
sample. Those pointing towards the right correspond to E,- exp(-icqt + ikj-r), while those
pointing lefi correspond to E; exp(ia5-t - ikj-r). Because the bra and ket are in dual
correspondence to each other — a complex prefactor on a ket appears as the complex
conjugate prefactor on the corresponding bra. ‘65 Therefore, arrows pointing towards the
center of the diagram indicate photon absorption while those pointing away indicate
photon emission. An electric field interaction occurs on either the bra or the ket, but not
on both. Thus, when only one electric field interacts with the system, a change occurs on
only one side of the Feynman diagram (bra or ket) giving rise to a polarization;
absorption or emission of a photon requires two electric field interactions. Detection of
signal from a particular phase-matching configuration, for example k, = k, — k1, + kc as
shown in Figure 1.2, determines the sign of the individual wave-vectors. Therefore, for
all diagrams fields E, and EC must be represented with right pointing arrows, +k-, and

field Eb with a left pointing arrow, -k,-.

85

I

put .mx

“Fr-11.

Figure 4.2. Double-sided Feynman diagrams corresponding to four-wave mixing
processes observed for phase-matching condition k. = k. - kn + kc. In all cases
the signal, emission from the ket side, has been omitted for clarity. Based on the
experimental constraints of our measurements, beams E, and E, are overlapped
in time and beam E, can be delayed or advanced with respect to these beams.
The label for each diagram, for example abg, indicates the two beams that form
the transient grating and the state in which the population is formed. The
molecular response function (R1, R2, R3, or R4) corresponding to each Feynman
diagram is also noted.78-87 (a) For positive time delays, E3 and E, form the
grating and cause a transformation of plolgg into pm“ or p(2)gg. When Ec scatters
from this grating, at positive time, ground state dynamics are obtained. (b) Here
[5.3 and E, form the grating and cause a transformation of pm)“, into pm”. or pme-e.
When Ec scatters from this grating, at positive time, excited state dynamics are
obtained. (c) These diagrams contain beam Ec between fields E, and Eb which
are overlapped in time. Therefore signal is only observed only for times within the
laser pulse duration. (d) For these diagrams Ec arrives first and, if resonant,
forms a coherence between the ground and excited states of the form pm”. The
coherence is allowed to evolve for a time t. The coherence dynamics are probed
by the arrival of field Eb, which forms the grating, and field E, that scatters from
the grating.

F.
’90 .
e 4“

86

Positive Time Delay (a) Ground and (b) Excited State Dynamics
R, R3 R; R2

Omar; pl” 63' pme's‘
In“) (at la’) <91 l°'> <9"

,, Trix. l .1fo
:xiixii xx

b‘>

t2 [2

lo) (:el <°l
t, 5.. ’1

 

 

 

la) (01 E"
pe..
:b: b:: :be b8:
(c) Time zero contribution only
R2 R3
p(3)°,8, p‘sh'g'
to') <91 ln') (at
A A A
t, Fri, t,
E. if"
I
E. 2 E.
'JJ" ‘2 <°' <o|
Be ‘t ‘1
EH“ like
In) pang“ 19) pm)” <91
bee DC:
((1) Negative Time Delay - Coherence Dynamics
R, R,
pmis pmcs'
la? (9| In) <01
5,, ’3 E;
E (at

Figure 4.2

87

 

or let sit
either of
alternatit
loin-eigl

ground 51

the Obser

Olll [DOSE

The first field interaction may involve any one of the three fields acting on the bra
or ket side. This results in six possible alternatives. The second interaction may involve
either of the two remaining fields acting on the bra or ket side, giving a total of 6 x 4
alternatives. Firmlly the remaining field can act on the bra or ket side giving a total of
forty-eight possible diagrams, representing the transformation of the initially incoherent

ground state medium p‘o’ into p‘3)(t) for this phase-matching condition.73,“5'9I64

For resonant or near-resonant excitation, not all forty-eight diagrams contribute to
the observed signal. In fact the rotating wave approximation (RWA) can be used to rule
out most of these combinations.“S6 First we define the transition frequency (2,3 =

E, —Eg

h = 423, as the energy difference between the ground and the excited states;

therefore, near-resonant excitation has a; z (2,8 where a; is the photon frequency. When

field E, acts on the ket at time t], the corresponding contribution to the polarizability is
proportional to (el p - Ea I g)/(Qeg —a)a). When the denominator is small, in this case near
zero, the contribution is large. However, if E, acts on the bra at time (1, the corresponding

denominator is ((2 ma) = (-—Qeg —a)a), about twice the optical fi'equency.

ge _
Contributions fiom these anti-rotating wave processes are very small and can be
neglected for weak near-resonant fields. One can identify eight of the forty-eight
diagrams in which all three field interactions satisfy the RWA and therefore these eight
diagrams have a significant contribution to the polarizability. This selection process has

been documented in the literature.73"649167

88

sites. i
are pain
'he lost

tamed

it}, to
resonant
3WD let'e
depicts t
Willem

 

The diagrams shown in Figure 4.2 assume near-resonant excitation between two
states, labeled here g and e. Some of the differences expected for non-resonant excitation
are pointed out later in the discussion. Time ordering of each field is given by the relative
vertical position of the wavy arrows and by the time labels t), t; and (3. In all eight cases
the last step, corresponding to emission of the signal field from the ket side, has been
omitted to simplify these diagrams. The transformation of p(°)= |g> <gl, designated as
pm)“, following each laser-sample interaction is labeled on the bra or the ket side. For
resonant excitation it is important to illustrate how the susceptibility tensor for an isolated

two level system depends on the laser’s frequency. The first diagram (abs) in Figure 4.2

depicts the transformtion p‘mgg 5“ (I) ___—9pm,, E_b__)(’) pmgg E (t) pmevg. The
nonlinear susceptibility associated with this particular interaction between the three laser

fields can be expressed as

(3) ocN 2 pm) (glp-Efle'Xe'Iu-Ec wlg'><g'lu°Eb.le>(el”'Edlg)o (4.3)

I
“be gg'.ee' 33 (Deg -—a)a )(Qgg waei+waQg —a)a+a),, ~06)

Notice that once this expression for the susceptibility is introduced in Equations (4.1) and
(4.2), the overall FWM signal depends on the square of the number density of the sample
N and the eighth power of the transition dipole u. Similar equations can be written for the
nonlinear susceptibilities associated with the other Feynman diagrams. However, these
formulae, which are usually used for frequency-resolved techniques, are not used to
derive the formalism used to simulate our time-resolved experiments. Frequency-resolved

DFWM techniques have been proven to yield very high-resolution spectra, especially for

89

 

D‘Jpp.

erirm

On {In

mg Fe)

Stile d}

Doppler-free configurations, taking advantage of the very large resonant

enhancement.“168

The eight diagrams have been divided into four groups. The first group, shown in
Figure 4.2a, represents the four-wave mixing process allowing the observation of ground
state population dynamics. The diagonal terms of the density matrix p3,, and pcc are
associated with populations while the off-diagonal terms represent coherences. The two
diagrams, labeled ab: and bag, indicate transient grating formation in the ground state
palm) or pmggfl) by fields E, and E, with positive time delay (or PS-I). Field E, induces
a polarization after a time delay 1, indicated by a break in the time arrows, and the signal
beam emitted by this polarization reveals ground state dynamics information. Two
different diagrams describe this observation because the sequence between fields E, and
Eb is not defined for Tab = 0. When fields E, and E, are separated in time, the sequence of
the pulses better defines each process. For example, in Figure 4.23, field E, precedes field
E, in the diagram shown on the left side, while field Eb precedes field E, in the diagram

on the right side. Thus, when Tab is greater than the pulse duration of the laser, only the

abg Feynman diagram applies.

The second group of diagrams in Figure 4.2b depicts the observation of excited
state dynamics at positive time delays (or PS-I). This observation requires that the excited
State is long-lived compared to the pulse width of the laser and that the laser pulses are

near-resonant with the electronic transitions. For the two diagrams, labeled ab. and ba.,

transient grating formation in the excited state p‘2)¢¢(t) or p054!) by Ea and Eb. This time

90

 

the si

exert

C0313

the signal beam resulting from the polarization induced by EC after a time delay 1 reveals
excited state dynamics. Again both diagrams contribute for rub = 0, but only abc
contributes to the signal for Ta], is larger than the pulse duration. The top of Figure 4.1

shows the pulse sequence that gives the TG signals arising fiom the diagrams shown in

Figure 4.2a and b.

The third group of diagrams in Figure 4.2c contains the two sequences in which
EC, the field that can be physically delayed in time in our experimental setup, interacts
with the system after field E, but before field Ea. The signal arising from these
interactions, labeled be. and bc,, is therefore limited to near-zero time delays when Tab =
O (with pulse sequence I). These diagrams show the nonlinear processes that are
responsible for generating signal in a different pulse sequence; when field E, is scanned
in time and arrives before fields E, and EC we measure stimulated photon echo

dynamicsslmt107

The fourth group of diagrams in Figure 4.2d corresponds to observation of signal
for negative time delays (or PS-II), i.e. when field E, precedes the other two fields (see
bottom of Figure 4.1 corresponding to the RTG pulse sequence). The first step in these
two diagrams is the formation of a coherence (off-diagonal term in the density matrix)
pmqa) between the ground and excited states. After a time delay 7 a transient grating
population is formed by field E1, in the ground p‘2)gag(t) or excited pmdo) states. The
signal is created when E. induces a polarization after time 22,], following the formation of

the transient grating. Notice that diagrams cbg and cbe are identical to abg and ab, except

91

 

grou

eoht

lino

Ch

'0

Ci.

for the labeling of fields E, and EC and thus the relative time ordering of 1. Unlike TG
(PS-I) measurements where the signal reveals the population dynamics in the ground or
excited states, RTG (PS-II) measurements reveal an electronic coherence between the
ground and excited states. Note tlmt both cbg and cbc diagrams apply for Tab 2 O. The

coherence signal decays according to the electronic dephasing time between the states
involved, 1'. e. a T2 type measurement. In most cases T2 is very different than T,, the

lifetime of the excited state.“

The observation of coherence dynamics for negative time delays (or PS-II) is not
common to all FWM experiments because it depends on the phase-matching
configuration, on the polarization of the three incident fields, and on the existence of a
resonant or near-resonant state. For experimental arrangements where all three incident
beams are in one plane, the direction of the signal wave vector for positive and negative
time delays, determined by the phase-matching geometry, may be different. '69 The
detection geometry can be used to discriminate a particular phase-matching geometry. In
the forward box arrangements, negative time delay signal is possible (see Figure 1.2) for
the pulse sequence discussed here and for other sequences.68’70 When the three incident
fields have the same polarization, as in the near-resonant experiment discussed here, the
negative time delay signal can be observed. For cases involving non-resonant excitation,
excitation of repulsive states, or condensed-phase measurements, a very short coherence
lifetime (~10'l4 s) is expected. Therefore, little or no dynamics are observed for time
delays exceeding the laser pulse duration for these systems. Additional discussion on the

negative time delay signals can be found in References 85,170 and 171.

92

 

 

A different diagram classification than the one discussed so far is possible. Notice
that for diagrams bag, bac, be. and beg, the first step involves formation of a coherence
p" 2,. The time evolution of the coherence involves dephasing processes. The dephasing
dynamics can be reversed by interaction with the third electric field forming p(3)¢'g'. This

reversal, analogous to the n/2 pulses in nuclear magnetic resonance (NMR), leads to the
formtion of an echo. Photon echo measurements are extremely usefill in the
measurement of coherence life times and have been used primarily in the study of
relaxation dynamics in condensed phases. For reviews on these studies see References
172 and 173. These types of measurements require a controlled arrival of field Eb with
respect to fields E, and EC. Experiments of this kind involving different pulse sequences

have been carried out in our group recently and will be published elsewhere. 107,109

4.2.3. Off-Resonant Excitation

Far from resonance both RWA (Deg —w,-) and anti-RWA (Qeg +(oj) terms
become comparable making the selection of the active Feynman diagrams more difficult.
For the particular arrangement discussed here with fields E, and E1, overlapped in time,
diagrams ab,; and bag in Figure 4.2 illustrate the nonlinear processes responsible for the
off-resonant transients. The general principle hinges on impulsive excitation of rotational
and vibrational states in the ground state. The polarizability response function of isolated

molecules for off-resonant excitation can be expressed as a combination of correlation

fimctions of the effective polarizability of the molecule ('2' ,‘74

93

that ;
Thtpol

nnhres

will},

{hilt it“

[(3) (t) = Zaa (t) = <% [6 (t),&(0)]> (4.4)

where 1a,, is the linear response function associated with the molecular polarizability.
The polarizability tensor can be expressed by expanding each element in a Taylor series

with respect to the normal coordinates of vibration q,- as

dzéo'i'

 

3n-50r3n-6 668 I 3n—50r3n—6 525
qi
0

_ _ .- . (4.5)
64.- 2 ,-,,. 646ml," 4,.

i=1
The first term corresponds to the equilibrium polarizability and can be separated into its

isotropic and anisotropic contributions by using the definitions a s %(ql + 2a,) and
,6 -_- (an —a,). Here an and a), are the parallel and perpendicular components of the

polarizability with respect to the principal symmetry axis of the molecule. This separation
leads to two contributions. The equilibrium isotropic term, having no orientation or
vibrational dependence, does not contribute to the observed dynamics except for a time-
zero instantaneous response (vide infia). The second contribution, corresponding to the
equilibrium anisotropic polarizability, depends on the molecular orientation and is
therefore responsible for the rotational component which has been expressed as

41w2 6

2,li (,) = -WE(P2 [cos0(t)]), (4.6)

where N denotes sample density, T is the sample temperature, and k3 is the Boltzmann
constant.‘74"76 For spherically symmetric molecules having ,6 = q, — at = 0, the pure
orientatioml contribution vanishes. Note that the derivative arises from the fact that

contributions to the time-dependent polarizability are purely irmlginary for off-resonant

94

excitat

3.
is
m

CUIMW

.11

.A\

..‘A K

 

excitation (purely real in the frequency domain). The above expression is relevant for the
case discussed here where all beams are linearly polarized in the same direction.
Different polarization arrangements are discussed elsewhere.34"74-J75 By expressing the
ensemble average and the second-order Legendre polynomial as done by Zewail and

coworkers,2"32933 the last term in Equation (4.6) can be evaluated using
ZP(J)1|:3cos2 th —1]
1(P2 [c030(t)])=_4_ J 2
dt dt 2 P (J)

J

3ZPU) stinZth
J

2 210(1)

 

(4.7)

 

The effects on the rotational recurrences caused by nuclear spin and centrifugal distortion

are discussed in the Results section.

