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' ' Ir ‘3‘7. :4 ' .3 :3ch ;-" h.~:._~‘r. p. ‘Ufiéflu- . ‘ L. 3...? y-«h “L ‘ u ‘ . 54"1111 "“L'Ll. w .t v . 1* Vrgarfl‘ ,, n 'n v. "if . a, A 3“».2!‘ Van"; 3’ 3‘} 6 ”an." . an: r . {‘3‘— 4.- 5; ‘u -4 <0- .7; If.» x ...‘ r n ‘7‘“: a A q». ,. “L2 A. - Mr 11’5"; . "J . :‘M‘ I': 2.9,, 55.1.7,” ' : u. $.19 "43?; ' J“ 3‘} 1n.._’.,:.'*.u.:.r A h;- “n (t J? 412;; ”kt ,p A' .r 35;}: n M‘ .1 - . I... . - i“ ’_,,.;:<.' ‘F‘. >gq-in‘ée‘ )3 "I ' :1‘131,“ f/X 3.‘ J Ml HIGAN STATE I ll llzlll Itl’i‘llllfllilllljljll ‘ 31 93 0091 ll This is to certify that the dissertation entitled INFRAREDv-INFRARED DOUBLE RESONANCE STUDIES OF COLLISIONAL INTERACTIONS AND POLARIZATION PHENOMENA presented by Uhyon Shin has been accepted towards fulfillment of the requirements for Ph.D. degree in Chemistry //) 4,! ~ 7 (_( /// $[M'W C{L,u~L (LL/X. Major professor May 9, 1991 Date MSU is an Affirmative Action/Equal Opportunity Institution 0-12771 LIBRARY MIChlgan State nIversIty PLACE IN RETURN BOX to remove We checkout from your record. TO AVOID FINES return on or before date due. I- DATE DUE DATE DUE DATE DUE !ll -—l|- l __Jl:]_l ICE—JD 7 l7 INFRARED-INFRARED DOUBLE RESONANCE STUDIES OF COLLISIONAL INTERACTIONS AND POLARIZATION PHENOMENA By Uhyon Shin A DISSERTATION submitted to Michigan State University in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1991 Ifj" 1 ABSTRACT INFRARED—INFRARED DOUBLE RESONANCE STUDIES OF COLLISIONAL INTERACTIONS AND POLARIZATION PHENOMEN A By Uhyon Shin Infrared-infrared double resonance experiments were used to study collisional in- teractions of CH3F molecules and laser-induced optical anisotropy. From the line- shapes of four-level double resonance signals recorded under intensity modulation, velocity changes of molecules as a result of collisions were calculated by using the Keilson-Storer collision kernel. Four independent forms of laser-induced optical anisotropy were related to various forms of polarization modulation experiments us- ing a Jones calculus. It is pointed out that linear dichroism, linear birefringence, circular dichroism, and circular birefringence can be independently detected with dif- ferent experimental configurations. Dispersion shapes of circular birefringence were recorded by passing a plane polarized probe through a polarizer with 9 = 45° while the polarization of the pump laser was modulated between left- and right-circular po- larization. The technique for measuring pure birefringence signals shows a promising future for measuring accurate transition frequencies as well as for assigning recorded spectra. Time domain measurement of intensity modulated infrared-infrared double resonance is also described. DEDICATION TO my parents wife, Young Gyo my daughter, Mina A. and many invaluable friends Acknowledgements I would like to thank Professor Richard H. Schwendeman for the many critical contributions and his moral support through all the difficult hours in this research, as well as in preparing this thesis. My thanks are extended to Professors George Leroi, Stanley Crouch, and Daniel Nocera who shared their scientific insights and their instruments for my research. All of previous and current group members deserve partial credits for this thesis. iv TABLE OF CONTENTS LIST OF TABLE LIST OF FIGURES 1 Introduction I Definitions ................................. II Saturation Absorption Spectroscopy ................... A Lineshape Problem in Saturation Absorption Spectroscopy . . B Lineshape Study of Transferred Spikes in 12CH3F ....... C Lineshape Dependence on the Polarization ........... III Polarization Spectroscopy ........................ IV Time Resolved Spectroscopy ....................... 2 Theory I Line Broadening .............................. II Creation and Detection of Bennett Holes ................ , III Lineshape Study of Transferred Spikes ................. IV M Selection Rules ............................ V Alignment and Orientation ........................ VI Absorption and Dispersion ........................ VII Optical Anisotropy ............................ A Saturation Absorption Spectrosc0py ............... viii QNUUMH 10 11 13 13 14 17 22 23 24 25 26 B Alignment Modulation vs. Orientation Modulation ...... 26 VIII Polarization Spectroscopy ........................ 28 IX Jones Calculus .............................. 32 Experimental 41 I Lineshape Study of Transferred Spikes ................. 41 II Polarization Spectroscopy ........................ 44 III Time Resolved Spectroscopy ....................... 51 A Electro-Optic Switch ....................... 54 B Data Acquisition ......................... 59 Results and Discussion 61 I Introduction ................................ 62 II Lineshape Study of Transferred Spikes in l2CH3}? ........... 64 A Three-Level Double Resonance ................. 64 B Four-Level Double Resonance .................. 68 C Summary ............................. 79 III Saturation Absorption Spectroscopy in 13CH3F ............. 80 A Three-level Double Resonance Lineshape ............ 80 B Four-Level Double Resonance Lineshape ............ 85 C Simultaneous Measurements of Spikes for Co- and Counter- propagating Beam Geometry. .................. 88 IV Polarization Spectroscopy ........................ 93 V Polarization Modulation ......................... 95 A Alignment Modulation (oi/7r) .................. 95 B Orientation Modulation (if/0+) ................ 98 C Laser-induced Birefringence ................... 100 VI Polarization Labeling ........................... 107 VII Backward and Forward Spikes: Revisited ................ 110 VIII Time Resolved Spectroscopy ....................... 113 vi A Measurement of Relaxation rates ................ 113 B Phase Separation of Ortho— and Para-transitions ........ 117 IX Summary ................................. 121 5 Conclusion and fixture Work 123 APPENDIX 127 REFERENCES 132 vii 1.1 2.1 2.2 4.1 4.2 4.3 4.4 4.5 4.6 LIST OF TABLES List of calculated coincidences between transitions in the V3 band of 12CH3F and C0; laser frequencies studied. ............... M selection rules for various polarizations states of laser. It should be noted that the laser propagates along the Y axis and the reference plane is YZ(1r). .............................. Comparison of calculated intensities using Jones calculus for different experimental conditions. ......................... List of transitions of the 21/3 «— V3 band in 12CH3F and their frequencies plotted in this Chapter. ......................... List of transitions of the 113 band in 12CH3F and their frequencies plot- ted in this Chapter ............................. Velocity changes upon collision for V3 band transitions in 12CH3F. The QR(11,9) transition in the V3 band was pumped ............. Velocity changes upon collision for 2V3 «— V3 band transitions in the CH3F. The QR(11,9) transition in the V3 band was pumped. ..... List of transitions and their frequencies (MHz) in 13CH3F plotted in this Chapter. ............................... Summary of relative signs observed in the population- and orientation- modulated double resonance signals. P, Q, R: Branch of the transition. +, -, and 0 are for positive, negative, and no observable signal, respec— tively. ................................... viii 23 39 89 89 90 5.1 Summary of identified relaxation paths, lineshapes, relaxation times, and their effects on velocity, alignment, and orientation ......... 125 ix 2.1 2.2 2.3 2.4 LIST OF FIGURES A typical absorption line shape with a Bennett hole. The X -axis is frequency in units of MHz. Y-axis is the absorption intensity. The line shape was simulated with a Gaussian of 30 MHz HWHM and a Lorentzian of 1 MHz HWHM. ...................... A typical double resonance absorption line shape with a modulated pump beam. The X -axis is frequency in units of MHz. Y-axis is the absorption intensity. The lineshape is Lorentzian of 1 MHz HWHM. . Alignment and orientation created by polarized lasers. In (a) the dashed lines are for YX plane polarized light (0*) whereas the contin- uous line is for YZ plane polarized light ( 1r). In (b) the dashed and continuous lines are for right- (0*) and left- (0") circularly polarized pump radiation, respectively ........................ Two different saturation absorption configurations: (a) 1r pump, 1r probe; (b) 1r pump, 0* probe. It should be noted that the selection of it is arbitrary, since there is no field applied to the sample. At some places the 1r and the 0* is interchanged for the convenience of explanation or calculation. Exchanging the it and the 0* should give the same result ............................... 15 16 25 27 3.1 3.2 A C0; laser infrared microwave sideband laser double resonance sys- tem. The two C02 lasers are frequency stabilized to the fluorescence Lamb dip of C02(FC). The sideband is generated by mixing one of the CO; lasers with high power microwaves (8 - 18 GHz) in a CdTe crystal (Mod) and its intensity is stabilized by monitoring its output (RD). Since the sideband is amplitude modulated at 33 kHz, detected signals (SD,RD) always get demodulated at 33 kHz first by L1 or L3. The output from L1 is double demodulated (L2) at the chopping frequency (~ 100 Hz). The signal from L2 comes therefore purely from double resonance effects. Since the pump laser modulated by a mechanical chopper has a horizontal plane of polarization, it can be separated from the sideband laser using two polarizers P1,P2. The use of a polarizer to separate the two laser beams allows easy and perfect alignment that is critical to the lineshape. ........................ Block diagram of the CO: laser — IMSL double resonance setup em— ploying an electro-optic modulator. When 2.1 kV is applied to the CdTe modulator, it converts the YX plane polarized (1r) pump laser into right circularly polarized (0*) light. The 0+ radiation is changed back to a x-polarized laser after the rhomb (Rh) that works as a quar- ter wave plate. The laser passes a blocking polarizer (Pl) whose angle is set to x and perturbs molecules in the sample cell. If -2.1 kV is applied instead, the pump laser becomes 0* polarized and is reflected off the polarizer to a beam stop. The result is a TTL controlled op- tical modulator with it plane polarized laser pumping (perpendicular configuration). The same setup can be used to modulate 0* plane polarized pump by rotating the blocking polarizer parallel to the YZ plane (parallel configuration). ...................... xi 42 45 3.3 3.4 3.5 3.6 Diagram of the electro-optic switching system. A TTL signal controls the high voltage control circuit and applies either +2.1 kV or —2.1 kV to the CdTe housing. A YX (1r) plane polarized pump beam (PL) is either converted to right circular polarization (0*) or to left circular polarization (0') by the CdTe, depending on the polarity of the high voltage applied to it. A Fresnel rhomb oriented at 45° converts the circularly polarized beams back into either 0* or it. A blocking po- larizer (P1) whose angle is set parallel to the YX plane blocks the 0* polarization of the pump beam and passes only the 1r polarized state of the pump beam. Since the intensity of the pump beam follows the shape of the TTL signal shown in the picture, this is called intensity modulation in the text. The different polarization states of the pump laser are shown with I (1r), II (0+,0"), III (1r,0*), and IV (1r). The blocking polarizer (P1) can be rotated to obtain 0* at IV. ...... Block diagram for alignment modulation between 0* and 1r. Note: The intensities of the two 0*- and w-polarized pump beams do not change. Only the polarization state of the pump beam is switched. Therefore, the pump always creates the same holes and spikes in terms of total population while the alignment of the molecules is different. ..... (a) Alignment modulated double resonance signal of the P(6,0), P(6,1), P(6,2), and P(6,3) in the 21/3 4— V3 band of 13CH3F. (b) Power modu- lated signal. The absolute intensity of the alignment modulated signal was about 1/3 of the normal double resonance signal. It is clear that the Gaussian signals are suppressed in the alignment modulation. The z-axis is the microwave frequency in MHz used to generate the side- band laser. When the transition is observed with negative sideband, the numbers are labeled in decreasing order. .............. Modulation of the polarization states between 0+ and 0‘. Again the intensity of the pump beam stays constant, as in alignment modulation. Either a circularly polarized probe beam or a plane polarized beam can 47 48 49 be used to observe the optical anisotropy created in this pump scheme. 