The second term in Equation (4.5), corresponding to the derivative of the
polarizability in terms of the vibrational coordinates, can be expanded in terms of

isotropic and anisotropic contributions. This separation yields‘74

[1'30 (1) = Z 5t],-

i=1

3n-50r3n—6 [ 60: T <‘;;[qi (t), qi (0)]> and (4.8a)

O

lam-so (I) = (Pz [6089(1)]l3n-sgn—6ng]: (fir: (1M,- (0)]> (4.8b)

95

 

1551

hen

where the first-order expansion terms are given by [aa/aq,]0 and [66/6q,]0 at the

equilibrium internuclear separation. Both of these expressions give the ro-vibrational
dependence of the polarizability. The difl‘erent isotropic and anisotropic contributions for
each normal mode can be sorted by experiments that are sensitive to the polarization of
the signal beam for different incoming polarizations.5373,34,164,177"183 The focus of our
study is on the molecular dynamics; no effort has been made to sort the isotropic and

anisotropic components as shown in Equations (4.8a) and (4.8b).

Because the correlation function for a coherent superposition of vibrational modes
is sinusoidal in time, the vibrational contribution 1" (t) of Equations (4.8a) and (4.8b) can

be modeled as a summation of sine functions,42

3n—50r3n—6

[(1): 2 B,- sin (w,t+¢,) (4.9)
i=1

where B,- and (13,. are time independent constants for the 1‘“ Vibrational mode and (a is the
fundamental frequency of the 1‘” normal mode. Notice that in Equation (4.9) we have
omitted the orientational term due to the anisotropic susceptibility in Equation (4.8b). We
have also omitted the anhannonic contributions that result from the higher-order terms in
Equation (4.5). For the different samples studied here, we found this level of
approximation to be satisfactory. Additional terms can be introduced when the harmonic
approximation is not suflicient to model the experimental data. The amplitude and phase
of each vibrational motion in the ground or excited state are left as fitting parameters to
be determined during the analysis of the experimental data. Thus by combining the

rotational and vibrational contributions, the overall expression for IMO) becomes

96

 

El

m“.

ailing
I'll), l
“idle l

311)an l

\

3n_50r3n_6 ZPU) stin2th
1 :: B. . .t . 2 J
Zaa() g1 .sm(w. +¢.)+fl 2W)
J

 

(4.10)

Equation (4.10) reflects a separation of rotational and vibrational contributions to the
anisotropy (at least to first order approximation), a fact that has long been recognized in
Raman spectroscopy.‘349'35 For time-resolved FWM experiments with homodyne
detection, Equation (4.10) leads to cross terms between the rotational and Vlbrational
contributions as will be shown later. Heterodyne detection would give a signal
proportional to P‘3)(k,,t) rather than its square, which would be flee from cross-terms of
the kind referred to above”,176 It is interesting to note that for time-resolved pump-probe
experiments the rotational and Vibrational contributions are multiplied.2"32a33 The purely
rotational component of the signal is typically isolated by the use of the anisotropy
measurement as defined in Chapter 3. For example, Equation (3.2) indicates that the
orientation dependence multiplies the isotropic molecular dynamics.32’339123 For the time-
resolved F WM presented here, we demonstrate that this multiplication is not applicable

for the separation of isotropic and anisotropic contributions to the signal.

For polyatomics, if the polarizability varies as the atoms are displaced collectively
along a given normal coordinate, the normal mode is observable by its contribution to
[(1). For linear triatomics of the type ABA, the symmetric stretch satisfies this condition
while the antisymmetric stretch and the bend do not. The latter modes are infrared active
but are not Raman active. In general, Rarnan active modes can be observed by four-wave

mixing techniques. This point is illustrated in the result section for Hglz.

97

 

"l
1..

The vibrational selection rules for Raman transitions are determined by integrals

of the form

(013a,, Mm (4.11)

where g, g' = x, y, or 2, as: is one of the components of the polarizability, and l/ly' and
VV- refer to the vibrational wave functions in the initial and final states,
respectively.136’187 These integrals vanish unless the vibrational normal mode involved
belongs to the same representation as one or more of the six components of the
polarizability tensor of the molecule, e. g. an, axy.188 The rotational Raman selection rule
is that the molecule must be anisotropically polarizable (i.e. ,6 = all — at at 0). In addition,
for linear molecules AJ equals 0, i2 and for nonlinear molecules AJ can equal 0, :1,

£486

The observation of rotational and vibrational dynamics for off-resonant
measurements depends on the impulsive excitation of vibrational and rotational levels in
the ground state, which are overlapped by the fiequency bandwidth of the laser pulse.
When the vibrational period is shorter than the coherence time of the laser pulse or when
all molecules are not vibrating in-phase, the nonlinear response averages to zero and does
not contribute to the overall signal. The short pulses employed in this study are nearly

transform limited and lmve a pulse width of approximately 50 fs. The availability of 5 fs

98

Oi

 

.l.\

0]

laser pulses”,189 will extend these types of studies by opening the possibility for

observing the real-time dynamics of all but C-H, N—H and O—H chemical bonds.

Equation (4.10) gives a satisfactory expression for the susceptibility that can be
convolved by the electric fields and squared according to Equations (4.1) and (4.2) in
order to simulate the data. However, in the impulsive limit, when the laser pulse width
can be neglected in comparison to the rotational and vibrational periods, the electric field
envelopes can be treated essentially as Dirac-delta filnctions and the FWM signal

intensity simply reduces to78
2
[FWM(T)=|1,, (T)| . (4.12)

In FWM experiments, when all three fields are present near time zero, a condition
of temporal degeneracy arises. During this time multiple nonlinear processes occur. The
observed signal enhancement near time zero, arising from the coherent interaction of the
three light fields with the medium, has been called the coherence coupling artifact or the
coherence spike.52’73"‘x’°"92 The coherent spike is typically symmetric about time zero
and in many cases can be removed by the antisymmetrization technique described by
Eisenthal, Fleming and their coworkers. 1929193 In the absence of chirp, the coherent spike
can be described as the square of the electric field autocorrelation of the incident laser
pulses. This is because the major contribution comes fi'om the equilibrium isotropic
polarizability (om) which has an instantaneous response limited to when the three fields
are overlapped in time. For most femtosecond measurements this feature can be

approximated by a Gaussian or hyperbolic-secant-squared fimction. Thus, by considering

99

Whe

of ti

PTO]

.4

X113,
0h;

"tn,

the coherent spike as a Gaussian function with amplitude A primarily depending on on)

and using Equations (4. 10) and (4.12), the FWM signal intensity can be modeled as

, 2
2 2 3n—50r3n-6 ZP(J) (”J stsz'
[FWM (r): Ae-T [A + Z B,sin(a),-r+¢,-)+Cfi2 J

i=1 EPU) l

 

 

(4.13)

where A corresponds to the filll-width at half-maximum (FWHM) of the coherence time

of the laser pulses, i. e. the pulse width divided by 2m (for Gaussian pulses) and C is a
proportionality constant.I94 For most cases convolution by the temporal response of the
laser system can be carried out easily when necessary. This formula is convenient for the
analysis of off-resonance TG data Note that we have not included the inverse-squared

dependence of the off-resonance signal on temperature.

This formulation allows the quantitative interpretation of the vibrational and
rotational characteristics of the TG off-resonant signals obtained. Atomic species exhibit
signals exclusively at time zero because of their instantaneous polarizability. Diatomics
and polyatomics exhibit, for positive time delays, ground state rotatiorml (as long as
,6 at 0) and vibrational dynamics. The vibrational modes must be Raman active and have a
vibrational period that is longer than the coherence time of the laser system to be
observed. In the results and discussion section, experimental data is presented to illustrate
the difi‘erent cases discussed. Of particular interest is the experimental observation of the

cross terms that arise upon squaring the sum of rotational and vibrational contributions to

100

 

0i

3111

4.2

the signal according to Equation (4.13). As we will demonstrate later, the off-resonance
F WM transients show rotational recurrence features that are quite different fiom those
observed by laser induced fluorescence (LIF).2‘v-"2v33a‘20~195 Most of the differences can
be explained in terms of the modulus square and the time derivative in Equations (4.1)

and (4.6).

4.2.4. Resonant Excitation

We now turn our attention to the types of molecular dynamics that are observed in
ground and excited states and how they are manifested in the induced molecular
polarization with resonant FWM. From the discussion in Section 4.2.2 (Feynman
diagrams), we know to expect ground and excited state signal at both positive time delays
(PS-I) and negative time delays (PS-II). For resonant TG experiments (or when using PS-
I) both ground state and excited state wave packets are formed. The rotational dynamics
are given by the time-dependent evolution of the population excited at t = 0. The
molecular orientations are averaged starting with the usual classical expression based on
the second Legendre polynomial P2 [cos 6(t)] where at) is the angle between the
molecular axis at time t and that at time zero. '24 This evolution has been extensively
studied in the time domain for pump-probe time-resolved gas-phase studies by Zewail’s
research group.2"32,33 A simple semiclassical expression can be used for the quantitative

study of the orientational dependent susceptibility and is given by

101

 

 

tiller

each]

Emmi

Equity,
r,

trefc

ZP(J) ;(3cosszt—1) ZP(J) 21i(1+30082a),,t)
_ J

1")“ gm) ‘ gm)

 

 

(4.14)

where P(J) represents the distribution of rotational levels for the molecules being probed

and the rotational frequency (a) is given by 27r[2Bc(J +1)] for AJ = i1 and
27r[4Bc(J + %)] for A] = :2 transitions where B is the rotational constant of the

molecule.

The vibrational dymmics can be easily modeled by a sum of cosine fimctions
each representing the frequency difference between adjacent vibrational levels of the

ground or excited states.42 The dependence of the susceptibility on vibrational motion is

3n—50r3n—6
2'" (t) = 2 B,- cos(a),-t+¢,-). (4.15)
i=1

Anharrnonicity of each vibrational mode can be included by explicitly adding the
fi'equency of all overtones that are populated in the excitation process. Note that the

observation of real-time vibrations hinges on the frequency bandwidth of the laser pulses.

In the limit of very short laser pulses, the resonant FWM signal is equal to the
square of the sum of the different components of the susceptibility (vide supra).

Therefore, the third-order resonant TG signal is of the form

102

 

«t
LU,

l
2 2 3n_50r3n_6 ZPU) a(l+3cos2a),,r)
Ae'r M + Z B,cos(a),-z'+(z),-)+C,B2 J

i=1 §2P(J)

 

I Resonant (T) =

 

 

(4.16)

where A is the amplitude of the time-zero feature that is caused by a contribution from all
eight diagrams in Figure 4.2. The second and third terms correspond to vibrational and
rotatioml contributions to the signal. Note that both ground and excited states have to be

taken into account for the resonant TG measurements.

For RTG measurements (or when using PS-II), the dynamics probed involve a
coherence between the ground and excited states as discussed earlier. However, based on
the Condon approximation,78 applicable for resonance excitation only, one can
demonstrate that the signal fiom RTG measurements tracks primarily the excited state.
For reverse transient gratings, the signals can be modeled by Equation (4.16) given for
TG measurements. The contribution for the excited state is expected to be about an order
of magnitude greater than that of the ground state. An additional term needs to be added
to account for the electronic dephasing time T2 which is long in the gas phase (10"2-10‘9

s) and very short in condensed phases (10"5-10’l3 s).

103

 

4.2.

(hm
the

folk

lari

00H

excl
“51‘.

pied

4.2.5. Controlling Observation of Molecular Dynamics in Iodine

For the resonant excitation of iodine, we used two different pulse sequences PS-I
and PS-II (see Figure 4.1) to investigate the differences in the observed molecular
dynamics when fields E, and E, are separated in time. We continue to detect signal in the
phase-matching direction k, = k, — k1, + k. For PS-I (fixed time delay between E, and Eb
followed by E, at a variable time delay), when tag, > 0, only nonlinear processes shown in
diagrams abe and abg in Figure 4.2 are possible. When rag, > 0 for PS-II (E, arriving at a
variable time delay before Eb which is followed by E, at a fixed time delay), only
nonlinear processes represented in diagrams cbc and cbg in Figure 4.2 are possible. Our
goal is to find the proper selection of Tab tlmt would yield signal predominately from the
excited state (i.e. ab, or ch.) or from the ground state (i. e. ab‘ or cbg). We also explore
which pulse sequence allows more control over obtaining molecular dynamics

predominately fiom one state.