50 xii 3.7 (a) Intensity modulated double resonance signal. of the R(4,3) tran- 3.8 3.9 sition in the V3 band of 13CH3F. (b) Orientation modulated double resonance signal. (c) Single resonance absorption signal. The single resonance absorption signal has a Bennett hole due to the laser pump— ing. The orientation modulated double resonance signal has dispersion line shape. The horizontal axis is the (negative) microwave offset fre- quency (MHz). .............................. Experimental conditions for (a) alignment pumping: x-polarized pump, w-polarized probe; (b) alignment pumping: x-polarized pump, 0*-polarized probe; (c) alignment modulation: 1r-polarized probe, * — 1r polarized pump; (d) orientation pumping: 1r probe, 0+ pump, 0 90° polarizer; (e) orientation modulation: 0+ probe, 0+ — 0‘ pump, and (f) orientation modulation: 1' probe, 0* — 0' pump, 45° polarizer. For historical reasons (a) and (b) are also called as saturation absorp- tion whereas (d) is called as polarization spectroscopy. Experiment (f) is named circular birefringent measurement because it measures laser-induced circular birefringence. ................... A schematic of the time resolved double resonance system used in this study. The flowing gas laser (Laserl) was used to pump QR(4,3) tran- sition in the V3 band. The beam paths of two C03 lasers and the high voltage cables are drawn with thick lines. The dashed line represents 52 53 the IMSL beam path. Details of the operation are described in the text. 55 xiii 3.10 3.11 3.12 Diagram of the electro-optic switching system used for time resolved measurement. A TTL signal controls the high voltage control circuit and applies either +2.1 kV or -—2.1 kV to the CdTe housing. A YZ(7r) plane polarized pump beam (PL) is either converted to right circular polarization (0*) or to left circular polarization (0") by the CdTe, depending on the polarity of the high voltage applied to it. A Fresnel rhomb oriented at 45° converts the circularly polarized beams back into either 0* or it. A blocking polarizer whose angle is set parallel to the YZ plane blocks the 0* polarization of the pump beam and passes only the x polarized state of the pump beam. The amplitude of the final pump beam (IV) follows the shape of the TTL signal that is applied. A 0* polarized sideband laser (SL) interacts with the sample, reflects off P2, and is monitored by the detector (SD) .......... Double resonance spectra of the QP(6,3) transition. Soft inelastic AJ = 1 collisions with a large impact diameter result in the sharp spike marked S whereas the Gaussian marked G comes from the vi- brational swapping mechanism. With sub-Doppler resolution, the two processes in the same transition can be time resolved separately. . . . Time resolved spectra of the QP(6,3) transition. G represents the signal from the Gaussian whereas S is from the spike. At time 0, the pump laser is turned off and relaxation is observed whereas at time 570ps the pump laser is turned on, and an increase in signal was observed. The difference between G and S can be seen at early time (< lOps) where the AJ = 1 process dominates ................... xiv 56 57 58 4.1 4.2 4.3 Graphical illustration of velocity distribution of molecules involved in the pump and probe. The Bennett hole can by studied by probing either the QP(4,3) or the QQ(4,3) transition while the Bennett spike can be done by using the QP(5,3) transition in 2V3 ‘— V3 band. The Bennett spike is collisionally transferred into different rotational levels and probed by four-level double resonance. It is not clear whether there exist transferred holes or not. ................... Three-level infrared-infrared double-resonance spectra of the QP(12,2) transition in the V3 band of 12CH3F; the QQ(12,2) transition in the same band was pumped by the 9P(20) 12C1603 laser. The horizontal axis is the (negative) microwave frequency (MHz) offset from the 9R(12) 130603 laser. The lower trace is the single + double resonance and the upper trace is the double resonance. ................ Three-level Infrared-infrared double resonance spectra of the QQ(11,9) transition in the V3 band of 12CH3F; the QR(11,9) transition in the same band was pumped by the 9P(22) 12C1803 laser. The horizontal axis is the microwave frequency (MHz) offset from the 9P(20) 12C1303 laser. The lower trace is the single + double resonance and the upper trace is the double resonance. The broad line was recorded after the first demodulation. For simplicity, the term single resonance signal is used to indicate this part in the text, since it is the average value of the single resonance and the double resonance. The spectrum with a sharp spike was recorded after the second demodulation. This part is called the double resonance signal in the text; it is the double resonance minus the single resonance. The area of the Bennett hole measured in the single resonance signal was ~ 1% of the total area, which implies that ~ 2% of the molecules in the ground state are excited by the laser pumping. ................................. XV 65 4.4 4.5 f 4.6 4.7 4.8 Three-level infrared-infrared double-resonance spectrum of the QQ(12,9) transition in the 2V3 4— V3 band of 12CH3F; the QR(11,9) transition in the V3 band was pumped by the 9P(22) 12C1802 laser. The horizontal axis is the (negative) microwave frequency (MHz) off- set from the 9P(36) 12C1603 laser ..................... Four-level infrared-infrared double-resonance of the QP(14,0)—Q P(14,5) transitions in the 2V3 i— V3 band of l2CH3F. The QQ(12,2) and QQ(l2,1) transitions in the V3 band, were pumped simultaneously by the 9P(20) 12C1603 laser. The horizontal axis is the (negative) mi- crowave frequency (MHz) offset from the 9P(12) 13C1603 laser. Trans- ferred spikes are seen on both the QP(14,2) and QP(14,1) transitions. (The QP(14,1) and QP(14,0) transitions are almost completely over- lapped.) .................................. Four level infrared-infrared double resonance of the QQ(9,3)-QQ(9,9) and QQ(l2,3)-QQ(12,9) transitions in the 2V3 i— V3 band of 12CH3F. The QQ(12,K) transitions are the result of absorption of the negative sideband while QQ(9,K) transitions are the result of absorption of the positive sideband, both of which are present in the probe radiation. The horizontal axis is the microwave frequency (MHz) offset from the 9P(36) 1201602 laser, negative for QQ(12,K), positive for QQ(9,K). The QR(11,9) transition in the V3 fundamental band was pumped by the 9P (22) 12C1303 laser. Calculated frequencies and relative intensities for normal single resonance spectra are plotted below the recorded spectra with + for J=9 and with O for J=12 ................... Four-level infrared-infrared double-resonance spectrum of the QR(13,9) transition in the 2V3 ‘— V3 band of 12CH3F; the QR(11,9) transition in the V3 band was pumped by the 9P(22) 12CmOg laser. The horizon- tal axis is the (negative) microwave frequency (MHz) offset from the 9P(36) l2C1303 laser ............................ A typical double resonance spectrum in the fundamental band. (QR(11,9) transition in the V3 band is shown.) ............. xvi 67 69 70 71 72 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 Comparison of observed (noisy line) and calculated (smooth line) four- level double-resonance spectrum for the QQ(9,9) transition in the 2V3 *— V3 band of 12CH3F; theQR(11,9) transition in V3 band was pumped by the 9P(22) 12C1803 laser. The horizontal axis is the mi- crowave frequency (MHz) offset from the 9P(36) 12C1603 laser. The calculated curve is the best fit to a single Keilson-Storer function + Gaussian. .......... i ....................... Comparison of observed (noisy line) and calculated (smooth line) four- level double-resonance spectrum for the same pump-probe combination and horizontal axis as shown in Fig. 8. Here, the calculated curve is the best fit to a sum of two Keilson-Storer function + Gaussian. . . . Plot of the ratio of the area of the wide spike to that of the narrow spike vs. AJ for the four-level double resonances listed in Table 4.2. . Plot of the r.m.s. change in speed vs. AJ for the molecules that con- tribute to the broad spike for the four-level double resonance transitions listed in Table 4.2. ............................ Plot of the ratio of the area of the wide spike to that of the narrow spike vs. AJ for the four-level double resonances. ........... Three-level double resonance spectra of QP(5,3) transition in the 2V3 «— V3 band while the QR(4, 3) transition in the V3 fundamental band was pumped. The intensities of both peaks were normalized. (a) 0* probe and 0* pump is broader than (b) it probe and 0* pump. Sample pressure was 19 mTorr. ......................... Three-level double resonance spectra of the QP(5,3) transition in the 2V3 +— V3 band while the QR(4, 3) transition in the V3 fundamental band was pumped. (a) 0* probe and 0* pump is weaker than (b) a probe and 0* pump. Sample pressure was 19 mTorr .......... Pump/ probe polarization dependence of three-level double resonance observed in the QP(5,3) transition, recorded with 3 mTorr sample. . . xvii 73 73 74 75 79 79 80 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 Pump/ probe polarization dependence of three—level double resonance observed in the QP(5,3) transition, recorded with 1.5 mTorr sample. . Calculated three level double resonance lineshape under (a) thin line: 0* /0* (b) thick line: 0* / 1r configurations, respectively ......... Pressure dependence of three-level double resonance observed in QP(5,3) transition. To suppress relatively slow four-level contributions, the pump laser is optically modulated at 1 kHz. ............ Four-level double resonance lineshape of the QP(6,3) transition recorded with 0* pump and (a) 0* probe (thick line) (b) 1r probe (thin line). The two peaks had different intensity values and were normalized for comparison. Sample pressure was 21 mTorr ....... Four-level double resonance lineshape observed in the QP(6,3) transi- tion at various pressures .......................... A dip observed from the QP(4,3) transition. Sample pressure was 1.5 mTorr. The skewed direction and its width are similar to the dip observed from the QP(6,3) transition. .................. Four-level double resonance lineshape observed in the QP(7,3) transi- tion. Sample pressure was 1.5 mTorr. The peak is symmetric at the top and does not show any sign of dip. ................. The QR(4,3) transition in the V3 band of 13CH3F was probed by an IMSL operating on the 9R(26) line of a 13003 laser while being pumped by another 9R(32) C0; laser. The spike under counter propagating condition is at —16339.0 MHz whereas that at -l6290.5 MHz is for the co-propagating condition. The difference between the two spikes is 48.5 MHz which corresponds to 24.25 MHz offset. ........... The QP(5,3) transition in the 2V3 i— V3 band of 13CH3F was probed by an IMSL operating on the 9P(16) line of a 13003 laser while the QR(4,3) transition in the V3 band was being pumped by another 9R(32) 003 laser. The center frequencies of the co— and counter-propagating spikes are 14596.0 MHz and 14547.0 MHz, respectively. ........ xviii 81 81 82 83 84 84 85 87 88 4.26 4.27 4.28 4.29 4.30 The QQ(l2,9) transition in the 2V3 «— V3 band of 12CH3F was probed by an IMSL operating on the 9P(36) line of a 12C03 laser while the C2R(11,9) transition in the V3 band was pumped by another 9P(22) C1803 laser. The spike under counter propagating conditions is at —9409.6 MHz whereas it is at -9361.7 MHz for co-propagating con- dition. The difference between the two spikes is 47.9 MHz which cor- responds to 24.8 MHz offset in the QR(11,9) after correcting for the Doppler effect ................................ QP(5,3) in 2V3 4— V3 of 13CH3F at 6 mTorr. The QR(4,3) in the V3 fundamental band was pumped by a 0+ 9R(32) C0; laser. Description of the experimental conditions is given in the text ............ QP(5,3) in 2V3 «- V3 of 13CH3F at 60mTorr. The QR(4,3) in the V3 fundamental band was pumped by a 0+ 9R(32) C03 laser. The exper- imental arrangement is described in the text ............... The frequency of the 0* polarized probe laser was scanned from the QP(5,0) to the QP(5,4) transitions in the 2V3 «— V3 band of 13CH3F while the polarization of the pump laser coincident on the QR(4,3) transition in the V3 band was switched between 0* and 1r. There is no sign of signal other than at the frequency where the ordinary spike is observed, which implies that only the spike changes its orientation to follow the change in polarization of the pump beam ........... The frequency of the probe laser was scanned from the QP(6,0) to qP(6,3) transitions while (a) the polarization of the pump laser was switched between 0* and 1t and (b) the pump beam was intensity modulated by blocking its 0* component. Signals from the Gaussian part are apparent in (b) intensity modulation, but not in (a) alignment modulation. ................................ xix 93 95 95 97 98 4.31 4.32 4.33 4.34 4.35 4.36 Photo-selected VCD observed from QP(5,3) in the 2V3 +— V3 band of 13CH3F while the QR(4,3) in the V3 band was pumped. (a) A 0* probe was used while the polarization of the pump beam was modulated between 0+ and 0". (b) A wire-grid polarizer was put in front of the sample cell to create a plane polarized probe beam. Other conditions were exactly same as in (a). (c) The polarizer used in (b) was moved to in front of the detector. The probe beam is circularly polarized while interacting with molecules but plane polarized at the detector ..... A dispersion signal observed in the QP(5,3) transition in the 2V3 4— V3 band of 13CH3F while the QR(4,3) transition in the V3 band was pumped. Two polarizers were used for the probe beam (one to gen- erate a plane polarized probe beam before the sample cell, the other after sample cell set to 45° relative to the first polarizer) while the polarization of the pump beam was modulated between 0+ and 0’. . Photo-selected VCD observed in the QP(6,3) transition in the 2V3 4— V3 band while the QR(4,3) transition in the V3 band was pumped. A 0* probe was used while the polarization of the pump beam was modu- lated between 0+ and 0". ........................ A dispersion signal observed in the QP(6,3) transition in the 2V3 i— V3 band of 13CH3F while the QR(4,3) transition in the V3 band was pumped. Two polarizers were used for the probe beam (one to gen- erate a plane polarized probe beam before the sample cell, the other after the sample cell set to 45° relative to the first polarizer) while the polarization of the pump beam was modulated between 0+ and 0'. . Intensity modulated double resonance signal observed in the QP(6,3) transition with the same conditions as in the previous figure. A 0+ probe was used while the power of the it pump beam was modulated with a mechanical chopper. ....................... Intensity modulated spectrum of the QP(5,3) transition in the 2V3 «— V3 band while the QR(4,3) transition in the V3 band was pumped ..... XX 100 103 105 106 4.37 4.38 4.39 4.40 4.41 4.42 4.43 4.44 Intensity modulated spectrum of of the QP(5,3) transition in the 2V3 +— V3 band while the QR(4,3) transition in the V3 band was pumped. A 1r probe was used with a analysing polarizer (0 = 45) in front of the detector ........................ I ........... Orientation modulated spectrum of the QP(5,3) transition in the 2V3 «— V3 band while the QR(4,3) transition in the V3 band was pumped. A it probe was used with a analysing polarizer (9 = 45) in front of the detector ................................... The (v, J, K) = (2,4,3) 4— (1,5, 3) observed in double resonance: (a) intensity modulated signal; (b) polarization modulated signal; (c) sig- 107 107 nal recorded after the first demodulation during polarization modulation. 109 The (v,J, K) = (1,5,3) +— (0,4, 3) observed in double resonance: (a) intensity modulated signal; (b) polarization modulated signal; (c) sig- nal recorded after the first demodulation during polarization modulation.110 The (v, J, K) = (2, 11, 3) i— (1,10, 3) observed in four-level double res- onance under conditions of polarization modulation. The sign changes from positive to negative .......................... The (v,J, K) = (2,4, 3) 4— (1,5, 3) transition of 13CH3F was probed by an IMSL while (v,J, K) = (1,5, 3) «— (0,4, 3) was pumped (a) by polarization modulation (PM) between 0* and 0‘ (b) by intensity modulation (IM). In both cases the pump laser was reflected back into sample cell to record both of the spikes occurring under co- and counter-configuration ............................ The (v, J, K) = (1,5, 3) 4— (0,4, 3) double resonance signal recorded (a) after the first demodulation from L1 (b) after double demodulation from L2. .................................. The (U, J, K) = (2,4, 3) 4— (1,5, 3) double resonance signal ....... xxi 110 112 112 113 4.45 4.46 4.47 4.48 4.49 4.50 4.51 Time resolved spectra of the (transferred) spike of QP(4,3), QP(5,3), QP(6,3), and of QP(7,3) transitions in the 2V3 ‘— V3 band. The QR(4,3) transition in the V3 fundamental band was pumped on at 3 psec. The transient digitizer was pro-triggered to record starting values ...... Time resolved signal of the QP(6,3) transition at (a) 20 mTorr (b) 40 mTorr ................................... Time resolved signal of the QP(6,3) transition. (a) when the pump laser is turned on; (b) when the pump laser is turned off. The measured ON signal is subtracted from a constant to have common starting level. 115 The on-stage time response is faster and more intense than the off-stage.117 Time resolved signals of (a) sharp spike (b) Gaussian + broad spike observed in QP(6,3) transition (c) Gaussian observed in QP(6,2) tran- sitions .................................... Double-resonance spectrum of QP(22,K) transitions in the 2V3 «— V3 band of 13CH3F upon which calculated frequencies and intensities are superposed. It is clear that the K = 3n transitions are stronger than calculated compared with K 74 3n transitions. The pump transition is QR(4,3) in the V3 band and the pump source is a 9P(32) 12C1603 laser. The probe source is the negative sideband on the 10R(14) l2le303 laser; the horizontal axis is the microwave frequency offset. ...... Time resolved spectra of K=3 and K=4 transitions in Figure 4.51. The K=3 transition is stronger and faster than the K=4 transition ..... Calculated output vs. phase setting of the lock-in amplifier for the peak double resonance signal for the QP(22,3) (thin line) and QP(22,4) (thick line) transitions shown in Figure 4.49 ............... xxii 117 119 119 120 4.52 Double-resonance spectrum of QP(22,K) (K=0..9, left to right) transi- 5.1 tions in the 2V3 «— V3 band of 13CH3F observed with the 110° phase. (The calculated spectrum is drawn with vertical bars for comparison.) The pump transition is QR(4,3) in the V3 band and the pump source is a 9P(32) 12C1603 laser. The probe source is the negative sideband on the 10R(14) 12C1603 laser; the horizontal axis is the microwave frequency offset ............................... Application of double resonance in remote sensing. By changing the incident angle of the pump beam, only a selected portion (a, b, or c) of the probe beam path is affected and its signal can be recovered after the double demodulation. ........................ xxiii 121 Chapter 1 Introduction In saturated absorption spectroscopy or in polarization spectroscopyl sub—Doppler resolution is achieved by probing molecules in a selected velocity group affected by a pump laser. The earliest optical saturation spectroscopy experiments (Lamb-dip spectroscopy), “discoveredm‘4 soon after the operation of the first gas laser by J avan in 1961,5'6 provided means for finding the center frequency of an inhomogeneously broadened line and for removing the inhomogeneous linewidth by responding selec- tively to the transition frequency of the gas media (atoms or molecules) at rest. The frequency of the laser can be locked electronically to the center of the dip and this technique continues to be used to stabilize laser frequencies. Later improvements in the experimental design of saturation spectroscopy exper- iments resulted in exciting new experiments to be performed. The incorporation of a sample cell inside the laser cavity allowed a wider variety of molecular species to be studied, even with fixed frequency lasers.7 Then, the cell was put outside of the cavity in an attempt to perturb the laser as little as possible and to study as much physics as possible.8 The extracavity techniques of saturation spectroscopy are complicated by the fact that an output beam reflected back into the laser cavity tends to destabilize the oscillation frequency. Some sort of isolation is necessary between the laser and the experiment. In the earliest stage, and still one of the most widely used owing to its simplicity, the isolation was achieved by crossing the pump and probe beams at a small angle in the sample cell. The finite angle 0 between the interacting beams introduces a residual linear Doppler width of roughly 000(5):) = Doppler width) in the resonance line width. The interaction length of the beams is also limited. But, the nonlinear resonances can be conveniently detected by chopping the pump beam and detecting the resulting modulation of the transmitted probe intensity.8 In our laboratory, Brewster angle windows were used at first to separate a plane- polarized probe beam from the pump beam whose polarization was orthogonal to the probe beam. Even though this procedure provided truly counter-propagating beams, the number of added optical components necessary to achieve the separation made the technique inferior compared to the design using two polarizers introduced in this study.”*10 This design is described in Chapter 3. Fewer optical components and the use of polarizers allowed an observation of a splitting of the Bennett spike in infrared double resonance experiments.“12 Later the use of a partially transmitting mirror was introduced,12 in which lasers with arbitrary polarization can be used either for pump or for probe. This design is suitable for a variety of saturation spectroscopy experiments, in which the polarization information can be used to obtain information about spatial orientation of molecules or to aid interpretation of observed spectra. Improved spectroscopic precision, better measurements of fundamental constants 13‘ 15 and new studies of collisional dynamics were only some of the and of basic units, exciting possibilities opened by saturated absorption and related techniques. Experi- mental and theoretical developments rapidly succeeded one another, making satura- tion spectroscopy now one of the most highly developed and best-understood non- linear techniques. A number of books, review articles, and original sources elucidate the many phenomena expected and observed."""“"19 As pointed out by Levenson'f0 saturation techniques have potential applications related to high-resolution spectroscopy and well-defined wavelength and frequency standards such as in computer memory and data storage by allowing at least 10,000 times higher storage density than the best video-disk technology, in optical transistors, in adaptive optical devices which can transmit high power laser beams through the atmosphere or to produce a pattern, or in remote sensing where spatial resolution can be achieved by crossing the pump and probe beams at different angles. A thorough understanding of the basic principles of various saturation phenom- ena may open exciting new techniques and is the subject of this thesis, which also deals with collisional energy transfer processes that are vital in global simulations such as global warming and ozone depletion. Collisional processes are studied not only because of the interest in the nature of the collision process and intermolecular potentials, but also because of the vital need for well-characterized line shapes and line widths for recovery of information in remote sensing experiments.“'23 In the next few sections a brief history and review of saturation absorption spec- troscopy, polarization labeling, and time resolved experiments is presented. Relevant theories, experimental designs, and the results of this study are discussed in Chapters II, III, and IV. A summary of this dissertation is presented in Chapter V along with the suggestions of future works to be done. 1. Definitions As new experimental techniques have developed, different names were devised to designate each experiment. Unfortunately in the many possible combinations of the polarization states involved in double resonance experiments, the terms saturation absorption spectroscopy or polarization spectroscopy have been used to describe many different types of experiments mainly because different experiments were performed in different groups. It was understood that the term saturation absorption spectroscopy represents experiments in which the total population changes induced by a pump are of interest, whereas for experiments in which the pump-induced optical anisotropy was of interest, polarization spectroscopy was used. Many different but confusing names were also used by different authors to describe different (sometimes the same) experiments and added more confusion to the polarization related experiments. I have tried to sort out the names and assign reasonable names for each experi- ment based on either the experimental technique or the source of the signals recorded. From the laser’s point of view the double resonance experiments can be divided into two categories: pumping and modulation. In the pumping experiments the laser prop- erties are kept constant, whereas in modulation experiments some characteristic of the laser is switched on and off to record the difference. Modulation experiments are further divided into two categories: intensity modulation and polarization mod- ulation. In intensity modulation the intensity (power) of the laser is modulated by a chopper or any other means, whereas in polarization modulation the polarization state of the laser is modulated by an electro-optic or an acousto-optic modulator. The polarization state of the laser used in either pumping or modulation can be either plane-polarized or circularly-polarized. Since a plane-polarized pump induces optical anisotropy“ as well as total population changes, we use the term alignment pumping when the optical anisotropy is of interest. Similarly, orientation pumping is used when the laser is circularly polarized. If the total population changes are of interest or if the source of the pump is not polarized, we have population pumping. Pumping experiments may be combined with a modulation technique to record the difference in absorption with and without pumping. In this case, a prefix intensity modulated will be added to the pumping experiment as e.g., intensity modulated alignment pump- ing. Similarly a plane- or circularly-polarized pump can be employed in polarization modulation experiments and we will call it alignment (orientation) modulation if a plane- (circularly-) polarized pump is used. ‘ Based on the characteristics of the signals recorded, saturation absorption (popu- lation), linear dichroism, linear birefringence, circular dichroism, or circular birefrin— gence measurement (or spectroscopy) seem to be useful names also. In many places, polarization spectroscopy was used to represent any of the polarization related exper- iments. Many of these definitions are mentioned repeatedly at various places in this thesis whenever they seem to be appropriate. “Terms such as alignment and orientation are described in Chapter 2. II. Saturation Absorption Spectroscopy A. Lineshape Problem in Saturation Absorption Spec- troscopy In spite of many years of effort, the present understanding of the line shapes ob- served in saturation spectroscopy is not complete. Even when collisions and power broadening are absent and long-lived states interact with a perfectly uniform beam with plane wave fronts, the line shapes remain more complex than expected. Numer- ous works have been published and others are still in progress. A list of problems and questions raised by Levenson20 is quoted directly to show the complexity of the lineshape studies at the highest resolution (10 kHz). The saturation resonances result from molecules emitting a photon in one direction and absorbing one propagating in the opposite direction. Either event can occur before the other, but the molecule recoils as the result of momentum transfer from the photon field. The result is a recoil splitting of the saturation resonance. When the intensity of the interacting beams is not uniform or the wave fronts are not plane, transit time effects alter the line shape. Time- dependent and time-independent optical Stark shifts lead to asymmetries and reduce the recoil doublet splitting. Collisions cause pure dephasing and thus broaden the resonances, but they also alter molecular trajecto- ries without damping the oscillations. Weak velocity changing collisions broaden the saturation resonances by increasing the width of the hole in velocity space. Strong velocity changing collisions remove molecules entirely from the resonant velocity groups thus adding a “lifetime” broad- ening. Finally, no laser is perfectly monochromatic. What effect do the inevitable phase and amplitude glitches have on the ensemble? How much of its history does an ensemble remember? Could there perhaps be a better means of determining the center frequency of a Doppler-broadened transition than saturation spectroscopy? Table 1.1: List of calculated coincidences between transitions in the V3 band of 12CH3F and C03 laser frequencies studied. Transition“ Frequency; Intensityc Laser Line U1 — V0a UQ(12, 2) 3138394001 0.1027 1""0603 9P(20) -39.60 °R( 11, 9) 3199858806 0.3658 120180, 9P(22) 26.10 03(31, 4) 3270807410 0.1279 120802 9R(10) 22.30 “ Transition in the V3 band. 5 Transition frequency in MHz. Calculated from the constants in Ref. 25. ° Calculated intensity. “ Laser frequency minus calculated center frequency of the transition in MHz. Constants for the laser frequency were taken from Ref. 26,27. At Michigan State University we have been working on theories of three-level dou- ble resonance and collision-induced four-level double resonance lineshapes at resolu- tions of ~ 100 kHz. We now have theories and computer programs that can calculate double resonance lineshapes for all of our experimental conditions. Although the the— ories and programs are constantly being updated as new experimental observations are made, they now seem to agree with nearly all of the experimental observations. I have carried out a series of studies of double-resonance effects in 12CH3F and 13CH3F. The first of these studies was an analysis of transferred spikes in 12CH3F. The main reason for undertaking a study of the normal species of methyl fluoride was our desire to attempt double resonance measurements in the V3 + V3 «— V3 band, for which precise spectroscopic constants are available only for the C-12 species.“ It seemed necessary to gain some experience with the strength of the double resonance effects in the stronger 2V3 o— V3 band before attempting the more difficult measurements in the V3+V3 4— V3 band. In addition, the C-12 species has convenient coincidences between C03 laser lines and transitions in both the ortho species (I: = 3n) and the para species (It 3:6 3n). The familiar Q(202,2) transition has been used many times for infrared pumping for double resonance and far-infrared laser generation. But this work may be the first extensive use of the C’R(11,9) coincidence for infrared pumping. Details concerning the laser coincidences in 12CH3F are shown in Table 1.1. The second part of this work is a more detailed study of the saturated absorp- tion lineshapes in 13CH3F previously studied by Matsuo and Schwendeman.28 Laser induced optical anisotropies and apparent splittings observed in the three. and four- level double resonance lineshapes are discussed. B. Lineshape Study of Transferred Spikes in 12CH3F State-to-state collisionally-induced transitions between molecular levels are key ingredients of energy transfer between gas-phase molecules. Information about the rates and mechanisms of such transitions is necessary for quantitative characteriza- tion of interstellar chemistry, air pollution, ozone depletion, and global warming?“23 Among the methods that have been employed to study collisionally-induced tran- sitions in the gas phase is the technique of four-level double resonance, pioneered 29—31 in the microwave region by Oka and his coworkers and subsequently extended to infrared-microwavem'“ and infrared-infrared double resonance.28"5'57 Infrared pumping has the advantage that substantial perturbations of the populations of the levels can be produced, in contrast to microwave pumping where the population changes are necessarily very small. Infrared probing also has an advantage in that Doppler effects at mid-infrared frequencies and above are many times larger than the homogeneous broadening for low-pressure gases. Therefore, four-level infrared- infrared double resonance can be used to obtain information about the changes in molecular velocity that accompany collisionally-induced transitionsffs'45 In recent communications from this laboratory the results of analyses of the line- shapes of transitions observed in infrared-infrared double resonance in 15NH3“5 and 13CH3F"3 were reported. The lineshapes were found to be adequately represented by the sum of two components, one of which is a Gaussian function whose center frequency and width are the expected center frequency and Doppler width of the transition, respectively. The second component is a nearly Doppler-free transferred spike whose lineshape is well-represented by a theoretical expression that was derived by assuming that the change in velocity of the molecules upon collision follows the prediction of a collision kernel that is the sum of two of the kernels originally intro- duced by Keilson and Storer.58 In the recent work, the double resonance experiments were carried out by pumping a single vibration-rotation transition in a fundamental band (V3 in 15N H3 or V3 in 13CH3F) by means of a single frequency C03 laser while scanning a single vibration-rotation transition in a hot band (21/20 «— V23 in 15NH345 or 2V3 +— V3 in 13CH3F2‘B) by means of an infrared-microwave sideband laser source. The advantage of this experimental arrangement is that as a result of the low rates of loss or gain of vibrational energy upon collision, the collisional effects involve al- most entirely the effective transfer of population from the upper state of the pump transition to the lower state of the probe transition. Two mechanisms were proposed to account for the double resonance lineshape. One mechanism assumes a near-resonant swapping of vibration-rotation energy be- tween colliding molecules. In this case a molecule excited by the radiation returns to the ground state upon collision with a ground state molecule that becomes vibra- tionally excited. The net result is that a molecule in the upper state of the pumped transition becomes a ground state molecule while a molecule appears in a different rotational state of the excited vibrational state. This is effective population transfer from the upper state of the pump transition to another rotational state in the ex- cited vibrational state. Since by this mechanism the molecule transferred is not the molecule pumped, the molecule probed should have a near thermal velocity distribu- tion and give rise to a Gaussian lineshape with the expected Doppler width of the probe transition. The second mechanism assumes that a molecule that was excited by the pump radiation undergoes one or more collision-induced rotational transitions to reach the lower state of the probe transition. If these transitions occur without much change in velocity, the double-resonance effect will be nearly Doppler-free and be centered near the center of the velocity group of the molecules pumped. It was found in this work, as had been determined earlier by theoretical ca.lculations,59'60 that the collision kernel for such transitions can be well represented by a sum of two Keilson-Storer kernels,58 a. narrow one to describe the results of collisions with large impact parameter and a broader one to describe the results of collisions of small impact parameter. For both ammonia and methyl fluoride, it was found that direct collisionally-induced transitions follow the A]: = 3n (n = 0 or a positive or negative integer) selection rule discovered for C3,, symmetric tops by Oka31 many years ago. The Al: = 0 spikes were narrow and increased in width as AJ = onbe - qum, increased. The A]: = :l:3 and A]: = i6 spikes were very broad, although still considerably narrower than the usual Doppler width. The widths of the transferred spikes and the resulting predicted r.m.s. change in velocity upon collision were reported for many transitions. The ratio of the area of the Gaussian to that of the transferred spikes was found to vary linearly with the inverse of the pressure and a rate constant theory was shown to account for this variation.45 C. Lineshape Dependence on the Polarization Double resonance lineshapes in saturation absorption spectroscopy have been studied in an attempt to understand optical pumping effects,61 collision dynamics,“63 28.45.6455 and relaxation paths of excited molecules and have been the subject of my merous papersdn‘m‘.’1 At very high pump intensities, absorption and emission line-shape functions are changed by the optical frequency fields and a splitting is observed. Two different physical descriptions have been used to account for the splitting observed. The strong optical field of the pump radiation creates mixed eigenstates of molecular resonant transition and radiation. The new eigenstates are shifted in energy with respect to the radiation field, thereby causing a splitting in the observed lineshape. The amount of shift is called the Rabi frequency. There exist numbers of papers describing the physics and necessary conditions for this kind of splitting.‘9'”‘78 Ingenious techniques dealing with this Rabi frequency and its application have resulted in fruitful measurements of related constants."