A more complete description of the density matrix theory that describes the
control of the molecular dynamics can be found in Reference 103. The density matrix
elements after two electric field interactions contain a dependence on rag, and this
parameter can be used to control the transition probability from the ground to the excited
state. 103,105,106 After the second pulse is applied, the population transfer between the

ground and excited states is given by

2 pg) —2 pg) cc cos (987%9)cos(-a-)—gzz‘lll) cos(a)rab —(ka —kb)r) (4.17)
e g

104

 

 

 

Will

rest

COT

iii

and

“h!

“‘6

where 603 and (a, are the vibrational fi'equencies of the ground and excited states,
respectively. After the third pulse is applied at time Tab + r, the signal is a sum of two
contributions — one fiom molecules that remain in the ground state after two interactions

with the electric fields,

S8 or: gzg lplzl _pglz oc(1+cos(a)erab))(l+cos(wgr)), (4.18a)

gfg

and the other from molecules in the excited state,

~(2)+

pee+ 2«(I + cos(a)grab ))(1 + cos ((0,1)) , (4.18b)

 

Seocez

::€

 

where 23(2) indicates only the terms of pm that satisfy our phase-matching condition. If

we define r, = 211/a), (and 13 = 211/0g), at a time delay rag, = re(n+‘/2), the signal for the
ground state goes to zero. When Tab = ten, the signal for the ground state reaches a
maximum. Similarly Tab = rg(n+‘/2) and Tab = z'gn correspond to minimum and maximum
signal from the excited state, respectively. Maximum control can be achieved for values
of Tab that maximize one contribution and, at the same time, minimize the other. These
values can always be found provided q ¢ at. In the Results section, we will show that
the time delay Tab can be used to discriminate among the processes that lead to the

observation of ground state or excited state dynamics.

105

 

0111’

und

I
9
£19

est
Neil

“fir

4.3. EXPERIMENTAL

For more specific details on the four-wave mixing method, see Chapter 2.
Experiments were carried out on 30-760 Torr on gas-phase samples (or neat vapors for
liquid samples) at room temperature unless otherwise noted. Three 622 nm beams were
crossed in the forward box geometry producing a signal beam at the upper right comer of
the box, identified by the wave vector k, = k, - k1, + k,, which we collected. For most of
our samples, we made off-resonant measurements. Iodine was the only sample that
underwent resonant excitation with 622 nm incident light. The three beams were either
fixed in time (Ea) or variable in time - either manually (Eb) or computer controlled (E) as
described earlier. Sweeping the time delay between field E, and the other two fields
yielded transients reflecting the temporal evolution of the dynamics. Typical transients

were obtained with 150-200 different time delays and 10-20 scans were averaged.

106

 

4,1

31 1

Carl

trivia

E.“

4.4. RESULTS AND DISCUSSION

4.4.1. Off-Resonance Excitation

4.4.1.1. Atomic Response

Transient grating data have been obtained for the atomic species argon and xenon
at 1 atm pressure. The results are presented in Figure 4.3. A single peak is observed in
each scan which can be fit by a Gaussian function with the center at zero time delay and
with a FWHM of 131 fs for Ar and 139 fs for Xe corresponding to the third-order auto
correlation of our laser system. The FWM response of these samples is only present
while the three laser pulses are temporally overlapped. At time zero, the intensity of the
F WM signal from Xe is about 14 times stronger than that from Ar. The ratio between the
linear polarizabilities of Xe and Ar is about 2.45.196"98 This ratio appears to indicate a
cubic dependence on the linear polarizability (a) for the time-zero signal. The signal
observed at time zero results from a non-resonant instantaneous polarizability. The
absence of signal away from time zero is to be expected in spherically symmetric samples

and in the absence of vibrations (see Equation (4.13)).

107

 

Signal Intensity (a. u.)

 

 

 

 

1 L i m L L I r I
-400 -200 0 200 400
Time Delay (fs)

Figure 4.3. FWM signal from xenon and argon samples at 1 atm pressure. The
data are represented by triangles for Xe and by circles for Ar. The black lines
show Gaussian fits to the data. FWM signal from Xe is 14 times greater than
from Ar because of the increase in polarizability of Xe over Ar. The width of the
Gaussian fits for Ar is 131 fs and 139 is for Xe.

4.4.1 .2. Rotational Contribution

The data in Figure 4.4 (top) show the TG signal obtained for air. The nonlinear
process responsrble for the signal are illustrated in diagrams abg and ba‘ in Figure 4.2a.

The features in the air transient are interpreted as the rotational recurrences37 of the

constituent molecules of air.”9 TG transients for pure nitrogen and for pure oxygen

molecules, each at 1 atm pressure, were also taken. The results are also presented in

Figure 4.4 (middle and bottom) for comparison. Based on the rotational constants of

nitrogen and oxygen (2.010 and 1.44566 cm'1 respectively) and the AJ = i2 selection

108

 

 

If:

rule, full recurrences are expected and are observed at 4.15 and 5.77 ps intervals
respectively. Recurrences have a period of (2 (0))"; thus, half recurrences are expected at

intervals 1/(8Bc) and firll recurrences at 1/(4Bc). The alternation in heights between the
half and full recurrences are caused by nuclear spin statistics. Whenever there is an

interchange of equivalent nuclei in a rotation, the Pauli principle defines that only certain
rotational states are populated. For molecules with a 2'; ground state, the ratio of the
population of odd J states to the population of even J states (nuclear statistics) is defined
by (I +1)/I for fermions and by I/(I +1) for bosons where I is the nuclear spin.186

Therefore, for N2 with integral spin equal to one, even J states are populated twice as

much as odd J states. The nuclear spin of O2 is zero. However, because the ground state

of O2 is 2; , only odd J states are populated; whereas, for CS2 with zero nuclear spin and

ground state 2; , only even J states are populated.

109

 

 

 

 

 

 

IllILTTFIIrTIIIIIII'lIIIITII'fiITI—ITI'TTTTl—Ir
Expenment .
Arr
Theory
A _.__.___-_ H _ __ __ _-_ __ _. _ __-_-._-__
”i N
a 2
v l
m
= I . .. ...,l, . .. ._ .1., _ . 1 '
0 l I 1
fl
I-l
- i :1 l ,.
a l. | l l
=
60
.- ..__._.___.L _. ._ ___...m _ __ A E. ._________.___. ._ _ __ __. _ _ __,_.._.___._q
(I:
l 02
t l
l l
l
lllllLlllllllll;¢llllll+l_ljllllllllllllljl

 

 

0 2 4 6 8 10 12 l4 l6
' Time Delay (ps)

Figure 4.4. Experimental (positive) and theoretical (negative) TG transients of air,
nitrogen, and oxygen. Full rotational recurrences are observed at 4.15 ps for N2
and at 5.77 ps for 02. Half recurrences are also observed. The peaks in the air
transient directly correspond to recurrences in the N2 and 02 scans. Simulated
TG signals for these samples were calculated using Equation (4.13) and are
shown as the negative mirror image of the experimental data. Note that in the
simulations, the full and half recurrences are reproduced at the same recurrence
times and with the same intensity and shape as in the experimental signal.

110

till

4' J
act.

rep

All features in the transient in Figure 4.4 can be identified and simulated using
Equation (4.13). In Figure 4.4 the simulations appear as negative reflections of the
experimental transients in the top, middle and bottom sections. As can be seen in the
figure, Equation (4. 13) predicts the rotational recurrences for N2 and O2 and the relative
peak heights and shape in each half and full recurrence accurately. Because of the square
in Equation (4.13), TG transients look very different from LIF measurements.21’32’33 By
adding the simulated transients of N2 and 02, the experimental TG signal fiom air is

reproduced.

Time-resolved TG experiments on carbon disulfide, CS2, (300 Torr) yielded
several transients showing multiple rotational recurrences, as depicted in Figure 4.5. This
molecule has been studied extensively using nonlinear techniques because of its high
degree of nonlinear polarizability.“’2°°‘207 Its x9) is 23x10” esu.203 Heritage and
coworkers observed short birefiingence at 38 and 76 ps after excitation with a picosecond
pulse and verified these positions for CS2 theoretically“,209 The data in Figure 4.5 allow
accurate molecular constants to be extracted for this molecule. As can be seen, the half
recurrence appears at 38.2 ps and the filll recurrence occurs at 76.4 ps. For 02, N2, and

CS2, it is important to include centrifilgal distortion in Equation (4.13) to reproduce the
TG signal well. In these cases, 0)) is replaced by 27w[(4B—6D)(J +-§—)—8D(J +%)3]
where D is the centrifugal distortion constant. From the positions of the first two
rotational recurrences, the rotational constant, B = 0.10912 i 0.00002 cm", and

centrifugal distortion constant, D = 6.4x10‘9 :t 0.2x10'9 cm", are obtained for CS2. The

effective rotational constant, before the centrifugal distortion effect is incorporated, is

111

 

 

82;

we;

0.10907 1 0.00002 cm'l. From the literature, the rotational constant for CS2 is 0.10910

cm'1 and the centrifugal distortion is 1.0x10'8 cm'l .2'0

WWW/WWW
CSz

 

 

L

.L/lihllhdAt-LAS

38.2 76 4 114.7 152. 9
Time Delay (ps)

 

 

Signal Intensity (a.u.)

 

[L

 

 

Figure 4.5. TG transient of carbon disulfide. The half and full rotational
recurrences are observed at 38.2 and 76.4 ps respectively. The inset shows a
magnification of the first full rotational recurrence (circles) with the simulation
calculated using Equation (4.13) (solid line). Notice that the x-axis is not
continuous; there are 30 ps gaps between each recurrence and the tick size is
822 fs for each expanded region. The decrease in signal as a function of time
delay gives the overall rotational dephasing due to inelastic collisions (see text).

The determination of highly accurate rotational constants for polyatomic species
by time-resolved coherence techniques is by now a well-known method (see for example
References 37 and 42). Because these data were obtained over hundreds of picoseconds

using a 10 inch long translation stage with a resolution of 0.2 urn/step, the equivalent

112

resolution in time delay can be estimated to be about one part per million. In principle,
this resolution translates into measurements of rotational constants with six significant
digits. To experimentally achieve this accuracy, it is important to meticulously align and
calibrate the translation stage, interferometrically or with a well-known standard, and to

take into account the index of refraction of air at the wavelength of the laser fields.

The inset in Figure 4.5 also shows a simulation of the first filll recurrence
calculated with Equation (4. 13) and the parameters obtained above. As can be seen in the
figure, Equation (4. 13) reproduces the experimental signal well, missing only in the
height of the last undulatory feature. The amplitude of the rotational recurrences in Figure
4.5 was found to decrease exponentially. A fit to the average intensity of the rotational
recurrences gives a single exponential decay corresponding to a dephasing time of 62 :l: 5
ps. By comparison, using Raman-induced polarization spectroscopy (RIPS) Chen and
coworkers obtained dephasing times of 175 ps and 154 ps for the smaller molecules 02
and N2 respectively.199 The observed decay time for CS2 implies a cross section for
rotational dephasing of 4 nm2 equivalent to a 11.3 A diameter assuming hard sphere
collisions. ‘99 This cross section appears to be very large and to depend on the rotational
angular momentum, leading to the distortion of the rotational recurrences that is not
accounted by the centrifugal term, especially those at later times in Figure 4.5. This J
dependent coherence relaxation is similar to the recent work on SF6 published by
Vasilenko et. 01.2“ A study of the inelastic collisions leading to the rotational coherence

dephasing based on measurements at different pressures seems warranted.

113

4.4.1 .3. Vibrational Contribution

The TG transient obtained for mercuric iodide, HgI2, heated to 280°C (150 Torr),
is presented in Figure 4.6. Notice that the data contain a strong and broad feature near
500 fs with 211 fs oscillations. This feature is due to the rotational and vibrational
coherence prepared in this large triatomic molecule. The Fourier transform of the
experimental transient is shown as line (b) in the inset. The top Fourier transform (a) is
obtained fi'om the original experimental transient with the time-zero feature removed. As
can be seen there are three major features in both transforms — one large peak at 19.7
i 0.1 and a set of two peaks at 148.4 1 0.2 and 167.9 i 0.2 cm". These peaks were fit
with Gaussian functions to determine the center position and uncertainty. The sloping
feature at low frequencies in the raw Fourier transform (b) results from the time-zero
coherence artifact; as can be seen in the upper Fourier transform, removing this time-zero
spike by subtraction eliminates this sloping background and more clearly shows the three
main features. A small peak (157.7 cm") between the pair of peaks in (a) seems to appear
as a result of removing the coherence artifact spike; this small peak is absent in the raw
data Fourier transform. We checked the possibility that this small peak is due to a cross
term between the first and second terms in Equation (4.13). Our simulations did not
support this argument probably because the equilibrium isotropic polarizability
contributes only during the first 150 fs of the data. For experiments using nanosecond

broad band lasers, this cross term becomes important.

114

 

 

 

 

Signal Intensity (a.u.)