°'81 Both “AC Stark” effect and “optical Autler-Townes” effect were used to describe this phenomenon. Another physical picture that can lead to the splitting (strictly speaking this should be called a dip rather than splitting) is called velocity selective optical pump- ing in which molecules in a selective velocity group in the ground state are pumped 10 to the second excited state by two-photon transitions. Since the population dip of the Bennett hole at the ground level also appears in the second excited level, scan— ning a probe which sees the difference in population between the second and the first excited level will lead to a dip at the center of the Bennett spiked“61 The following arguments were added in proof to support this explanation; (1) velocity changing col- lisions destroy the splitting; (2) longer transit time creates bigger splitting; (3) certain time-delay is required to form the splitting; and (4) the experimental conditions are different from those required for the observation of the AC Stark effect. III. Polarization Spectroscopy Polarization spectroscopy1 is an important variation of saturation spectroscopy, useful when the coupled energy levels are spatially degenerate. In polarization spec- troscopy, the pump wave is polarized in such a way that it excites preferentially different components of transitions with equal frequency. As a result, the polariza- tion state of the probe beam is altered by the anisotropy induced by the pump beam. The signal probed in polarization spectroscopy depends on the difference in absorp- tion constants and/or refractive indices for the two polarization components of the probe beam. An important result is that the polarization signal shows a Doppler-free line profile. A detailed description of polarization spectroscopy is given in Chapter 2. A slightly different type of polarization technique which is a combination of po- larization spectroscopy1 and lower level labeling“3 -polarization labeling spectroscopy— has been developed to simplify complex spectra.84 A circularly polarized pump wave is tuned to a transition. Circular dichroism and birefringence appears on transitions coupled to the one that is pumped. This anisotropy is usually detected using a lin- early polarized probe and a crossed (or nearly crossed) polarizer before the detector. Polarization labeling has been used successfully to simplify the spectra and identify the origin of transitions in Nag,85 in 082,86 and Li3.87'88 It is well known that polarized laser radiation can create spatially oriented molecules.“"9 Consideration of this polarization on the lineshape has been the sub- ject of many papers."°"“"°"'90 Bain and McCaffery91'9‘ derived expressions for laser 11 fluorescence polarization following excitation by linear or circularly polarized light. Amino 5'96 calculated the velocity selective optical pumping (VSOP) line shape including collision effects. Naka.yama9"‘101 dealt with linear and circular optical anisotropies induced in polarization, VSOP, and saturation spectroscopy. Gawlik et al.102'm3 reported observation of a splitting of the Na D1 line is the result of the .104 observed a nonstationary effect in velocity-selective optical pumping. Kim et a1 polarization-modulated optical signal of Na. All of this work involved electronic tran- sitions in atoms or simple diatomic molecules. This thesis presents the first report of polarization effects in vibration-rotation spectroscopy. IV. Time Resolved Spectroscopy Although a number of time-resolved experiments have been extensively used to study relaxation processes,55'1°5'115 there still remain questions to be answered at the level of sub-Doppler resolution. From the sub-Doppler infrared-infrared double resonance lineshape experiments described in this thesis and those performed previ- ”"5 we learned that there exist at least three collisional relaxation processes in ously, pure gaseous samples. The three processes have distinct selection rules and relaxation rates, therefore contributing to different portions of the observed lineshape; 1. AJ = in,AK = 0; sharp spike CH3F(v,J, K) + CH3F —» CH3F(v, J :l: n, K) + CH3F 2. AJ = :En, AI: = 3n; broad spike CH3F(v, J, k) + CH3F —+ CH3F(v, J :l: n, k :1: 3n) + CH3F 3. vibrational swapping; Gaussian CHaF(1,J,K) + CH3F(0, J’, K’) -+ CH3F(0, J”, K”) + CH3F(1, J’”, K’”) It is a still an unresolved question whether the sharp spikes observed at levels for which n is large are the result of a series of consecutive AJ = 1 collisions or a single or a few AJ = n collisions. 12 According to microwave-microwave double-resonance experiments, when the equi- librium population of molecules in the ground vibrational state is disturbed, as by interaction with powerful microwave radiation, there are selection rules governing the collisionally-induced rotational energy transfer that leads to a return to equilibrium.31 The strongest of these selection rules for molecules of C3,, symmetry is that upon col- lision the ortho (k = 3n in vibrational states of A symmetry, where n is a positive or negative integer) or para (10 76 3n) symmetry of a molecule is unchanged. There is good theoretical reason for this finding, based on the difficulty of changing the nuclear spin state of a molecule as a result of collision.31 Evidence for this ortho 74» para selection rule in excited vibrational states of C3,, molecules has been obtained by Harradine et al. in CDF352 and from this laboratory in ‘5NH3,‘5 13CH3F28 and in the present work. As still further evidence for a AI: = 3n rule, it has been shown that it is possible to make a partial ortho-para separation in a sample of 13CH3F molecules by the technique of light-induced drift in which a vibration-rotation transition is irradiated slightly off resonance by a moderately strong infrared laser.“°"2° The ortho-para separation requires that molecules retain their symmetry after many collisions. Chapter 2 Theory General understanding of the broadening mechanisms in the spectral line is necessary to understand saturation absorption spectroscopy or polarization spectroscopy. In the first section of this chapter, a variety of line broadening mechanisms are discussed. Then, definitions such as a laser burned hole (Bennett hole), polarization, alignment, orientation, and a few related theories are discussed in subsequent sections. I. Line Broadening The interaction of a molecule with a radiation field does not occur at the single sharp frequency 0“, but is instead broadened by a variety of mechanisms to give a res- onance line shape with some finite width (1.". Homogeneous or Lorentzian broadening gives rise to a line shape of the form 93.. (w — ('2)2 + Q?” (21) a(w) = 0., where 010,02, 0, and Q", are the peak absorption intensity, probe beam frequency, transition center frequency, and half-width at half-maximum (HWHM), respectively. Lorentzian broadening arises from radiative decay (natural broadening), collisions, or power-broadening resulting from saturation by high-intensity radiation. “In this thesis 0 is used for a fixed frequency related value whereas at is used for variable frequency. 13 14 Inhomogeneous broadening, arising from a distribution of resonant frequencies in an ensemble of molecules, generally has a Gaussian line shape: a(w) = cramp-("2% (2.2) In this inhomogeneously broadened line shape, different molecules are responsible for different portions of the absorption line. The absorption frequencies, however, are the same in the rest frame of each molecule. In gas-phase molecules with a Maxwell- Boltzmann velocity distribution, molecules moving away from a light source with a velocity component v absorb a frequency below that absorbed by stationary molecules due to the Doppler effect. w(v) = wo(1- v/c) where w(v), we, and c are the frequency felt by the molecule, the radiation frequency, and the speed of the light, respectively. The HWHM caused by this Doppler effect is on = fl/q/2len2/M = 3.58 x 10-7a,/T/M (2.3) Here T is the absolute translational temperature of the molecules and M is the molar mass in atomic mass units. An important difference between the two broadening mechanisms is in their re- sponse to high-intensity radiation. A monochromatic radiation source can saturate only a particular velocity group of molecules, leaving the rest unaffected; it is thus possible to “burn a hole” into a Doppler line profile. A homogeneous line, on the other hand, is uniformly affected by pumping at any point along the line shape. In this case, the effect of monochromatic pumping is to “bleach” the entire line rather than to burn a hole. II. Creation and Detection of Bennett Holes If one laser (the pump laser) is used to burn a hole in an inhomogeneously broad- ened absorption line, a second (probe) laser scanned across the absorption will detect a profile similar to Figure 2.1 - an absorption line with a hole in it. Modulating the 15 L -100 -50 50 100 °————_—— Figure 2.1: A typical absorption line shape with a Bennett hole. The X -axis is frequency in units of MHz. Y-axis is the absorption intensity. The line shape was simulated with a Gaussian of 30 MHz HWHM and a Lorentzian of 1 MHz HWHM. pump laser or employing polarization techniques can separate the effect of the hole from that of the rest of the line, yielding the narrow profile in Figure 2.2. In the most common saturation spectroscopy geometry, two counter-propagating waves of the same frequency, E(t) = %{E,e‘l(‘”‘+k”) + lips-““4”” (2.4) interact with an inhomogeneously broadened absorption line. If the saturating pump wave (19,) is much stronger than the probe amplitude(E,), the absorption and dis— persion at the probe frequency can be calculated rather simply. In the steady state, the effect of the pump beam on the population difference is given by, _ __ lzil272/7l o _ o Paa(v) - Pbb(v) '- [1 (n _ w + k”); + 73 + lxsl272/71Kpaa pbb) (25) In this equation p“(v),pu,(v) are the populations of the levels a and b, respec- tively (E. < E) and v is the axial velocity of molecules in the positive y direc- tion. (1,0), k,a:.,71, and 73 are the center frequency of the transition, probing laser 16 1 I l -100 -50 0 50 100 Figure 2.2: A typical double resonance absorption line shape with a modulated pump beam. The X -axis is frequency in units of MHz. Y-axis is the absorption intensity. The lineshape is Lorentzian of 1 MHz HWHM. frequency, magnitude of the wave vector, Rabi frequency of the saturating beam, population relaxation rate, and coherence relaxation rate, respectively. For molecules moving with axial velocity v in the positive Y direction, the detuning from the pump frequency is A=Q-w+h and the Rabi frequency of the saturating laser is $0. = [lab - E./h where E, is the electric field of the saturating laser. All of the terms have been written here in circular frequency units, but a: has been used instead of V to clearly distinguish from velocity v. 17 III. Lineshape Study of Transferred Spikes The lineshapes of the three-level double resonance spectra were fitted by least squares to a theoretical lineshape that was calculated by solving the density matrix equations for a three-level system (the algebraic solution reported in Ref. 121,11 was used). The three-level fitting program includes provision for summation over the pro- jection of the angular momentum (mh) along the space-fixed axis and for numerical integration over the component of velocity in the direction of the radiation. The program also accommodates either co—propagating or counter-propagating geometry and all four of the possible arrangements of energy levels for three-level double reso- nance. For the summation over m states, the program assumes that the only effect of changing the radiant power of the probe beam is to change the overall intensity. Thus, as shown in the Appendix, only one three-level calculation is required for each possible m if the space-fixed Z axis is assumed to be parallel to the electric field of the pump radiation. Details concerning the three-level calculation and some results are given in Ref. 11. The fitting routine adjusts the center frequency of the probe transition, the vibrational contribution to the Rabi frequency, the relaxation rates for the populations and coherence, the overall amplitude, and the background of the spectrum to provide a best least-squares fit to the observed spectrum. The lineshapes of the four-level double resonance spectra were fit by least squares to a theoretical lineshape that was derived in Ref. 45. In that work, however, only the shape and not the overall amplitude of the lineshape was derived. In this work, in order to lay the foundation for more careful intensity and lineshape studies, we rederive the four-level lineshape equations. The theoretical relations necessary for comparative intensity measurements are given in the Appendix where it is shown that the spectrometer output for four-level double resonance is AS. = Cu.S,,.AJ';, (2.6) in which 16x’p3N C — 0101 (T) . (2.7) 18 In the Appendix, Eq.