 

 

 

 

 

 

 

..t i , ,
I .
i j l 0 100 200 _1 300 A
’ ' ‘ a k Frequency (cm ) .
l. l ,
“J l1 hg‘IN’~MW‘W ..
0 2 4 6 8

Time Delay (ps)

Figure 4.6. Bottom: TG transient of mercury(ll) iodide. Ground state vibrations
and rotations can clearly be seen in the transient. Inset: The Fourier transform of
the experimental transient is shown as line (b). The top Fourier transform (a)
corresponds to the experimental transient with the coherence spike subtracted.
The symmetric stretch of Hgl2 has a frequency of 158.2 cm". The cross term
resulting from Equations (4.13) causes the Fourier transform to have peaks
corresponding to 203; (19.7 :t 0.1 cm“), (a, - an (148.4 d: 0.2 cm“), and at, + at»,
(167.9 :1: 0.2 cm“) as seen. The 26), peak is probably masked by the high
frequencies from the experimental noise because of the low signal to noise ratio.

The fi'equency exactly between the latter two peaks at 158.2 :1: 0.2 cm'1
corresponds to the syrmnetric stretch, 158.4 cm'1 determined by gas-pimse Raman
spectroscopy.212 Vibrational fiequencies have also been obtained for gas-phase HgI2
using electron thion yielding 156 cm’1 for the symmetric stretch, 235 cm’1 for the
antisyrmnetric stretch, and 49 cm'1 for the bending mode.213 As can be seen in Figure 4.6,

frequencies corresponding to the antisymmetric stretch and bending are not observed;

115

these two modes are not Raman active in a linear triatomic molecule so bands for these
norrml modes should not be observed for HgI2. The results from the Fourier transform

will be discussed in more detail below.

As was shown above, Equation (4.13) can be used to simulate the rotational
dynamics for N2, 02, and CS2. The HgI2 data allows us to examine the separation of
vibrational and rotational components in TG transients where the two are summed and to
compare with the analysis of rotational anisotropy in pump-probe transients where the
two are multiplied (see theory section). Figure 4.7 shows the HgI2 experimental data
(top), a transient simulated by 1,241) having a vibrational contribution of the formula

given in Equation (4.9) added to a rotational component according to Equation (4.6),

gm (t) = z” (t) + x” (1) (middle), and a transient simulated by multiplying the

vibrational and rotational components, 1,,“ (t) = 1" (01” (t) (bottom). As can be seen

in the figure, the product of rotations and vibrations produces a series of oscillations that
is out-of-phase with the experimental data between 1.7 to 4.5 ps. However, the sum of
rotations and vibrations produces a series of oscillations that corresponds in-phase to the

vibrational oscillations of the data for all times.

116

 

 

 

 

Signal Intensity (a.u.)

 

 

 

 

‘__I\) \I. “I, ‘\” \l‘~l\’~ ____________ _
2 3 4 5
Time Delay (ps)

Figure 4.7. Top: Experimental TG transient of H912. Middle: Transient resulting
from 22,20) equal to the sum of f(t) and [(0. Bottom: Transient resulting from

22mm equal to the product of [(1‘) and {(1). Notice that the product transient
(bottom) is out-of-phase with the experimental data but the summation transient
(middle) is in-phase with the experimental data for all times (see text).

The summation of the vibrational and rotational components of the polarizability
provides the correct phase relationship in the data because of the cross term that is
obtained from the square of the sum of sine fimctions. As is seen in the bottom simulation
in Figure 4.7, the effect of the cross term is to invert the phase of the vibrations near r>
1.7 ps and to cause a doubling of the vibrational fiequency for r > 3.5 ps. The Fourier
transform shown in Figure 4.6 confirms the validity of this model. The Fourier transform

should contain peaks corresponding to 2011,, 2mg, (0, + are, and a), - are, where an and (a,

117

are the average rotational and vibrational frequencies respectively. Note that the square of
the summation of cosines also yields a constant term which causes a peak at zero

frequency in the Fourier transform as seen in Figure 4.6 for both transforms.

Looking at Figure 4.6, a splitting around the symmetric stretching vibrational
frequency (at = 158.2 cm") is evident; thus a). — 22,, (148.4 cm") and at + (03, (167.9
cm") are obtained. In addition, there is a peak corresponding to 2602 (19.7 cm") reflecting
the 1.7 ps modulation. This corresponds to twice the average rotational frequency that
arises fiom the sum of all the rotational levels (third term in Equation (4.13)). The 260.,
peak, corresponding to periodic oscillations of 105.4 fs, is not observed. This is probably
because of a lack of time resolution as determined by the FWHM of the coherent spike,
138 fs for this transient. It is also possible that 1" is small compared to the other terms
that enter Equation (4.13). The summation of the equih'brium anisotropic polarizability
(responsible for rotational dynamics) and the derivative of the polarizability with respect
to the vibrational coordinates is consistent with Raman scattering theory.'349‘35 The HgI2
experimental data confirms that the analysis of time-resolved molecular dynamics by TG
requires a smnmation of rotational and vibrational components and this is in contrast to

the analysis of time-resolved pump-probe transients.

118

4.4.1.4. Early time response and comparison to liquid data

The results presented in Figure 4.8 compare the early time TG response for two
gem-dihalomethane molecules, CH2C12 (340 Torr) and CH2Br2 (40 Torr). The two
transients can be described by a time-zero coherence spike followed by a rotational
coherence feature. As expected, based on the rotational moment of inertia, the dichloro
compound has a faster rotational dephasing component. The dibromo compound is much
slower. In both cases the rotational dephasing and time-zero coherence spike can be
simulated using Equation (4.13) and the rotational constants for these compounds are
recuperated, 0.12 and 0.050 cm‘1 for CH2C12 and CH2Br2 respectively. The rotational
constants calculated fi'om moments of inertia are 1.1, 0.106 and 0.10 cm'1 for CH2C12 and
0.88, 0.0412 and 0.041 cm'1 for CH2Br2.214 The B rotational constants for each molecule
are close to the values we found; however, because CH2C12 and CH2Br2 are not
symmetric tops, the measured rotational constant is a combination of the three rotational
constants. From these early time TG signals, we observe that even in the absence of
rotational recurrences, the initial dephasing is suflicient to determine the rotational
constant of a molecule with two-digit accuracy or the rotational temperature of a known

molecule or product of the reaction.

119

 

 

CH2Br2

Signal Intensity (a.u.)

 

 

 

 

a l

-500 0 i 500 1000

Time Delay (fs)

Figure 4.8. T6 transients of methylene chloride (upper) and methylene bromide
(lower). The experimental data are shown as circles and the simulations
calculated using Equation (4.13) are shown by the solid line. In both scans, the
time-zero coherence spike is observed and is more intense than the rotational
dephasing. As expected, the rotational recurrence is faster in CH2CI2 than in
CHzsz.

j 1

1500 2000

120

oscil
confi
moti
megs

lend

90m
0.19
Sloll
11 nt
13111:
r01a:

age]

In addition to the rotational dephasing, the data on CH2Br2 contains a weak
oscillatory modulation with a period of 190 fs. The frequency of this oscillation,
confirmed by Fourier transformation of the data, corresponds to the Br-C-Br bending
motion fiequency around 173 cm".215 Impulsive stimulated Raman scattering
measurements by Ruhman et al. on CH2Br2 have demonstrated the persistence of this

bending motion for several picoseconds in the liquid phase.216

Figure 4.9 compares the early time TG response for larger polyatomic molecules,
in this case benzene (90 Torr) and toluene (30 Torr). These molecules are highly
polarizable with [(3) coeflicients of 10.1 and 9.81 x10'14 esu for benzene and toluene,
respectively.208 Simulations to the data using Equation (4.13) yield rotational constants of
0.1896 for benzene and 0.146 cm’1 for toluene. In the literature, the three rotational
constants for benzene are 0.18960, 0.18960 and 0.09480 cm",217 and for toluene are
0.19106, 0.08397 and 0.05834 cm".218 Our rotational constant for benzene, an oblate
symmetric top, is in excellent agreement with the literature value for B. Because toluene
is not a symmetric top, the B value fiom the literature is not corresponding well with the
value we determined. However, if the reduced moment of inertia is used to calculate the
rotational constant for toluene,214 the rotational constant becomes 0.146 cm'] which does

agree well with our value.

121

 

 

 

Signal Intensity (a.u.)

 

 

 

. Toluene
.l
. . _
.
C
. -
\\
-250 F 0 I 250 L 500 L 750 L 1000
Time Delay (fs)

Figure 4.9. T6 transients of benzene (upper) and toluene (lower). The
experimental data are shown as circles and the solid line shows the simulations
from Equation (4.13). The intensity of the rotational dephasing in benzene is
stronger than the time-zero spike. However, in toluene the intensities of the
rotational recurrence and the time-zero spike are about equal. The rotational
recurrence time is similar for both compounds as expected from their rotational
constants.

122

The femtosecond gas-phase CARS measurement by Hayden and Chandler on
benzene gives the overall 12 ps rotational deplmsing signal.67 Our transient (in Figure
4.9) gives the early (first 500 fs) dynamics where the initial rotational dephasing is
observed; a subsequent oscillation of the rotational coherence has also been observed at
1.2 ps (not shown). The data of Hayden and Chandler show the 1.2 ps feature as well as

one at 4 ps and one at 8 ps.67

In benzene, the rotational dephasing component of the signal is more intense than
the coherent spike at time zero. A similar effect for the relative intensities of time zero
and the rotational dephasing was also observed for CS2 and is expected for molecules
with large anisotropic polarizabilities. For toluene, the relative intensities of the coherent
spike and the rotational deplmsing are about equal. At time zero, the signal results from
the coherence coupling artifact through the instantaneous polarizability of the equilibrium
isotropic component as well as other combinations of interactions between the three
electric fields as discussed in the Theory section; the anisotropic orientational
dependence contribution [(1) in Equation (4.6) is zero at time zero. For positive times,
only [(1) contributes to the TG signal observed for these off-resonant transients. Both
normal mode dependent contributions, Equations (4.8a) and (4.8b), average to zero
because of the very fast vibrational frequencies in comparison to the coherence length of

our laser pulses.

The gas-phase measurements presented in this study provide the isolated
molecular response of the material. When compared to condensed-phase measurements,

one can immediately recognize the intermolecular influence on the polarizability of the

123

 

system
measur
our do
WP

semiem
from N.
Silntllati
dephasi,
molecule
lime con
Slow dil
ailment

lmafast

system. In Figure 4.10 (top) we present both the early time response of gas-phase CS2
measured in our laboratory and the simulation fiom Equation (4.13). In order to compare
our data with liquid-phase measurements, we have simulated the data from Nelson’s
group on CS2 obtained by impulsive stimulated Raman scattering using the same
semiernpirical formula used to simulate their data56’2‘9 This simulation of the liquid data
fiom Nelson’s group is presented as the solid line in the bottom of Figure 4.10. In their
simulation, three time scales were identified: (i) a fast component due to inhomogeneous
dephasing, (ii) a fast emergence of an ensemble of aligned and coherently h'brating
molecules, and (iii) a slow difliisional dephasing of the orientational anisotropy. The fast
time constants in the simulation were given l/e values of 114 and 102 fs respectively, the
slow diffusional dephasing was simulated by a time constant of 1.37 ps, and the
coherence coupling artifact was ignored.”219 It is clear that the condensed-phase data

has a fast initial dephasing rate followed by a much slower decaying component.

124

 

I U f I T Y t I

CSz ~

 

 

Signal Intensity (a.u.)

 

 

 

 

-300 0 300 600 900 1200
Time Delay (fs)

Figure 4.10. Top: TG transient obtained for CS2 near time zero. The
experimental data (circles) contain a very small coherence coupling artifact
followed by a large rotational dephasing component. The data has been
simulated using Equation (4.13) as shown by the solid line. Bottom: The curve
with the circles corresponds to the simulation of our gas-phase TG signal for CS2
multiplied by a fast decaying function which simulates inhomogeneous dephasing
and by a slow decay function which simulates diffusional dephasing (see text).
The smooth line corresponds to a simulation curve used by Nelson and
coworkers to fit the liquid-phase experiments (see References 56 and 219).

125

Based on the simulation of the gas-phase data, we have attempted to reconstruct
the condensed-phase measurements. Our simulation is achieved by multiplying our gas-
phase simulation for CS2 (from Equation (4.13)) with a function that includes both a fast
decay time of 65 fs to simulate the inhomogeneous dephasing and a slow decaying
component to incorporate the diffusive reorientational dephasing of 1.37 ps. The resulting
curve, shown by the connected circles in the bottom of Figure 4.10, is very similar to the
one generated by Nelson and coworkers. The differences between the two curves are a
slight delay in the peak of the transient and a dip at ~ 420 fs. These differences may
provide a more accurate simulation to the data presented in their publication. 56,219 The
position where the signal achieves its maximum value is very sensitive to the fast decay
which simulates the inhomogeneous broadening. Liquid-phase measurements have found
that upon dilution the inhomogeneous decay rate decreases because the CS2-alkane
interactions are weaker than those between CS2 molecules.205’220,221 These findings are
consistent with a physical description in which a weakening of the intermolecular
interactions leads to dynamics that more closely mimic a gas-phase environment. Based
on our preliminary model, only the inhomogeneous dephasing rate would need to be
modified to simulate such behavior. The preliminary analysis presented here indicates
that gas-phase dynamics can be used to provide a starting point toward the simulation of
liquid-plume dynamics, especially during the first picosecond before dephasing is

complete.