(Al4), it is shown that the constant C may be determined by analysis of the lineshape of a three-level double resonance recorded under the same conditions as the four-level lineshape. In Equations (2.6) and (2.7), A34 = the spectrometer output with the pump beam on minus the output with the pump beam off; Va = the center frequency of the probe transition; $1,. = the linestrength of the probe transition for plane-polarized radiation summed over the space-fixed axis m components (expressions for SJ). are given in E(14411)); G = the spectrometer gain factor; 1., = the intensity of the incident probe beam; 1 = the absorption path length; N = the number of absorbing molecules per unit volume in the lower level of the pump transition; p” = the vibrational contribution to the transition dipole moment for v = 2 «— 1. Finally, A331,, the integral of the difference in the reduced value of the imaginary part of the off-diagonal density matrix element over the velocity in the direction of the probe beam for the probe transition, is taken to be the usual low power (:ch < 73) expression for a two-level lineshape, “i _ °° Ad’b’a _ ’72 0° (Apaa(vv) "Apbb(vv)) A0,, _ l... the dv, _ 2 m (u—u.,— kv,)3+7§ d0, (2.8) Here, an... = p5.E°/h, where p5. is the transition moment for the probe beam; E“ is the probe beam electric field; 73 is the coherence relaxation rate for the probe transition; V and k are the frequency and the magnitude of the wave vector for the probe beam, respectively; and N Ap“(v,)dv, and N Apu,(vy)dv, are the pump on minus pump off populations for the lower and upper levels, respectively, of the probe transition for molecules with velocity component in the direction of the probe beam between vv and vy + dvy. To simplify Eq.(2.8) we make two assumptions. First, we assume that the pump modulation rate is too fast for vibrational relaxation, so that Apu, is negligible if level 19 b is in v = 2. Then, we assume that the spectral width of Apaa is large compared to 73 so that Ap“ may be removed from the integral to give Ad'b'a = nApaa([V - Vo]/k)/2k. (2.9) To obtain an expression for Apa. we write rate equations for p“ = dpaa/dt and 3,... = dpm/dt in which level n‘is another rotational level in v = 1. A“ = "Aoapas ‘l' Aaepee "l’ 2 Aanpnn (2~10) [Inn = "Annpnn + Anapaa + Anepee + Z Ann’Pn’n’ (211) n’#n In these expressions, level e is the upper level of the pump transition and the A,‘.‘ are scalar rate constants, but the Aij for 2' ;£ j are integral operators, so that for example, A..p.. = f: A..(v..v;)p..(v;)dv;. (2.12) In the steady state, the time derivatives vanish, so that p... = Ag: {3...}. +2A..p..] (2.13) and Pnn = «4,7,1 [Anapaa + Amp“ + a: Ann'pn’n’] . (2-14) After substitution from Eq. (2.14) into Eq. (2.13), Pas = 14:31 { [Ace 'i" Z 14;: AanAne] Pee "l’ 2: A;:AanAnaPaa “I" Z 14;; AanAnn’Pn'n'} (215 n fl n¢n' This process can obviously be repeated indefinitely, but, for simplificity of writing, we choose to stop the iteration after one more collision by using, on the righthand side of Eqs. (2.13) and (2.14), the approximations, Pas g A;:Aeepee (216) and pain! g A;,L, An'epee, (2.17) 20 in which case Pas = Asepee, (218) }.(2.19) A;: A...A;,} A...A;,;.An.,(vy, 3;) = l ’ I ’ II I m A A A ' ' // Aan(vm vJ)Ann’(v;’3U;’)Ante(vy,,U;)d‘l);dy . (220) where the effective collision kernel A“ is n’ #n A“ = A;; {AM + Z A..A;,} [AM + ism/1;“1 A... + Z A...A;.1..A,.., The products of operators are defined such that, for example, The effective collision kernel A... may in principal be calculated from extensive information about the potential functions for collisional interactions. We choose to try to express A... as a sum of simple collision kernels of the form introduced by Keilson and Storer.58 To this end we write lanolin 1);) = Z Advil, UL) = E(Az/fian-(w-ww’m? (2.21) where a.- = (1 — 3.3/M)”2 in which u2 = 2k3T/m with 103 the Boltzman constant, T the absolute temperature, and m the molecular mass. The constant 6.- determines the velocity—changing effect of the collisions. For collisions defined by a single kernel 11., [ids/2 may be shown to be the r.m.s. change in velocity upon collision."’8 We show evidence below that in CH3F the lineshapes of the collision-induced double resonance may be satisfactorily represented as a sum of three terms of the form in Eq.(16). In one of these terms 6.- is the limiting value, fl.- = u, in which case a.- = 0. This term is interpreted below as arising from collisionally-induced vibrational energy swapping (V — V transfer) in which a vibrationally-excited molecule exchanges vibrational energy upon collision with a ground state molecule. With the representation just given for A... Apes = :(Ai/fifl) I: e-(v'-aw;)2m?APee(v;)dv;n (2°22) 21 in which Apee(vy) is the pump on minus pump off difference in the population of the upper level of the pump transition for vy between vy and v, + do... For this quantity, we use the usual saturation formula for two levels with m degeneracy, (1 - 5) (72/702:2 amid“): A cc = m e 2.23 p (vy) Zfiu Zn: (”in " ”or + krvvy + 73+(72/71)312n ( ) In this expression, b = ezp(-hVo,/IcBT) is the Boltzmann factor for the upper state of the pump transition whose center frequency is V..,; 71 and 73 are population and coherence relaxation rates, respectively, for the pump transition; V, and k, are the fixed frequency and the magnitude of the wave vector of the pump laser; and 3:... is the Rabi frequency for the m component of the pump transition. We assume Am = 0 selection rules for the pump, so that 3:... = (E;/h)(0p/6Q), < 0|Q|1 >< J’km|zz|ka > (2.24) in which 0 z, is the direction cosine between the space-fixed direction of the electric field E; of the pump radiation and the molecule-fixed symmetry axis. The induced population Ape: is calculated at intervals in v, and the integral in Eq.(2.22) is per- formed numerically. If both sides of Eq.(2.22) are integrated over v... it is found that 3 Am=2fl_ 0%) i=1 in which A?“ is the total relative pumped population of level a, the lower level of the probe transition, and ’53 = 43A?“ (2.26) in which AI)... is the total relative pumped population of level e, the upper level of the pump transition. Thus, A? is the ratio of the population of molecules that reached state a by the ith mechanism to the total pumped population of molecules in state e. By recasting Eq.(5),(6), and (8)—(l4) in terms of rate constants for the total population, irrespective of velocity, an interpretation may be given for the A? in terms of ratios of rate constants. Thus, if 7.... is the rate constant for loss of population from 22 state n and 7..... is the corresponding constant for collisionally-induced transitions from state n to state m, 53. = —7¢mfiaa "l' Vaefiee + Z'hnfinn (2-27) 73 and firm = —7nnfinn + 7nap_aa + 7nefiee + z: 7nn’l3n'n“ (2'28) n’¢n Manipulation of the 7’s in much the same way as the collision kernels earlier leads to the result, [-500 = 1:: pee (229) in which To: = Tee '1“ E 70137;: 7ne '1' 771673-3170: + Z 7nn’7'TILI7n’c . (2.30) n n’¢n Clearly, [Tao/fie. is the ratio of the effective rate constant for transitions into state a from state c, with any number of intermediate states, to the total effective rate con- stant for loss of population from state a by any mechanism. Comparison of Eq.(2.29) to Eq.(2.18) and consideration of Eq.(2.25) and (2.26) then shows that A? may be viewed as the ratio of the effective rate constant for transitions from state e to state a by mechanism i to the total effective rate constant for loss of population from state a by any mechanism. IV. M Selection Rules The M quantum numbers are associated only with the e*‘M¢ dependence of the wave functions in the integral / f / ammo. ¢)l7°E¢an'(",9, ¢)r’dr sin 0d9d¢ (2.31) where [i = r sin 0 cos 455+ r sin 0 sin 0337+ r cos 02'. The three components of the electric dipole moment can be associated with three polarizations of the light wave. If the 23 Table 2.1: M selection rules for various polarizations states of laser. It should be noted that the laser propagates along the Y axis and the reference plane is YZ(7r). Polarization AM 0* :l:1 x 0 a" —1 0+ +1 incoming radiation is linearly polarized, E“ = E2, with the electric vector coincident with the z axis defined, then there is no <33 dependence in the [I - if part of the integral and M’ = M in order for the integral to be nonzero. Therefore the selection rule is AM = 0 for a 1r polarized light. For right circularly polarized light (0*) where E = E(i + iii), the dot product is [I - E1 = r13 sin 9(cos d) + isin d2) = r sin 0e“ (2.32) and the integral / e‘M‘e+‘¢e“M"d¢ (2.33) is nonzero only if M - M’ = -1, so that AM = +1; similarly, for left circularly polar- ized light (0"), AM = -1. For a": linearly polarized light obviously the selection rule is AM = :l:l. Table 2.1 summarizes the M selection rules for different polarization states. V. Alignment and Orientation When a single rotational level in an array of molecules is excited by highly polar- ized laser radiation, a non-uniform distribution of M states is created. The polariza- tion of such an array may be completely described in terms of the spherical tensor moments (or state moments), ”pg, of the density matrix. H the space-fixed z axis is chosen as the symmetry axis, only the Q = 0 components of ”pg survive, and the density matrix becomes diagonal and thus the state moments can be related to the occupation numbers of individual m levels. The three tensor moments of relevance 24 in single photon experiments are the population, “/23, the orientation, ”p3, and the t, J" p3.91‘9‘"” They are related to the individual density matrix elements alignmen by: J J K J] K 1.] = 2.34 p0 2“ (M —M 0) pm" ( ) J J M -M Molecules pumped by a polarized laser are aligned or oriented depending on the in which ( 1;) is the 3j symbol. polarization of the laser. A typical double resonance technique utilizes two linearly polarized lasers which are orthogonal to each other. If a plane polarized pump excites the R(O) transition shown in Figure 2.3, for example, it creates an unequal population of the [MI levels in the excited M degenerate state. This unequal population distri- bution in |M| sublevels is called alignment. It should be noted that the alignment created by a parallel pump (continuous line in (a), AM = 0) is different from another alignment created by a perpendicular pump (dash line, AM = :lzl). If a circularly polarized light is used for pumping, the selection rule is AM = +1 for right-circularly polarized (0*) pump and AM = —1 for left-circularly polarized (0") pump. The unequal population of M sublevels in this case is called orientation. Align- ment modulation is used to describe experiments where only the alignment of samples are modulated while the total population is kept constant whereas orientation mod- ulation is used when only the orientation of molecules is changed. Aligned samples are polarized since the populations of different |M| levels are unequal. In addition an oriented sample is magnetized because the population of +M and of —M are dif- ferent. Figure 2.3 and Table 2.1 show the different M selection rules under different conditions of the polarization state of the pump. VI. Absorption and Dispersion When an electromagnetic wave passes through a medium with refractive index n, not only the wave amplitude decreases (absorption) but also the phase velocity changes from its value c in vacuum to v = c/n (dispersion). The refractive index n depends 25 +1 (1,M) -1 0 +1 7— (JaM)=(0v0) ' (a) alignment (b) orientation Figure 2.3: Alignment and orientation created by polarized lasers. In (a) the dashed lines are for YX plane polarized light (0*) whereas the continuous line is for YZ plane polarized light ( 1r). In (b) the dashed and continuous lines are for right- (0+) and left— (0") circularly polarized pump radiation, respectively. on the frequency w of the electromagnetic wave and is related to the absorption by the Kramers-Kronig relationships; n(w)= -— :1::—,-_—(wldw’ (2.35) a(w)= l j: :T—(f'Lw'. (2.36) A homogeneously broadened absorption lineshape 18 a Lorentzian whereas a dispersion lineshape can be obtained for n(w). VII. Optical Anisotropy There are two kinds of optical anisotropy: circular and linear. Circular opti- cal anisotropy consists of circular dichroism (Aac = or” — a‘) and birefringence (Ana = n+ — n") , which are differences in the absorption coefficient and the refrac- tive index, respectively, between right- (0*) and left- (0') circularly polarized beams, respectively. Linear optical anisotropy consists of linear dichroism (AaL = a"* - a”) and birefringence (An; = n"* - n”), which are differences in the absorption coeffi- cient and the refractive index, respectively, between two linearly (at and 1r) polarized beams whose polarization planes are perpendicular to each other. Isotropic samples may exhibit linear or circular optical anisotropy when excited by a plane-polarized laser or by a circularly-polarized laser, respectively. Aligned samples created by a plane polarized pump laser show linear dichroism (LD) and/or linear birefringence 26 (LB) whereas oriented samples created by a circularly polarized pump have circular dichroism (CD) and/or circular birefringence (CB). A. Saturation Absorption Spectroscopy . In saturation absorption spectroscopy where a plane polarized pump (1r) and probe * or 1r) are used, the signal from the laser induced optical anisotropy is (either 0 relatively small compared with the signal from the total population changes and is usually hidden behind the strong signal. Nevertheless, the laser induced optical anisotropy (alignment in this case) can be observed by comparing the lineshapes of a three-level double resonance under different pump and probe configurations (shown in Figure 2.4). Even though most double resonance experiments are result of a saturation effect “saturation absorption” has been used for experiments involving two plane polarized lasers for historical reasons. Since the pump laser is mechanically chopped in these experiments in order to record only the double resonance effects, we refer to these experiments either as intensity modulation or population modulation when only the total population changes are of interest or as intensity modulated alignment pumping when our interest is in the linear anisotropy induced by the laser. B. Alignment Modulation vs. Orientation Modulation Instead of the two separate measurements done in the alignment pumping with parallel and perpendicular configurations, the polarization state of the pump (either pump or probe but not both) can be modulated between 7r and 0* and the laser induced optical anisotropy can be directly measured. Since modulating polarization states of the pump results in changes in the orientation as shown in Figure 2.3-(a), this is called alignment modulation to distinguish from orientation modulation where the polarization state of the pump is modulated between 0+ and 0‘. In alignment modulation, 0;, = ofr — at"1t is recorded using a linearly polarized probe whereas in orientation modulation ac = 0"” — a“ is measured with a circularly polarized probe. 