126

4.4.2. Resonant Excitation

4.4.2.1. Rotational and Vibrational Response (1.), = 0)

The transient grating data (positive time delay with tag, = 0) and reverse transient
grating data (negative time delay with r01, = 0) obtained from an iodine sample heated to
130-140°C (160 Torr) are shown in Figure 4.11. The long undulation (~1.5 ps)
corresponds to the early dephasing in the rotational anisotropy. The fast oscillation
corresponds to ground and excited state vibrations, which are excited impulsively by the
short pulse lasers. Unlike the previous experimental transients, both excited and ground
state dynamics of 12 are observed. The difference stems from whether or not the TG

interactions are resonant with the appropriate electronic transitions of the molecule in

1
question. In this case, all three fields are resonant with transitions between the X ( 2;)

and the B (3110“,) states.‘30"31’227«223 Transitions to other states with smaller transition

probabilities at the wavelength of excitation, such as the A], state, are not observed
because of the us dependence of the signal. All eight diagrams in Figure 4.2 contribute to
the observed signal. In Figure 4.11, ground state and excited state dynamics are clearly
obtained by FWM with three resonant beams. Schmitt et al. have carried out CARS and
DFWM measurements on this molecule showing both ground and excited state dynamics,
evident in the Fourier transform of data from positive time delays.69’70 Below we present
the analyses of our iodine experimental data for positive and negative time delays

separately.

127

 

 

 

     

 

 

 

 

 

 

 

 

 

 

 

 

 

.1 I T I I T T {12:
2 ii 1 r
3 t.

9;: " 0 A 100 200 A 300 400 ‘ 0 100 200 300 400'
5 _- Frequency (cm'l) ‘ Frequency (cm'l) :
#2.? ° iii“!l iii 1

r . 3 ‘ ‘1 . . q

2%”_ Mid/”Nil filhl) ll l )1 {WW
1 it ‘ .3 L i) ‘ i 4 i l .
Time Delay (ps)

Figure 4.11. Bottom: TG and RTG transient of iodine. \fibrations can clearly be
seen at both negative (left) and positive (right) time delays. Lasers with central

wavelength of 622 nm are resonant with the X e B electronic transition. Left
inset: Fourier transform of the data at negative delay times. There is one main

peak at 107.1 :1: 0.3 cm'1 and another smaller peak at 209.9 i 0.3 cm“. Right
inset: Fourier transform of the data at positive delay times. The frequencies of the
three main peaks are 107.8 1 0.4, 210.8 :1: 0.1, and 312.0 i 0.2 cm". Taking
these values and accounting for the combination frequencies that should be
observed in each Fourier transform because of the summation of cosines, values
for the excited vibrational frequency (105 cm"), ground vibrational frequency
(208 cm"), and average rotational frequency (3 cm") can be obtained.

For positive time delays (Figure 4.11 - right) the dynamics arise fi‘om wave
packets formed in the ground state (diagrams ab,! and bag in Figure 4.23) and in the
excited state (diagrams abe and ha. in Figure 4.2b). It has been shown that vibrational

levels v' = 7—1 2 form the coherent superposition in the B excited state following

excitation with 620 nm pulses.34t33,42’126 Each population in the ground and excited states

128

contributes Vibrational and rotational dynamics to the signal. To simulate the
experimental data, it is best to include each fiequency component explicitly in Equation
(4.16); however, for simplicity we can understand the data if we assume average
frequencies for the excited and ground states. Thus we have two vibrational frequencies
(02," and all!) and two rotational frequencies (am" and cm') which we know from the
literature for the ground and excited states respectively.'309‘31’222'224 When these four
terms are introduced in Equation (4.16), the squaring results in a total of sixteen terms.
The first four terms give dynamics proportional to 2am", 2am ((m" + (m') and lam" -
aJR' l , all in the range of 0-50 cm". The next four terms give frequencies proportional to
22' ~ 220 cm“, 2m" ~ 420 cm" (not observed), (av + (2;) ~ 310 cm" and lat" - at'l
~ 105 cm". The remaining eight terms correspond to the sums and differences arising
fiom the four cross terms between vibrations and rotations. Because the rotational
fiequencies are very small compared to the vibrational frequencies only two peaks from
these cross terms are expected, one at ca," ~ 210 cm’l and the other at ar' ~ 110 cm".
The Fourier transform (right inset) shows the low frequency rotational contributions and
the three peaks at 107.8 s 0.4, 210.8 i 0.1 and 312.0 s 0.2 cm". Taking these values and
accounting for the combination fiequencies that should be observed in each Fourier
transform because of the summation of cosines, values for the average excited vibrational
fiequency (105 cm'l), average ground vibrational frequency (208 cm"), and average
rotational frequency, JmBm (3 cm") can be obtained. Here BM is the average of the
ground and excited rotational constants and Jm is the average J level (leO). These
values agree well with the available spectroscopic data of 12 for the ground and excited

states.‘3°,'3'a222'224 Based on the spectrum of our pulses, the sample temperature, and the

129

Frank-Condon factors, we can determine which states contribute to the ground and
excited state dynamics. For the ground state, the observed motion arises from a linear
superposition of states v" = 2-4 with a collective frequency of 160 fs. Although levels v"
= 0 and 1 are the ones which are most populated in the sample at 140 °C before the
interaction with the laser pulses, the Frank-Condon overlap between these levels and the
excited state at 620 nm is very small.223 For the excited state, the observed motion arises
from a linear superposition of states v' = 6-11 in the B state, corresponding to a

Vlbrational time period of 307 fs.34,126

An accurate determination of the magnitude of each of the contributions
mentioned is not possrhle with the available data. Typically the anisotropic equilibrium
polarizability (leading to the observation of rotations) is larger than the derivative of the
polarizability (vrhrational dependence), therefore rotational-vibrational cross terms are
expected to have a major contribution. Quantum calculations have also been performed in
connection to the phase-locked experiments by Scherer et al. on 12 where the time
dependence of the ground and excited state coherence was critical to their
interpretation225 The ground state motion has been studied quantum mechanically by

Jonas et al.226 and Smith et al.227

Based on the guidelines in the theory section, a semiclassical calculation (using
Equation (4.16)) can be performed that takes into account the rotational and vibrational
contributions to the TG signal fiom ground and excited states as well as the coherent-
coupling term, which contributes near time zero. In Figure 4.12, we show the simulated

transient and corresponding Fourier transforms. The calculated transient looks similar to

130

the positive time experimental data. The Fourier transform shows peaks of similar
position and shape to those obtained from the experimental data. The finite pulse duration
in the experiments causes a loss of resolution for the high fiequency components. We
have not included convolution in the simulation; most likely this explains why the heights
of the high fiequency components are higher in the simulation Fourier transform than in
the experimental one. If the parameters of the simulation, such as the magnitude and
phase of each contribution (each vibrational level in the ground and excited states), were

optimized by a fitting routine, an even better agreement could have been obtained.

 

 

 

-.-,-,- -.-,E2EI
. 2

_ r q

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A. l’ 1 _.
g. .
a: . t , -
v - . 2 L m . z - . . - -
3., _ 0 100 200 300 400 0 100 200 300 400 g
.5 Frequency (cm'l) Frequency (cm‘l)
r: i .
o .
H l
g _ . _
1—1
7: 4
= .
.3.” .. s
U)

-4 A -2 i 0 A 2 A 4 L

Time Delay (ps)

Figure 4.12. Semiclassical simulation of the iodine signal for positive and
negative time delays (see text). The insets show the corresponding Fourier
transforms. The simulations agree well with the experimental results presented in
Figure 4.11.

131

The negative-time signal in Figure 4.11 (lefi) is observed when field E, precedes
fields E, and Eb. Notice that the labels of the fields are arbitrary except for the fact that E,
is the only field that we delay or advance in time. The term “negative time delay” does
not imply that E, is scattered towards the detector before grating formation E, and Eb has
occurred. When EC precedes the other two fields, (see bottom of Figure 4.1 and diagrams
cbg and cbc in Figure 4.2d), an electronic coherence between the ground and excited
states is formed (see Theory section). The time dependence of this electronic coherence is
probed by the formation of a transient grating by E5 and scattering of E, from the grating
into the direction of the signal detector. In the absence of collisions, the coherence
persists for long times and yields coherence decay information. Our group has
investigated the relaxation times of this coherence in iodine at different temperatures with

different FWM pulse sequences.81

The Fourier transform of the negative time delay experimental transient (Figure
4.11 - lefi inset) shows frequencies in the 0-10 cm’1 range as well as a strong component
at 107.1 :03 cm'1 and a weaker peak at 209.9 $0.3 cm". As indicated earlier, the
coherence probed in the RTG measurement contains primarily a contribution from the
excited state. This can be understood by considering the wave function launched by the
first pulse as a coherent superposition of vibrational eigenfunctions from the ground and
excited states. The signal is proportional to the overlap between the initial wave fimction
lI’(t = 0) and the wave function at later times ‘I’(t). For iodine the range of motion (center
of mass) of the ground state components has been found to be 0.12 A, while that of the B

excited state is 0.6 A and it is significantly displaced fiom the ground state equilibrium

132

geometry.34,226~227 Therefore, the signal observed is dominated by the dynamics on the
excited state. This point was tested with a calculation of the overlap between two ground
and excited state model oscillators and it is a manifestation of the Condon

approximation.78

The rotational component of the signal depends on the rotational dynamics of the
coherence. When the excited state vibrational dynamics, the time-zero component, and
the rotational dephasing terms are introduced in Equation (4.16), one obtains a transient
that is very similar to the observed data. The simulated transient and its Fourier transform
at negative time delays, shown in Figure 4.12, are in good agreement with the
experimental observations (Figure 4.11). Convolution of the simulated transient, not
included for this figure, reduces the relative height of the high fiequency component near

210 cm".

Other sources for the negative time signal have been considered. Most
importantly we can rule out the possibility of a two-photon resonant excitation by which
other potential energy curves are probed. For gas-phase iodine the only two-photon
allowed transition is to a repulsive state)“,228 Repulsive states can only contribute to the
observed signal within the first r< 100 fs. In the liquid phase, the ion pair states of iodine
are solvated and can be reached by two photons with wavelength in the visible. These
states have been implicated in the studies from Fleming’s group on phase locked
dynamics of molecular iodine.229 The contribution of ion pair states in the data presented
here is ruled out because for gas-phase iodine three photons are required to reach them.

Most importantly, the simple semiclassical calculations presented here, involving the B

133

and X states closely reproduce the data and its Fourier transform. The observation of
coherence dynamics for negative time delays in four-wave mixing has been discussed
theoretically by Mukarnel et al.5354170,”1 and has been observed in the gas phase by M.

Schmitt et al. (for 12) and by Motzkus et al. (for Na2).‘53’7O

4.4.2.2. Control of Molecular Dynamics (m, it 0)

Now we turn to examining the molecular dynamics of iodine obtained when E,
and Eb are not overlapped in time. First we consider Pulse Sequence 1. When field E, acts
on the sample before field E2, the sample has a certain amount of time (rub) to evolve. We
have explored how to use the time dependence of the molecular system for controlling
the excitation process. The two transients shown in Figure 4.13 and Figure 4.14 were
collected consecutively under identical conditions. The only difference between them
was the time delay (Tab) between the first two pulses. Based on the theory, various
multiples of the ground or excited state vibrational periods can be used to achieve control
over the population transfer. 103 We have tried a number of combinations with great
success. We have chosen to use 460 fs (3/2 2'2) and 614 fs (2 1'2) which correspond to times
when the ground state population is at a minimum and a maximum respectively. We

chose 2n 1, rather than (n + 1/2) 2;, in order to maximize the ground state contribution.103

134

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ll fiIIII'IT‘TTIIIIITDTUTTTITI‘IIIIITTUIIIIIIIFTI
PS-I
. .l
,3. Tab=460fs
=5
3 t
z: 0 50 100 150 200 250
.... Frequenq(cm'l)
m
G
0
H ll .1
s l l l
m
E h
=
.20 A.
U)
'-IIIUII[VIIUIIUIIUIIIllllLlellllllllllllllLllllll-i

 

 

 

 

 

 

 

 

0 1 2 3 4 5
Time Delay r (ps)

Figure 4.13. Experimental transient for PS-I (only the first 5 ps are shown) where
tab = 460 fs corresponding to one and a half vibrational periods of iodine in the
excited state (3/219). Observed vibrations have a period of about 307 fs. The
power FFT of the transient shows a predominant frequency of 107.7 :1: 0.2 cm‘1
corresponding to vibrations of the excited B 3110... state of molecular iodine. It

reflects that the detected FWM signal is exclusively from the excited state. The
slow modulation with a dip near 1 ps is due to rotational dephasing.

Figure 4.13 shows the three-pulse FWM signal obtained with r21, = 460 d: 10 fs
(3/2 re). The transient shows vibrational oscillations with a period of 307 fs
corresponding to dynamics in the B 3I10,“ state involving vibrational levels v' = 6-11.
Also observed is a long undulation dipping around 1 ps. The power FFT of the transient
is shown in the inset of the figure. The most prominent peak is centered at 107.7 :l: 0.2

cm’l and corresponds to vibrations of the excited state. A small peak centered at 218.2 :1:

135

0.2 cm" is the second harmonic of the excited state signal and is not a contribution from
the ground state.103 The small peak centered at 10.8 i 0.5 cm’1 corresponds to the
rotational dephasing dynamics.86 The dynamics observed are consistent with the excited
B 3110+u state. By comparing the FFTs in Figure 4.11 and Figure 4.13, we can see that the
ground state molecular dynamics are suppressed (i. e. no peak at 208 cm") with this

selection Of Tab-

 

PS—I
N Tab = 614 fs

 

 

 

 

 

 

 

’?