27 fir— fir— fir— Jc=2 __ Jb=3 Ja=2 (b) parallel configuration 000 Jb=3 J a = 2 (a) perpendicular configuration Figure 2.4: Two different saturation absorption configurations: (a) 1r pump, 1r probe; (b) 1r pump, 0* probe. It should be noted that the selection of 1r is arbitrary, since there is no field applied to the sample. At some places the 1r and the 0* is interchanged for the convenience of explanation or calculation. Exchanging the 1r and the 0* should give the same result. 28 At some places in this thesis polarization modulation is used to represent either alignment modulation or orientation modulation, or both to differentiate from inten- sity modulation in which the intensity of the pump laser is modulated. Nalcayama101 used the term velocity selective optical pumping for the alignment modulation de- scribed here. VIII. Polarization Spectroscopy Historically, polarization spectroscopy has been used for experiments in which laser induced optical anisotropy is recorded. In typical polarization spectroscopy, a circu- larly polarized pump beam induces a circular dichroism and birefringence to a sample and the detector sees a plane polarized probe beam through an analyzing polarizer rotated perpendicular to the incident probe polarization. The qualitative theory fOr polarization spectroscopy and measurement of circular birefringence is presented here following similar derivations by Demtroder.16 A right circularly polarized (0*) laser beam excites molecules following a AM = +1 selection rule, producing a nonuniform population of the M sublevels, which is equivalent to an anisotropic distribution for the orientations of the angular momentum vector J. Such an anisotropic sample becomes birefringent for the incident linearly polarized (0*) probe beam, and the plane of polarization is slightly rotated. Since a linearly polarized probe wave” (2.37) can be always composed of a right and a left circularly polarized component, 5* = 133'." + E" where 55+ = -%(E.,z‘:‘+ iEuae‘M‘k”) (2.38) E- = %(E.,e- iEnije‘M‘m (2.39) ‘In this section at is in angular frequency. 29 where 55,37, and 2 are unit vectors along 2:,y, and z direction, respectively. After passing a sample cell of length L the two components are "+ — E025 + iEozE 13+ = Eye‘lw-mle-N; . 2 (2.40) E- = E'io-eflwt-k'ue-a'L; E“: = E0313 -2 lEozZ. (241) Due to the differences An = n+ — n' and Aa = 0+ — 0‘ caused by the anisotropic saturation, a phase difference Ad = (lc+ — k’)L = (:..:L/c)(n+ — n“) (2.42) and a small amplitude difference AB = %(e-°*L — e-a'b]. (2.43) have developed between the two components. If both components are again super- imposed at y = L after the sample cell, an elliptically polarized wave comes out with a major axis which is slightly rotated against the 3: axis. E = 5+ + E" E9;- ei(wt-k+L)-0+L [(1 + 6(a+-a‘)L+i(k+-k')L)5 + i(1 _ 6(a+_a‘)L+i(k+ -lc")L)5] . 2 If the differences Aa and Ale are small, (0* — 0")L << 1 and (k+ — k')L << 1, (2.44) we can expand the exponential factor -I:£e‘(“""”'l’°*‘ [253 + i(Aa + iAIc)L2] (2.45) and obtain for the transmitted amplitude after a linear polarizer whose angle is set to 0 relative to z axis E: = %£e‘(‘""k+m‘°+l’ [2 sin 0 + i(Aa + iAlc)L cos 0] (2.46) 30 Since the detector sees the the transmitted intensity I, = EfEt, [(40) = L, [4 sin 02 — 4 sin 0cos 0(Ak)L + (Alc2 + Aoz2)L2 cos2 0] = I. [4 sin 9’ — 23in(20)AkL + (A1:2 + an?»2 cos? a] . (2.47) where L, = 133,620” /4. When 0 = 0, the laser induced optical anisotropy, 1(w) = 1.,(Ak2 + Aa’)L2, (2.48) is observed whereas with 0 = 90, the intensity modulated signal, I(w) = 41°, (2.49) is observed. If signals recorded with 9 and -0 are subtracted from each other a pure birefringent signal, I (w) = —4L, sin(20)AkL, (2.50) can be recovered. The maximum birefringent signal is observed at 9 = 45°. The differences A0 = 0* - a" in absorption coefficients and An = 12* - n' in refractive indices are due to the different M sublevel populations experienced by the right or the left circularly polarized probe component. Although each coefficient on" and a“ itself shows a intensity modulated spectral profile, the difference Aa exhibits the small difference between these two lineshapes. For weak saturation with homogeneous linewidth 7, a Lorentzian spectral profile is obtained for A0 2 _ 7 A(Jr—(n-w)’+7’ where A0,, is the maximum difference at the center w = Q, and using the Kramers« A0,, (2.51) Kronig dispersion relationship, we obtain _ —272w - [(n - w)” + 7“]2 The magnitude of A0,, depends on the pump intensity 1,, the transition probability Alc Aao. (2.52) for the optical transition, and on relaxation processes which tend to restore ther- mal equilibrium. For the general case where pump wave and probe wave may come 9F" 31 from different lasers tuned to the coupled transitions (J’ = Jb) 4— (J” = J“) and (J' = J.) 4— (J” = J.) with a common level J5, Aa can be calculated from the expressionw'86 A0 = -;—QO(I,/I.) . ((J., J,, Jc,AM). (2.53) Here an is the unsaturated absorption coefficient and I,p the pump intensity. The saturation intensity I __ hwab . 7a7b . - (2.54) 01...]. 73 + 7:. depends on the cross section 01,], for the pump transition and on the homogeneous widths 7., and 75 of lower and upper levels, respectively. The numerical factor C depends on the pump transition (J5 «— Ja), the probe transition (Jc +— Jb), and on the pump polarization. The factor C can be calculated from a sum of the Clebsch-Gordan coefficients over the M levels if weak saturation is assumed.” For QR(4,3) pumping the calculated values of C(J5,J.,Jc,+l) are close to 1, %, and —1 for P—,Q—, and R—branch probe, respectively. Therefore P-branch transitions have opposite signs from R—branch transitions whereas Q-branch transitions are too weak to be observed in general. These intensity changes are used to identify the branch of transitions in polarization labeling spectroscopy. 32 IX. Jones Calculus The Jones calculus is a procedure for treating the effect of optical components on a beam of polarized light. In the Jones calculus,123‘ ”" the light beam is represented by a vector (Jones vector), the optical device encountered by the beam is represented by a matrix (Jones matrix), and the two are multiplied to yield another vector representing the light beam after interaction with the optical element. Following the notation used by Kliger et. al.,131 examples of Jones vectors and matrices are described assuming that the polarized light propagates along the z direction. The Jones vector for polarized light is i W) — Ayeffv where A and 43 are a positive amplitude factor and a phase factor of the light along the :e or y axis, respectively. The intensity of the light can be calculated from I=J'-J=A:.+A: Using the standard normalized forms of Jones vectors, in which the vectors are reduced to their simplest forms and have a magnitude of 1, corresponding Jones vectors for 0*(A, = 1,11,, = 0) and 7r(A,, = 0,14, = l) polarized light are M43442)- The Jones vectors for right- (0*) or left- (0‘)circularly polarized lights are Ja+=2<:>,J«-=-;—.(:) Various forms of the Jones matrix are listed here for the optical components treated in this thesis. For a linear polarizer at angle 0 from the 2: axis, cos2 0 sin 0 cos 9 M (a) = sin 0 cos 0 sin:2 0 1o 0 o M”): 0 0 MM): 0 1 ‘m‘ 33 l l 1 1 l -l M(4s)=§ 1 1 M(-45)=§ _1 1 The absorption by a sample is treated as the effect of an optical component. For an isotropic sample, 12 0 _ L M = 0 where p = e a , L = path length. P . For linear dichroism, 3 0 z = —a,L/2 MLD = (p ) where {p e L 0 Pv P9 = 5.0” ’2 where a,(ay) is the absorption coefficient for zz(yz) plane polarized light. For linear birefringence, 6“ 0 w(n,t - n,)L MLB = ( 0 845) where 6 = 2c and m: (n,) is the refractiVe index for xz(yz) plane polarized light. For circular dichroism, 1 . I» + p: -i(pr - 1):) pr = WWW"2 Mop = - , where L l2 2 2(pr - pz) pr + pa p: = eXP‘°' and a,(a¢) is the absorption coefficient for right (left) circularly polarized light. For circular birefringence, cos6 sin6 w(n,. — n;)L 2c and n1(n,) is the index of refraction for left (right) circularly-polarized light. M03 = ( ) where 6 = —sin6 cos6 We assume a linearly polarized pump beam creates only linear anisotropy (LD,LB) and a circularly polarized pump beam creates only circular anisotropy (CD,CB). We can then find Jones matrices for the optical anisotropy induced by polarized pump lasers. Since M“; and MLB commute, the induced anisotropy by a linearly polarized laser can be expressed as a product of MLD and M13, ° i6 i6 Mam-(z: m: :34: .2.) 6If the two matrices do not commute, this can not be done by a simple multiplication of two matrices. Although, this greatly complicates the derivation, similar operation can be performed using Jones N matrix. The Jones N matrix is discussed by Jones129 in detail. 34 where Ma: represents the Jones matrix for alignment induced by a my plane polar- ized laser. Similarly, the Jones matrix for a polarization oriented sample can be represented by Mar = MCDMCB = g (.p, +1” —i(p, -170) ( €0.86 sin6) z(p,. - 19:) p, + p; - sm6 cos 6 = l ( (p, + p;) cos6 + i(p, -— p1) sin6 (p, + p;) sin 6 — i(p,. - p1) cos 6}.56) 2 -(p,. + p1) sin6 + i(p,. - p1) c086 (p, + pg) cos6 + i(p,. — p1) sin6 We obtain Map induced by a 0* from Eq. 2.55 by exchanging p, and pH and replacing 6 by -6 and M0,: induced by a 0’ from Eq. 2.56 after exchanging p, and p; and by replacing 6 with —6. Since the infrared detector sees only the power of incident radiation, we are inter- ested in the intensity of the resulting radiation I = J“ - J. We now consider the case where the sample is probed with a linearly polarized beam under various pumping conditions. 0 x pump, 7r probe: The sample has LD and LB due to 7r pumping. Therefore the necessary calculation is MLDMLBJ,¢: 3 ‘5 0 0 0 (a w H 3 0 Pve ' \1 Pve ‘ I=p2 v. (2.57) This is the typical double resonance configuration where two orthogonal plane polarized lasers are used for pump and probe. 0 0* pump, it probe: Map can be derived from Ma; by interchanging p, and p, and replacing 6 with —6. o 0 M“ (I) = (pse““‘)) I = p2. (2.58) 35 If pumping induces a linear dichroism (p, 75 py) as well as population changes, Eq. 2.57 is different from Eq. 2.58 and different intensities are observed for different configurations. This difference can be directly measured by modulating the polarization states of the pump beam between 0* and 1r. 0* / 1r pump modulation, 7r probe: 13: - 13 = pi - p: (2.59) This value increases as the effect of linear dichroism increases. If the pump changes only the population without inducing a linear dichroism (p, = py = p) there will be no signal observed. 0+ pump, 7r probe: The 0+ pump induces circular dichroism and birefringence to the sample. Therefore, the required calculation is McpMcg J,r = M0,.J," M... (a) l((Pr+pz)sin6-i(p,—p1)cos6) l - 5 (p,+p;)cos6+i(p,. —p;)sin6 I = (103+ pf)/2- (2-60) M0,: induced by a 0' pump is identical to the Mo, induced by a 0+ pump, if the p, and 6 in Eq. 2.56 is replaced with p; and —6, respectively. Therefore a detector sees the same intensity as in Eq. 2.60. 0+/0‘ pump modulation, 1r probe: Obviously, modulation of the polarization between 0+ and 0" should not change the intensity seen by the detector. I = 13+ — 1:- = (2.61) However, adding an analysing polarizer in front of the detector leads to a com- pletely different story. 