=!

a

v

3‘ La— —I— ——-‘A— A
.5 0 50 100 150 200 250

= Fre enq(cm' ) ,
o l
«H

=

_

—

a

=

00

O-

m

l
I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5
Time Delay 1 (ps)

Figure 4.14. Experimental transient for PS-I where I", = 614 fs (only the first 5
ps are shown). This value of Tab is equivalent to two vibrational periods of the
excited state of iodine (2 1'9). Observed vibrations have a period of 160 fs. The
power FFT of the transient shows a predominant frequency of 208. 3 d: 0. 1 cm'1
corresponding to vibrations of the ground X 20.9 state of molecular iodine. It
depicts that the detected FWM signal is predominately from the ground state.
There Is a minor peak at 107. 1 :1: 0. 1 cm corresponding to a small contribution
from the excited state. Note that the slow dip in modulation around 1.5 ps is due
to rotational dephasing.

136

Figure 4.14 shows the three-pulse FWM signal obtained for rat, = 614 j: 10 fs
(2 re). Notice the large change in the experimental transients that occurs with this change
in Tab (compare to Figure 4.13). The transient shows vibrational oscillations with a period
of 160 fs corresponding to dynamics in the X 1210+g state involving vibrational levels v" =
3,4. Also apparent in the transient is a slow undulation with a dip around 1.5 ps. The
power FFT of the transient is shown in the inset. The most prominent peak is centered at
208.3 :t 0.1 cm'1 and corresponds to the vibrational fiequency of the ground state. By
examining the pattern of vibrational oscillations in these two transients (Tab = 460 and
614 fs cases), a clear mismatch is observed; this confirms that the dynamics in the 23;, =
614 fs case are not caused by a doubling of the excited state fi'equency and are ground
state dynamics.103 A smaller peak centered at 107.] :t 0.1 cm"1 corresponds to a minor
contribution from the excited state which is expected for this value of Tab (see Equations
(4.18a and.4.18b)).‘03 The small peak centered at 15.9 :1: 0.4 cm’1 corresponds to the
rotational dephasing dynamics. The observed dynamics correspond almost exclusively to
the ground X '20”; state. Again by comparing the FFTs in Figure 4.11 and Figure 4.14, it

is apparent that the excited state dynamics are greatly reduced with this section of 22.1,.

In Figure 4.15 we examine the difference in the Fourier transforms for Tab = 460
fs and 614 fs as shown in Figure 4.13 and Figure 4.14. We first highlight the selectivity
of this method for detecting ground or excited state dynamics. For rat, = 460 fs, we
observe a dominant peak at 108 cm'l corresponding to the excited state; a small peak at
218 cm'1 is most certainly due to the second harmonic of the same dynamics given that
the FFT shows no amplitude at 208 cm". For Tab = 614 fs, we observe a peak at 208 cm'1

that corresponds to the ground state vibrational frequency. For this time delay between

I37

fields E, and Eb, we also see a minor peak at 107 cm'I that indicates a small contribution
from the excited state. The insert shows the low frequency end of the Fourier transform
with two distinguishable contributions. The moment of inertia of the X state is quite
difierent fi'om that of the B state; the rotational constants are 0.03696 and 0.02764 cm'l
respectively.34t‘3° This diflerence is manifested in the low fiequency components due to
the differences in the rotational dephasing dynamics. The observed positions are 11 :l: 1
and 16 i 1 cm'I respectively. The ratio between these positions is 1.5 i 0.3 and the ratio
of the rotational constants is 1.34; these are in fair agreement. This observation is firrther
proof that the dynamics correspond primarily to the ground or the excited state. Based on
these experimental data (Figure 4.11-Figure 4.15), we confirm that the time delay Tab can

be used to control the transfer of population between the ground and excited states.

138

 

IIIITTIITTTIl—lellll‘ljll

 

 

 

 

 

 

PS—I

—— Tab = 614 fs .1
i; — ab = 460 fs
a. _

 

 

 

 

 

 

 

 

 

 

Frequency (cm'l)

Figure 4.15. Close-up of the power F FT for the transients shown in Figure 4.13
and Figure 4.14. When rab- 614 fs (gray line ,the data show a small contribution
at 107 cm 1and a prominent peak at 208 cm corresponding to the vibrational
frequency of the ground state. When 181,- '460 is (black line), the data show a
prominent peak at 108 cm'1 corresponding to the vibrational frequency of the
excited state, and a minor peak at 218 cm1which Is most likely a second
harmonic of the 108 cm 1.peak The insert shows the enlarged region at low
frequencies with peaks at 16 :t 1 and 11 i 1 cm1.These correspond to the
different rotational dephasing dynamics occurring in the X state (rab‘ - 614 fs) and
the B state (Tab = 460 fs), respectively. The difference in the frequency is caused
by the difference in the moment of inertia between these two states. These data
confirm the ability to select ground or excited state dynamics based on the choice
of Tab in three-pulse FWM.

I39

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The previous data in Figure 4.11-Figure 4.15 show how the delay between the
first two pulses in PS-I can be used to control what type of dynamics are observed,
ground state, excited state, or both. It is interesting to ask what are the relevant dynamics
of the system after a single interaction with the electric field that influences the control
process. In the Theory section, we theoretically discussed the coherence peg“) formed
between ground and excited states after a single interaction with the electric field Ea. One
can carry out an experimental observation of these dynamics by having field E. interact
with the system and, after a variable time delay I, have fields Eb and E0 interrogate the
system (PS-II). Note that in our experiments, fields E, and E, are interchangeable; for
practical reasons we have carried out measurements with beam EC preceding beams Eb
and Ea. Recall that the RTG measurement in Figure 4.11 shows 307 fs oscillations,

corresponding to the vibrational frequency of the excited state, dominating the transient.

In the Theory section, we discussed the signal dependence on rag, and r for PS-I.
Converting the formalism to PS-II turns out to be quite simple. For this, we will maintain
the definition of Tab as a fixed time delay and ras the time that is scanned. Note that for
PS-II, ris the delay between the first two pulses (tz-tt) and Tab is the delay between the
last two pulses (t3-t2). The expressions for the ground and excited state contributions to
the signal need to be modified accordingly by interchanging Tab and 2'. This modification
converts the ground (excited) to an excited (ground) state contribution.103 Thus, we can

use the fixed delay Tab to ‘filter’ the ground and excited state dynamics.

140

delay I

lied

5613011
93 are
grour.
ls eii
Figup
used

'th

 

In Figure 4.16 and Figure 4.17 we have explored the possibility of using the
delay time Tab between beams Eb and E, to filter the type of dynamics that are observed.
The data in Figure 4.16 (only the first 5 ps are shown), which was taken with rat, = 460 d:
10 fs, show excited state dynamics. The small contribution at 218 cm'1 is due to the
second lmrmonic of the excited state dynamics. The data in Figure 4.17 (only the first 5
ps are shown), which was taken with rob = 614 i 10 fs, show an increase in the amount of
ground state contribution as compared to the contribution when Tab = 0 fs. This difference
is evident by comparing the 210 cm'1 peaks in the Fourier transforms in Figure 4.11 and
Figure 4.17. These experiments show that the delay Tab between fields Eb and E, can be
used effectively to filter the relative contributions from ground or excited state dynamics

in the initially prepared coherence. We note that this filter does not provide the same

amount of control as can be achieved with PS-I. '03

141

 

III.III.I'II'I'IIIIIUUVIYIIIIIIIIIIIIIIIIIIIIIUII

 

IIII’I'II'IVT1TIIY'UII’U

    

 

- PS-II
H
Tab = 460 fs g; '

 

 

 

 

 

 

0 so 100 150 200 250 a
h Fnrprenq (cm‘l)

 

Signal Intensity (a.u.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5
Time Delay 2' (ps)

Figure 4.16. Experimental transient for PS-Il where res = 460 fs (only the first 5
ps are shown). Notice the well-resolved oscillations with a period of 307 fs. The
power F FT of this transient shows a predominant frequency of 108 cm'1
corresponding to vibrations of the excited state. A minor contribution at 218 cm'1
is most probably a second harmonic of the 108 cm'1 component.

 

142

 

.l'lfjiilIIUIIIiTTTIllIT‘T‘IT‘IIIIIIIIIIII‘Ir‘tFII

 

VIVIVVIVVVII‘IVTTT‘TYT

 

1 l

I. PS-II
' Tab = 614 fs

lLLJll

 

 

 

l

 

  

1
I

 

1 l

0 so 100 150 200 250 "'
Frequenq(cm'1)

d

 

 

Signal Intensity (a.u.)

 

 

 

 

 

 

 

 

 

: ll

0 2 3 4 5

Time Delay 1 (ps)

Figure 4.17. Experimental transient for PS-ll where tab = 614 is (only the first 5
ps are shown). The power F FT of this transient shows frequencies at both 108
cm‘1 and 208 cm1. Note that for this value of Tab, there is an increase in the

amount of ground state contribution as compared to the case tab = 0 fs (see
Figure 4.11).

143

4.5. CONCLUSIONS

In summary, we have presented several types of femtosecond dynamic responses
from atomic, diatomic and polyatomic gases. The nonlinear interactions between the laser
fields and the sample have been sorted using double-sided Feynman diagrams. We have
combined the quantum mechanical dependence of the molecular polarizability with the
semiclassical expressions for the time-resolved rotational dynamics to arrive at a formula
that describes the observed rotational dynamics in diatomic and polyatomic molecules as
well as describing the vibrational dynamics. The experimental TG transients on atoms
and molecules have been simulated using this formulation. The TG transient from air
demonstrated the ability of Equation (4.13) for simulating rotational recurrences.
Furthermore, it also demonstrated the capabilities for using TG techniques in the analysis
of multiple component mixtures such as N2 and 02. Using the CS; transient, we
demonstrated the accuracy that this time-resolved technique can achieve in the
measurement of rotational temperature, rotational constants and centrifugal distortion
directly from the time-dependent data without the need for Fourier transformation. For
HgIz, vibrational coherence fi'om the symmetric stretch, which is the only Raman active
mode, was observed. The cross terms arising from the sum of rotational and vibrational
dependent terms on the molecular polarizability have been identified in the Fourier
transform of the Hglz data. Vibrational and rotational dynamics from both the ground and
B excited states of 12 were obtained for positive time delays and are consistent with

previous observations.‘59t70t23o For negative time delays, corresponding to the RTG

144

configuration, coherence dynamics for 12 were observed and simulated. The early time
responses of polyatomic molecules including benzene, toluene and the dihalogenated
methanes were investigated. Finally, for molecules with large anisotropic polarizability,
we showed that the rotational dephasing signal may be stronger than the time-zero
coherence spike. The understanding and analysis of these simpler non-reactive systems
that we have developed here will aid us as we expand TG and FWM studies to reactive

systems in the firture.

We have also demonstrated that pulse sequences can be found for resonant three-
pulse FWM experiments to optimize population transfer between two electronic states.
For PS-I, the populations of the ground and excited states were controlled based on the

time delay between the first two pulses. We showed that for 22.5 = 460 fs only excited

state dynamics are observed, while for rat, = 614 fs primarily ground state dynamics are
observed. In PS-II, we observed the time evolution of the coherence between the ground
and excited states induced by one laser field interaction. In this case, we found that we
changing Tab from 614 to 460 fs can increase or decrease (respectively) the contribution
of the ground state to the FWM signal we collected; thus, we can isolate excited state
dynamics in this case as well. We plan to expand these types of experiments to systems

where it will be possible to control the outcome of chemical reactions.

The experimental data presented here show that the time delay between the first
two pulses in a three-pulse F WM experiment can be uSed to control the population
transfer between ground and excited states. We have used this technique in order to study

the vibrational dephasing in the ground and excited states of iodine as a function of

145

temperature. By changing Tab we were able to obtain both separate values from the same
setup.“ The ability to transfer populations between different states is the chief tenet of
the pump—dump control theory of Rice and 'l‘annor.2319232 With three-pulse FWM we
have shown that this control can be achieved with great efficiency. This technique can be
useful to study ultrafast dynamics involved in chemical reactions where one may want to

follow processes that occur in the excited or ground state exclusively.

Experimental control using multiple laser pulse excitation has been explored by a
number of groups.88 While some of these experiments have been carried out without
phase-locked pulses or phase-matching conditions,63t233t234 the most striking control over
the excitation process is observed for phase-matched or phase-locked setups. Scherer er
al. measured this efl°ect by observing a change in the total fluorescence of 12.96 Warren
and Zewail used collinear phase-locked pulses to observe photon echos in 12.235
Pshenichnikov et al. used a phase-locked FWM arrangement where the grating and echo
processes interfere constructively or destructively.236 Time-delayed pulses can be
combined to achieve population inversion by adiabatic passage.237t238 From Equation
(4. 17), one can see that the population transfer is modulated by an electronic term with
control parameter (crab, spatial condition (k. — kb)r, and phase-locking condition. The
amplitude is further governed by the vibrational motion of both electronic states with
control parameters we rub and cg Tab. Our measurements use the vibrational time scale,

which is independent of phase-locking, to achieve the control.

146

APPENDICES

147

5. APPENDICES

LabVIEWT“ is a programming application based on the G graphical programming
language and is offered by National Instruments.239 Other text-based programming
languages like Fortran, C, BASIC have lines of code that the programmer writes. The G
graphical programming language has block diagrams that display the code written by the
programmer. A program in G is called a VI, virtual instrument. This language can be
used to write programs that collect data, analyze data, and store data just as text-based
ones do. It also comes with a standard set of subroutines (subVIs) for many simple tasks,
operations, and filnctions; in addition, manufacturers of scientific instruments or
hardware also provide programs and/or subroutines to help facilitate writing programs to
control their hardware. The "front panel" is what the user may see (it is hidden in some
programs) and may look like the front of an instrument (buttons, knobs, switches, etc.)
The front panel is not the program; it is the display of what the program needs as input or
provides as output. The block diagram contains the graphical code. Various types of
rectangles symbolize loops - "while" and "for-next" - and structures - "sequence", "true-
false" or other "case" conditions, and formula calculations. The operations and tasks that
should occur in these loops or structures are placed inside the rectangle. Wires show how
information is transferred and flows fi'om one part of the program to another. SubVIs are
associated with an icon which may contain text and/or simple picture giving an idea of
what that VI does. In addition, the icon shows input (left-side connections) and output
(right-side connections) information of the subVI; this is called the connector pane. When

a V1 is written that calls upon a subVI, the icon of the subVI is shown on the block

148

diagram of the VI. In some cases, variables need to be defined and used across a number
of subVIs. These variables are defined globally so they can be accessed by a number of
VIs without the value changing or resetting between difl‘erent VIs; these are called global

definitions (global VIs) and are shown with a "worl " or "globe" on the icon and block

diagram.

There are two main programs that I wrote for acquiring data with our CPM laser
system - a time transient scan (fispgm) and a spectral wavelength scan (specpgrn). I also
wrote a small instrument control program (instrcontrol) for finding ideal settings on the
scientific equipment. These three programs control a Standford Research 245 computer
interface board240, a SPEX 270 M monochrorrmtor?“ and a Unidex 100 actuator?42 The
VIs that control the interface board and actuator are available fi'om the Instrument Driver
Network on the National Instruments web page?39 The VIs that control the
monochromator are available from the manufacturer?41 Below are the hierarchical
structures of the data acquisition programs. The VIs that I wrote/modified are indicated
with a label, such as A.1 which correspond to the Appendix heading under which the
documentation will appear (see below). The subVIs that are not labeled are either
standard LabVIEWT“ VIs or VIs distributed by the equipment manufacturers/National
Instruments for the controlling the hardware. The VIs that control the equipment are
easily identified by the text in the icon; the interface board VIs show "245", the
monochromator VIs show "ISA" or "ISA Utils", and the actuator VIs show "U100".
These hierarchies of the programs are followed by the LabVIEWm-generated

documentation of the V15 I wrote. These are pages that contain the filenames, icons,

I49

descriptions, connector panes, front panels, and block diagrams; the labels on the
hierarchy correspond to the subheadings of these pages. (In a couple cases (A.5.1. B.5.1,
D.3. and D.6.), I modified a standard VI from one of the instrument manufacturers and I
have included that modified VI below.) The descriptions indicate the purpose of the VI.
The overall structure of the two scanning programs is very similar. The documentation of

these VIs for the programs are found in Sections A-D.

Another program used in this research is the fitting program for the rotational
anisotropy measurements. This program is written in Fortran and was originally written
by Una Marvet. I have modified it as needed for analyzing the unidirectional data and the
pump intensity/saturation data on iodine. I have included the code for this program in the
last Appendix section. In addition to this file, we also need a file containing the initial
parameter values (rotational constants, saturation and perpendicular state parameters,
temperature) and a file containing the rotational anisotropy data (time delays and

fluorescence intensity) to conduct the fitting procedure of the data.

150

APPENDIX A

LABVIEWT" PROGRAM: TIME TRANSIENT DATA ACQUISITION

151

A. LABVIEWT” PROGRAM TIME TRANSIENT DATA ACQUISITION -
g TAKEFTS4.VI (TAKE DATA)

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Take
DuTa

This vi is the part that controls the taking of the data. It presents other interactive vi's to
the user which are described elsewhere. These vi's are used to setup files, hardware, etc.
This vi uses this info to then start its scan, show summed and unsummed fts scans to user
as they are taken, allow the user to pause/stop fis scan, and saves fis scans of data as they
are successfully completed. This vi then sends this data to the file management vi and
forces it to show the recorded data without input from user needed. Then the user can
choose to take more data or to look at other files.

Within data acquisition, it can either discriminate or not discriminate depending on user
preference and if a long wait or high %discarded shots occurs it alerts the user and asks
for proper method to continue.

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A.1. ftspgmxi (Main)

This vi is the starting point of the spectral scan program. The user decides between taking
data and looking at previously taken spectra- either *.wnm or *.spc files. If the program
is properly begun here, the user can go between both parts of the program easily. Ie. start
with file management and then go to take data and back again, or start with take data and
then go to file management and back again. (Or stay within one part of the program the
whole time.)

Connector Pane
Main ”'9‘“
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Femtosecond (Time Data) Program-

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A.2. paramfte4.vi (Setup Param)

This vi writes the parameters to the global parameters vi so that all subsequent vi's have
access to the initial conditions. If the program has been run earlier without Labview
having been quit, the parameters from the previous run are shown on the screen (allowing
the user to make only the necessary changes). The parameters are used to setup the
resulting data file and data acquisition and setup the spectrometer and actuator. The user
has the ability to control the spectrometer and the actuator during this screen in order to
find the best locations. (OR use instrumental control vi to move/change settings).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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A.2.1. Errorftsxi (Error 7)

This vi examines the setup parameters for any errors including too many scans, slit size out of
usual range, wavelength range and/or grating error, max-min or increment problems. If there is a
problem, this vi closes the opened file and the take data vi returns user to parameters setup screen
to try again.

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A.3. Testfts.vi (Test file Setup)

This vi opens the intermediate files (to save every 10 scans incrementally). It opens
them, closes them and then opens them in the write-only truncate mode so that the file
is overwritten each time a new scan completes successfully.

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A.4. Headerftsxi (Header)

This vi assimilates the setup parameters into a header cluster that is used by other vi's.

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discr.

A.5. rediscrimftsxi (Rediscr)

This vi takes 500 shots of data from the reference diode to determine the maximum and
minimum values for the discrimination. The SRS 245 vi is written to compute max/min
based on user preference for standard deviation. The max and min determined for
discrimination is then passed back to takefts vi.

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A.5.1. SR 245_rediscr_ftsz.vi (245 DISC)

This vi is a variation on the SRS 245 vi fi'om NI. This vi allows for input of GBIP, scan
channels, # of scans, trigger setting and gives output of status and maximum and
minimum values for discrimination. It determines these values fi'om global variable
defined by user for method of discrimination (standard deviation).

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A.5.1.1. refpower.vi (Power Ref)

This vi allows for raising each data point to a particular power before summing the final
transient. (This is important for multiphoton experiments - You cannot sum and then raise
to a power.)

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A.6. discrimdataftsti (Discrimin)

This vi takes discriminated data (reference max/min determined by rediscrim vi). If a

long wait occurs, vi asks user for action to take- ignore discrimination, ignore until next
preset discrimination, ignore until end of scan then rediscriminate, or rediscriminate now.
If the last option is chosen and a long wait occurs again, the computer alerts the user but
will then take data by ignore discrimination until end of scan and then rediscriminate. If
any ignore type options are chosen in the first screen, ignore becomes true within this vi
and is transferred back to take data vi so that other data acquision vi (hen-discrimination)
is used until proper time for rediscrimination (depends on option chosen).

 

 

 

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This is the vi that appears if there are too many bad shots in a row (called wait limit). This
alerts user and waits for instruction on options. If redo now is called, this vi reruns
rediscrim vi. For the other options, it sets the global variable to proper setting and returns
to discrimdata vi.

 

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A.7. Saveftsxi (Save Data)

This vi saves the data afier each scan completes successfully into one of the intermediate
vi's. For example, if the user selects 50 scans total, test1.fis will contain the sum of scans
1-9, test2.fls will contain the sum of scans 1-19, test3.fts is the sum of scans 1-29, etc.

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A.8. discrimactperftsxi (Discr Action)

This is the vi that appears if the percentage discarded is too high. This alerts user and
waits for instruction on options. For the options, it sets the global variable to proper
setting and returns to discrimdata vi.

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This vi saves the data under the filename given in the setup parameters. This save occurs
whether the set of scans completes nomnlly or is stopped in the middle using the
pause/stop button on the screen. (This save will not occur if the hard stop at the top of the
screen is used.)

A.9. Finalflsxi (Final Save)

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A.10. viewflsxi (View FTS)

This vi will plot newer *.fls as well as older *.pts files (removed in recent versions). It
allows the user to print the spectrum, choose another file to view, or to return to taking
data. The exit returns the user to the initial its program screen. The opennewfis and
openoldfis vis directly communicate the proper info to this vi.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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A.10.1. opnnewfts2.vi (Open New)

This vi opens *.fis files (time data taken with this Labview program). Header info is
transferred along with actuator position and data points to the viewing vi.

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A.‘IO.2. PrintftsNi (Print)

This vi prints the spectrum. Any user changes to range made in the view screen vi's (2 or
3) is kept for the final printing.

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APPENDIX B

LABVIEWT” PROGRAM: WAVLENGTH SPECTRUM DATA ACQUISITION

213

B. LABVIEWT“ PROGRAM: WAVELENGTH SPECTRUM DATA
Acounsmou - TAKESPECZNI (TAKE DATA)
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Take
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This vi is the part that controls the taking of the data. It presents other interactive vi's to
the user which are described elsewhere. These vi's are used to setup files, hardware, etc.
This vi uses this info to then start scan, show summed and unsummed scans to user as
they are taken, allow the user to pause/stop scan, and saves scans of data as they are
successfully completed. This vi then sends this data to the file management vi and forces
it to show the recorded data without input from user needed. Then the user can choose to
take more data or to look at other files.

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8.1. Specpgm.vi (Main)

This vi is the starting point of the spectral scan program. The user decides between taking
data and looking at previously taken spectra- either *.wnm or *.spc files. If the program
is properly begun here, the user can go between both parts of the program easily. Ie. start
with file management and then go to take data and back again, or start with take data and
thengo to filemanagementandback again. (Orstaywithinonepartoftheprogramthe
whole time.)

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B.2. paramspec3.vi (Setup Param)

This vi writes the parameters to the global parameters vi so that all subsequent vi's have access to
the initial conditions. If the program has been run earlier without Labview having been quit, the
parameters from the previous run are shown on the screen (allowing the user to make only the
necessary changes). The parameters are used to setup the resulting data file and data acquisition
and setup the spectrometer and actuator. The user has the ability to control the spectrometer and
the actuator during this screen in order to find the best locations. (OR use separate instrumental
control vi to move/change settings).

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8.2.1. Errorspecxi (Error ?)

This vi examines the setup parameters for any errors including too many scans, slit size out of
usual range, wavelength range and/or grating error, max-min or increment problems. If there is a
problem, this vi closes the opened file and the take data vi returns user to parameters setup screen
to try again.

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8.3. Testepecxi (Test file Setup)

This vi opens the intermediate files (to save every 10 scans incrementally). It opens
them, closes them and then opens them in the write-only truncate mode so that the file is
overwritten each time a new scan completes successfully.

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3.4. Headerspecxi (Header)

This vi assimilates the setup parameters into a header cluster that is used by other vi's.

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8.5. rediscrimspc.vi (Rediscr)

This vi takes 500 shots of data from the reference diode to determine the max and min
values for the discrimination. The SRS 245 vi is written to compute max/min based on
user preference for std dev. The max and min determined for discrimination is then
passed back to take its vi.

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8.5.1. SR 245_rediscr_spc.vi (245 DISC)

This vi is a variation on the SRS 245 vi from N1. This vi allows for input of GBIP, scan
channels, # of scans, trigger setting and gives output of status and maximum and
minimum values for discrimination. It determines these values from global variable
defined by user for method of discrimination (standard deviation).

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This vi takes discriminated data (reference max/min determined by rediscrim vi). If a
long wait occurs, vi asks user for action to take- ignore discrimination, ignore until next
preset discrimination, ignore until end of scan then rediscriminate, or rediscriminate now.
If the last option is chosen and a long wait occurs again, the computer alerts the user but
will then take data by ignore discrimination until end of scan and then rediscriminate. If
any ignore type options are chosen in the first screen, ignore becomes true within this vi
and is transferred back to take data vi so that other data acquisition vi (non-
discrimination) is used until proper time for rediscrimination (depends on option chosen).

8.6. discrimdataspcxi (Discrimin)

 

 

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Action

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alerts user and waits for instruction on options. If redo now is called, this vi reruns

rediscrim vi. For the other options, it sets the global variable to proper setting and returns

 

to discrimdata vi.
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Data
8.7. Savespecxi (Save Data)

This vi saves the data after each scan completes successfully into one of the intermediate
vi's. For example, if the user selects 50 scans total, testl .spc will contain the sum of scans
1-9, test2.spc witll contain the sum of scans 1-19, test3.spc is the sum of scans 1-29, etc.

Connector Pane

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8.8. discrimactperspcxi (Discr Action)

This is the vi that appears if the percentage discarded is too high. This alerts user and
waits for instruction on options. For the options, it sets the global variable to preper
setting and returns to discrimdata vi.

Connector Pane

 

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This vi saves the data under the filename given in the setup parameters. This save occurs
whether the set of scans completes normally or is stopped in the middle using the
pause/stop button on the screen. (This save will not occur if the hard stop at the top of the
screen is used.)

8.9. Finalspec.vi (Final Save)

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8.10. viewnewspecxi (View New)

This vi will plot newer *.spc files and allow the user to print the spectrum, choose
another file to view, or to return to taking data. The exit returns user to initial scan/spec
program screen. The opennewspec vi directly communicates the proper info to this vi.

Note: the only difference between this vi and the viewoldspc vi is that older *.spc files
had an error in the last wavelength recorded- and viewospc removes this incorrect 0

when finding max wavlength These two vi's may be able to be combined 1f the 0 (and its
corresponding data pt) can be deleted and then the range can be found using the Max/Min
fcn vi.

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266

8.10.1. opnnewspec.vi (Open New)

This vi opens ‘.spc files (spectra taken with this Labview pgrn). Header info is
transferred along with wavelength and data pts to the viewing vi.

Connector Pane
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267

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8.10.2. Printspecxi (Print)

This vi prints the spectrum. Any user changes to range made in the view screen vi's is
kept for the firm] printing as well as cursor position.

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270

APPENDIX C

LABVIEWT" PROGRAM: INSTRUMENTAL CONTROL

271

c. LABVIEW’" PROGRAM: INSTRUMENTAL CONTROL — INSTRCONTROLNI
(INSTR CONTROL)

This vi allows the user tO move actuator or change spectrometer settings without needing
to start one Of the data acquisition programs.

Connector Pane

Front Panel

 

 

firstru mental Control

 

 

 

| Change Spectameter Settings' I Change Actuator Settingsl

Block Diagram

 

 

 

 

 

 

 

272

APPENDIX D

COMMON LABVIEWT" VIS

273

E

 

D. COMMON LABVIEWT" VIS

D.1. fteglobxi (Param)

This is the global vi for initial conditions. This vi allows these conditions to be read fiom
or written to during any vi's Of the scan pgm.

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274

 

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D.2. Actcontrol.vi (Actuator Control)

This vi is called when the actuator is to be moved. It first checks whether the Remote LED is lit (ie
communication between UNIDEX 100 and computer serial port 2 has been established). If not it
initializes the U100 and sets up communication. It sends actuator home twice and then goes to a
user interface vi (Move Actuator) so the user can interactively move the actuator tO desired setting.
If the Remote LED is lit, the vi goes directly tO the Move Actuator vi for interactive
communication.

This vi checks In Position LED status before allowing another command to be completed avoiding
lockups and crashes. Occasionally a separate RESET command may need to be sent if actuator is
not responding (this may happen during along period of being "on” but not used- communication
seems to be forgotten in these cases.)

Connector Pane
Cured Pm

 

Fro Panel

  

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

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D.3. spexcontrol4.vi (Spex Control)

This program is a modification Of the ISA Labview program Control Demo.

If requested within the scanning programs, this window Opens to allow user to input
information tO set up the spectrometer - grating, wavelength, slit widths. After the user
findis the Optimal settings for the current experiment, this program transfers the
information back to the scarming programs. This program may also be run separately
fiom the scanning programs.

 

 

 

 

Connector Pane
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This vi allows the user tO interactively move the actuator while it keeps track of where
the actuator is (Counter global vi). This vi waits for In Position LED to be lit before
allowing another move to avoid lockups and crashes.

 

D.4. Moveactvi (Move Act)

 

Connector Pane

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286

 

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287

 

 

 

D.5. stddev_mean.vi (alu)

This global vi keeps track Of the ratio Of the standard deviation to the mean Of the

 

 

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reference data. (This gives the user an idea Of how stable the laser is; this info is updated

on the scan window for user tO monitor.)

Connector Pane

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Front Panel

 

288

 

 

 

1%“

This vi is a variation of the SRS 245 vi fi'om NI. This vi takes non-discriminated data for
Its scans. It allows for input of GPIB address, # scans, scan channels, triggered setting
and gives output of error, sum ref, sum data.

D.6. SR245_takedata.vi (245 DATA)

Connector Pane
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289

 

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WAIT FOR DATA ON READ &
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CHECK STATUS FOR ERRORS.

 

 

 

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READ SCAN any?

 

 

 

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D.7. cnclpaus.vi (Pause Stop)

This vi allows the user to choose between stopping the scan or resuming the scan once
the pause/stop button was pushed on the main take data vi screen. This info is passed to

the take data vi and the appropriate action taken.

Connector Pane

 

 

 

 

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Front Panel

 

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293

 

0.8. Actconversionxi (Act Conv)

This global vi keeps track of actuator position whether in move act vi or within its take
data vi.

Connector Pane

G
at

 

Front Panel

 

294

3
For

This is the global vi for initial conditions. This vi allows these conditions to be read from
or written to during any vi's of the scan pgm.

 

0.9. specglbxi (Param)

Connector Pane

E

 

Front Panel

_
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Don't Use Previous D-«v'

295

 

AclPos
D.10. actposforspexxi (Act Poe)

This global vi keeps track of actuator position whether in move act vi or within its take
data vi.

Connector Pane

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Front Panel

EctPos for Sfl
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296

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l-ego

 

D.1 1 . Messages
D.1 1 .1 . spexinitmess.vi (Message)

This vi just lets the user know that the spectrometer (Spex) is busy being initialized.
Connector Pane

|r1osl
~09.
Front Panel

(Spectrometer is being initialized
(one moment please)

 

 

 

 

 

 

Block Diagram

@4

 

 

 

 

0.11 .2. spexparamess.vi (Message)

This vi just lets the user know that the spectrometer (Spex) is busy configuring its
settings (slits, grating, wavelength).

Connector Pane

lr1ess
'09.
Front Panel

Spex parameters are being set
(one moment please)

 

 

 

 

Block Diagram

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D.1 1.3. actmess.vi (Message)

This vi just lets the user know that the actuator is busy being initialized.
Connector Pane

lr1IIs
'09. ‘
Front Panel

Actuator is being initialized
(one moment please)

 

 

 

 

 

Block Diagram

mI

 

 

 

D.11 .4. homemess.vi (Message)

This vi just lets the user know that the actuator is busy being sent home.
Connector Pane

M."
l ‘09.
Front Panel

Actuator is being sent home
(one moment please)

 

 

 

 

 

Block Diagram

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D.1 1 .5. rediscrmess.vi (Message)

This vi lets user know that there will be a slight delay until reference data is read and
calculated for max/min discrimination values.

Connector Pane
New

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Front Panel

[2:386 wait while program

 

es rediscrimination data

 

 

Block Diagram

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299

APPENDIX E

FORTRAN PROGRAMS: ROTATIONAL ANISOTROPY FITTING

300

APPENDIX E. FORTRAN PROGRAMS: ROTATIONAL ANISOTROPY FITTING

E.1. Unidirectional Detection with A3 and A l

subroutine gencal (np,nd,cy,param,xdata,ydata)

implicit real*8 (a-h, o-z)

parameter (npt=100, ndt=2500)

dimension cy(ndt), param(npt), xdata(ndt,2), ydata(ndt,2)
parameter (pi=3.1415926d0)

real*8 k, J, jmax
dimension r(2000)

B = param(l)

BX = param(2)

T = param(3)
back = param(4)
scale = param(S)
As = param(6)
Aperp = param(7)

tmin xdata(l,1)*1.0d-15
tmax = xdata(nd,l)*1.0d-15
dt = (tmax-tmin)*l.Od-lS/dble(nd-1)

wl = 4.0d0*pi*B*2.99792458d10
k = 0.69506d0
taul = 180.0d0
BkT = BX/(k*T)

do i=l,nd
c convert femtosecond to second
t = xdata(i,1)*1.0d-15
tau = taul*1.0d-15

amp = dexp(—(t/tau)**2)

tmp = 0.0d0
Q = 0.0d0
do J=0.0d0,500.0d0, 1.0d0

rjt = (0.13333d0+0.26667d0*dcos(2.0d0*w1*J*t)) -
As*(O.l3333d0+0.26667d0*dcos(2.0d0*w1*J*t)) - Aperp*amp

c pj = dexp(-((J-jmax)/dj)**2)
pj = dble(2*J+1)*dexp(-J*(J+1)*BkT)
tmp = tmp + rjt*pj
Q=Q+pj
end do
r(i) = tmp / Q
cy(i) = back + scale * r(i)
end do
return

end

301

E.2. Unidirectional Detection with As and Ana

subroutine gencal (np,nd,cy,param,xdata,ydata)

implicit real*8 (a-h, o-z)

parameter (npt=100, ndt=2500)

dimension cy(ndt), param(npt), xdata(ndt,2), ydata(ndt,2)
parameter (pi=3.l415926d0)

real*8 k, J, jmax
dimension r(2000)

B = param(l)

BX = param(2)

T = param(3)
back = param(4)
scale = param(S)
As = param(6)
AAB = param(7)

tmin xdata(l,l)*l.Od-15
tmax = xdata(nd,1)*1.0d-15
dt = (tmax-tmin)*1.0d-15/dble(nd-1)

wl = 4.0d0*pi*B*2.99792458le
k = 0.69506d0
taul = 180.0d0
BkT = BX/(k*T)

do i=1,nd

c convert femtosecond to second
t = xdata(i,l)*l.0d-15
tau = tau1*1.0d-15

amp = dexp(-(t/tau)**2)

tmp = 0.0d0
Q = 0.0d0
do J=0.0d0,500.0d0, 1.0d0
rjt = (O.13333d0+0.26667d0*dcos(2.0dO*w1*J*t)) -
As*((O.13333d0+0.26667d0*dcos(2.0d0*w1*J*t)) + AAB*amp)
c pj = dexp(-((J-jmax)/dj)**2)
pj = dble(2*J+l)*dexp(-J*(J+1)*BkT)
tmp = tmp + rjt*pj

Q = Q + pj
end do
r(i) = tmp / Q
cy(i) = back + scale * r(i)
end do
return

end

302

REFERENCES

303

6. REFERENCES

1 F emtochemistry -Ultrafast Dynamics of the Chemical Bond, Vol. I and 11, edited
by A. H. Zewail (World Scientific, Singapore, 1994).

2 A. H. Zewail, J. Phys. Chem 100, 12701 (1996).
3 M. Dantus, M. J. Rosker, and A. H. Zewail, J. Chem. Phys. 87, 2395 (1987).

4 F emtosecond Chemistry, Vol. I and H, edited by J. Manz and L. Woste (Verlag
Chemie GmbH, Heidelberg, 1995).

5 F emtochemistry: Ultrafast Chemical and Physical Processes in Molecular
Systems, edited by M. Chergui (World Scientific, Singapore, 1996).

6 F emtochemistry and Femtobiology, edited by V. Sundstrom (World Scientific,
Singapore, 1997).

7 U. Marvet and M. Dantus, Chem. Phys. Lett. 256, 57 (1996).
8 Q. Zhang, U. Marvet, and M. Dantus, Faraday Discussion 108, 63 (1997).
9 Q. Zhang, U. Marvet, and M. Dantus, J. Chem. Phys. 109, 4428 (1998).

10 U. Marvet, Q. Zhang, B. J. Brown, and M. Dantus, J. Chem Phys. 109, 4415
(1998)

H I. Pastirk, E. J. Brown, Q. Zhang, and M. Dantus, J. Chem. Phys. 108, 4375
(1998)

12 U. Marvet, E. J. Brown, and M. Dantus, PCCP Phys. Chem. Chem. Phys. 2, 885
(2000).

13 U. Marvet and M. Dantus, Chem Phys. Lett. 245, 393 (1996).
14 P. Gross and M. Dantus, J. Chem. Phys. 106, 8013 (1997).

15 U. Marvet, Q. Zhang, and M. Dantus, J. Phys. Chem. Special Edition:
Femtochemistry 102, 4111 (1998).

304

16 M. Dantus and P. Gross, in Encylcopedia oprpIied Physics, Vol. 22 (WILEY-
VCH Verlag GmbH, 1998).

17 E. J. Heller, Acc. Chem Res. 14, 368 (1981).

13 Y.-X. Yan and K. A. Nelson, J. Chem. Phys. 87, 6240 (1987).

19 R. Bersohn and A. H. Zewail, Ber. Bunsenges. Phys. Chem 92, 373 (1988).
20 D. Huber and E. J. Heller, J. Chem Phys. 89, 4752 (1988).

21 J. s. Baskin and A. H. Zewail, J. Phys. Chem 98, 3337 (1994).

22 J. s. Cao and K. R. Wilson, J. Chem Phys. 106, 5062 (1997).

23 J. Manz, in F emtochemisny and F emtobiology, edited by V. Sundstrom (World
Scientific, Singapore, 1997).

24 L. Dhar, J. A. Rogers, and K. A. Nelson, Chem. Rev. 94, 157 (1994).
25 L. Zehnder, Zeitschr. f. lnstrkde. 11,275 (1891).

26 L. Mach, Zeitschr. f. Instrkde. 12, 89 (1892).

27 G. Porter, Discuss. Faraday Soc. 9, 60 (1950).

28 G. Porter and B. Ward, Proc. R. Soc. London 287, 457 (1965).

29 R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. v. Shank, Opt Lett. 12, 483
(1987)

30 A. Baltuska, Z. Y. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22,
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241 JY Horiba formerly Instruments S. A., Inc. SPEX, JY, Dilor, Raman,
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242 Aerotech Motion Control Positioning Systems. [Online] Available
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318

 

 

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