36 0 0+ pump, 7r probe, polarizer(0 = 90): Required calculation is Mo=9oMcoMch«-= 0) = (o 0)1((Pr+p7)sin6-,i(p,-p1)cos6) M Mo, ‘90) (1 0 1 2 (p,.+p;)cos6+i(p.---Pz)SiIl6 1 0 ) _ 2 ((Pr +p1)0085+i(p,. ‘1’!)3in6 I = [Pi + pf + 22.104008” 5 - sin” 6)]/4 = [p3 + p? + 21r’r197003(25)l/4- (2.62) The corresponding I for a 0‘ pump is [p3 + p? + 2p,p; cos(—26)]/4 . s 0+/0" pump modulation, 7r probe, polarizer(9 = 90): 13+ — 13.. = 0 (2.63) 0 0+ pump, 7r probe, polarizer(0 = 0): l 0 0 _1 (p,+p1)sin6—i(p,.-p1)cos6 (0 0)M°'(1)’§( o l I = [p3 + p? + 2p,p;(sin2 6 - cos2 6)]/4 = [P3 + Pi - 2pm: C08(25ll/‘1r- (2'64) 0 0+/0" pump modulation, 1r probe, polarizer(9 = 0): 13+ _ 13.. = 0 (2.65) 0 0+ pump, 1r probe, polarizer(0 = 45): 4c M)--i(:2:1:::::::::::::;:::§::33:22:32) I = (p? + p? + 2p,pg sin 26)/4. (2.66) 37 o 0+/0‘ pump modulation, 0* probe, polarizer(0 = 45): 13+ — I}- = prp; sin 26 (2.67) If 25 < 1 this can be expanded to -2p,p16 from which the laser induced circular birefringence 6 = 1rw(ng — n,)d/2 can be deduced. On the other hand, linear dichroism can be measured from Eq. 2.59. Similar expressions for a circularly polarized probe are derived, as follows, 0 0* pump, 0+ probe: i6 Me a (1) = .1. (:23) I = (P: + PEN2 (2-68) 0 0*/1r pump modulation, 0+ probe: I = 13;; - I: = 0 (2.69) o 0* pump, 0+ probe, polarizer(0 = 0): i6 (.1, Elm—«13(1) #56?) I = pg/2 (2.70) 0* / 1r pump modulation, 0+ probe, polarizer(0 = 0): I = (P3. - PW? (2-71) 0 0* pump, 0+ probe,polarizer(0 = 45): 1 1 l 1 1 1 P33“ ) M M" — = - — . ‘5 'fili) 2 (1 1) film-‘5 «g p3855+pye-55 I = [p2 + p: + 210.12. cos(26)]/4 (2-72) For 1r pump, the intensity is I: = [(p: + pf, + 2pyp, cos 2(-6)]/4. 38 0*/7r pump modulation, 0+ probe,polarizer(45): [=0 0* pump, 0+ probe: 1 (I) 1 ( 2p,(cos6+isin6) ) Mof— . = — . . 3 \f2- -2p,(sm6 — 2 cos 6) 0‘ pump, 0+ probe: I=fi 0+/0" pump modulation, 0+ probe: 1 = 123: p? 0* pump, 0* probe, polarizer(0 = 0): 1 l)_ 1 (2p,(cos6+isin6)) M°M°'7'§ (i 72 o I = 4?? 0+ pump, 0+ probe, polarizer(0 = 90): Merfi (i) = 1le (—2p.(cos:+isin5)) I=4p?- 0+/0" pump modulation, 0+ probe, polarizer(9 = 0): 'I=p3-pz’ (2.73) (2.74) (2.75) (2.76) (2.77) (2.78) (2.79) 39 Table 2.2: Comparison of calculated intensities using Jones calculus for different experimental conditions. Probe Pump P-ol I Comment 7r 7r no 1): 7r 7r 0 0 1r 7r 90 p: 1r 7r 45 123/2 7r 0* no p2 1r 0* 0 0 7r 0* 90 p: 7r 0* 45 123/2 7r 0* / 7r no p: -— p2 LD 7r 0* / 7r 90 p: — px LD w 0* / 1r 45 [p2 - 23,]/2 LD 7' 0+ "0 (P. + P: 53/2 77' 0+ /0"‘ no 7? 0+ 90 [P3 + p? + 2pm: 008(25)]/ 4 1r 0+/0' 90 0 1r 0" 0 [P3 + p? - 21m co8(2<5)l/4 7r 0+ /0' 0 0 1r 0* 45 [(103 + p?) + 210.1): sin(25)l/ 4 7r 0+/0' 45 prpl sin(26) CB 0"“ 0* no [p2 + py] / 2 0+ 0* /1r no 0* 0* 0 / 2 0+ 0*/1r 0 [p2, _p1:]/2 LD 0+ 0* 90 2 / 2 0+ 0* / 7r 90 [p3 — p§]/2 LD a+ 0* 45 wz+p3+2p.p.cos(26)1/4 0+ 0* / 7r 45 0 0+ 0* —45 [p2 + p: - 2193p, cos(26)]/4 0+ 0* /1r -45 0 0+ 0* no p? 0* 0‘ no p? 0* 0‘70" n0 ' (Pg-P12) CD 0+ 0+ 0 122/2 0+ 0+ 90 p, / 2 0* 0+/0' 0 (p3 - p?)/2 C D 0* 0V0“ 90 (PE-PW? CD 40 Derivation of Jones calculus for all possible optical pumping experiments are de- rived and listed in Table IX. It will be worth mentioning a few findings from this Table. First the four components of laser induced optical anisotropy, namely LD , LB, CD, and CB, can be independently measured using different experimental schemes listed in Table IX. 1. The LD (Aal’ = 0,; — 0,.) can be measured directly when the polarization of the pump is modulated between 1r and 0* using either a plane- or a circularly- polarized probe. 2. The LB (An‘ = nf — 12,.) can be calculated from two different measurements taken with circularly polarized probe under plane polarized pump with a linear polarizer rotated to 45° and to —45° from the reference axis. 3. The CD (A00 = a; — 0,.) can be measured directly with a circularly polarized probe while modulating the polarization of the pump between 0"” and 0'. 4. The CB (Anc = n; - n.) can be directly measured using a plane polarized probe while modulating the polarization of the pump between 0+ and 0’ with a polarizer rotated to 45° relative to the reference axis. Chapter 3 Experimental I. Lineshape Study of Transferred Spikes A block diagram of the spectrometer used for the present study, which includes some improvements from that used previously in this laboratory, is shown in Fig- ure 3.1. A C0,» laser (Laserl)" serves as the pumping source, while an infrared microwave sideband laser (IMSL) of the Magerl design132 (Laser2) is used for the probe source. The two single mode CO; lasers are each stabilized by monitoring the Lamb dip in the fluorescence from a C02 sample in a cell outside the laser cavity(F C). The frequency jitter of each of the two sources is estimated to be < 150 kHz including the intentional frequency modulation used for the stabilization. One of the lasers is a flowing gas system that is normally used as the pumping source for the double resonance, while the second laser is a semi-sealed model that is normally used as the carrier frequency for the IMSL system. In this work the two lasers were interchanged when the QR(11,9) transition in 12CHgF was pumped, because in this case 1201802 is required for the laser transition. The microwaves for the IMSL system were generated by a computer-controlled synthesizer (accuracy ~ 3 kHz) and amplified to ~ 20 W by a traveling wave tube amplifier (TWTA). The infrared and microwaves were mixed in a CdTe crystal in an RF-matched housing (Mod). The IR radiation leaving the crystal contained the laser carrier at frequency w; and upper and lower sidebands at “The abbreviations in parentheses refer to abbreviations used in Figure 3.1 41 42 / [1 fi\ [I G Li V H \ I Laser2 Laserl ‘ l @_.’ Stab I Stab wail]? C F C Mod It? BS Sample cell p1 \ ' " ’ ' ‘ A'J --------- - 1\ ‘ ‘ : Chopper ll \-- TWTA L 1 __ . Power 1 PIN : Control ‘ [ PC [:1 33 kHz clock gicrowave _ generator ~ IEEE—488 Figure 3.1: A C0; laser infrared microwave sideband laser double resonance sys- tem. The two CO; lasers are frequency stabilized to the fluorescence Lamb dip of CO;(FC). The sideband is generated by mixing one of the C02 lasers with high power microwaves (8 — 18 GHz) in a CdTe crystal (Mod) and its intensity is stabilized by monitoring its output (RD). Since the sideband is amplitude modulated at 33 kHz, detected signals (SD,RD) always get demodulated at 33 kHz first by L1 or L3. The output from L1 is double demodulated (L2) at the chopping frequency (~ 100 Hz). The signal from L2 comes therefore purely from double resonance effects. Since the pump laser modulated by a mechanical chopper has a horizontal plane of polarization, it can be separated from the sideband laser using two polarizers P1,P2. The use of a polarizer to separate the two laser beams allows easy and perfect alignment that is critical to the lineshape. 43 frequencies to; in)... where to... is the microwave frequency. The carrier and sidebands had orthogonal planes of polarization so that the carrier was reflected by the first polarizer (P2) after the modulation. The two infrared sources, pump radiation and IMSL probe, had orthogonal planes of polarization and the arrangement of polarizers shown in Figure (3.1) was used to separate the two beams for the usual geometry of counter-propagating pump and probe radiation. When co-propagating radiation was needed, as in some three-level double resonance experiments, it was necessary to slightly misalign the two beams. Although the probe radiation included both upper and lower sidebands, the spec- trum of methyl fluoride is sufficiently sparse that only one of the two sidebands was absorbed in any given experiment.133 The sample cell for all of the measurements was a l—m long glass tube, 25 mm in diameter, with NaCl windows mounted at a slight angle to reduce etalon effects. The methyl fluoride sample was (purchased from Peninsula Chemical Research and used as received. Sample pressures, which were 1-20 mTorr, were measured by means of a capacitance manometer. All of the spectra were recorded at room temperature ( ~ 295K). As shown in Figure 3.1, the double resonance effects were recorded by means of a double modulation scheme. The infrared-microwave sidebands were 100% amplitude modulated by chopping the microwaves by means of a PIN diode. A portion of the sidebands, monitored by a reference detector (RD) and processed by a phase-sensitive lock-in amplifier (L3), was used for stabilization of the amplitude of the probe beam by controlling the microwave power applied to the sideband generator. The frequency of the sideband chopping (~ 33 kHz) was high enough to eliminate much of the laser noise, but low enough to ignore the effect of modulation sidebands. The output of the lock-in amplifier (L1) that processed the output of the signal detector (SD) contained the single+double—resonance spectrum and was often recorded by the computer. The S / N ratio of this spectrum was rather high, not only because of the low time constant filtering required to allow the second lock-in amplifier (L2) to process the double resonance effect, but also because of the intensity changes that resulted from the intensity modulation of the pump beam. The pump beam was amplitude modulated 44 by a mechanical chopper at 100 Hz for four-level double resonance, but at frequencies up to 1 kHz for three-level double resonance. The output of the second lock-in amplifier (L2) contained only the doubleoresonance effects, which were recorded by the computer (PC) for later numerical processing. II. Polarization Spectroscopy Figure 3.2 shows the experimental diagram of a C02 laser-IMSL double resonance system employing an electro—optic switch used for polarization experiments. The main differences from a typical intensity modulated double resonance technique are (a) pump laser guiding optics and (b) the electro-optic polarization modulator shown in Figure 3.3. The heart of the guiding optics is a 90% reflecting mirror that passes 10% of incident radiation through the mirror. When a pump beam hits the mirror, 90% of the radiation is reflected off the mirror into the sample cell while approximately 10% of the IMSL probe radiation passes the mirror and is detected by the usual double demodulation scheme. The electro—optic switch system consists of a CdTe crystal mounted in a high-voltage housing, a Fresnel rhomb rotated at 45° angle, a wire-grid polarizer, two 2.1 kV variable high voltage power supplies, a home made high voltage switching circuit, and a programmable trigger circuit. The details of the flowing gas C0: laser, the infrared-microwave sideband laser, and the handling of the sample were already explained in the previous section. In Figure 3.3, for the intensity-modulated studies the flowing gas C02 pump laser (PL) was essentially 100% amplitude modulated by passing the beam successively through a CdTe electro-optic crystal (CdTe), a ZnSe Fresnel rhomb (Rhomb), and a polarizer (P1). By repetitively switching a voltage across the electro Optic crystal (CdTe) between +2100 V and -2100 V, the plane-polarized infrared beam entering the crystal was switched between right and left circularly-polarized radiation. The rhomb converted the circularly-polarized light to horizontal or vertical plane-polarized radiation and the polarizer (P1) then reduced the beam power by almost three orders of magnitude during one-half of each cycle. The switching can be controlled by any pulse generator that provides TTL pulses at rates up to 10 kHz. For the experiments 45 Control F 33 kHz clock IEEE-488 Figure 3.2: Block diagram of the CO; laser — IMSL double resonance setup employ— ing an electro-optic modulator. When 2.1 kV is applied to the CdTe modulator, it converts the YX plane polarized (a) pump laser into right circularly polarized (0") light. The 0* radiation is changed back to a x-polarized laser after the rhomb (Rh) that works as a quarter wave plate. The laser passes a blocking polarizer (P1) whose angle is set to 7r and perturbs molecules in the sample cell. If -2.1 kV is applied instead, the pump laser becomes 0* polarized and is reflected off the polarizer to a beam stop. The result is a TTL controlled optical modulator with 7r plane polarized laser pumping (perpendicular configuration). The same setup can be used to modu- late 0* plane polarized pump by rotating the blocking polarizer parallel to the YZ plane (parallel configuration). 46 described here, the switching was performed by means of an electronic switch designed by Martin Rabb at MSU. Unlike previous double resonance setups where intentional misalignment, Brew- ster angle windows, or polarizers were used to separate a probe beam from the pump beam, the current setup with a partially transmitting mirror (MP) allows a unique and rich environment for various double resonance experiments by allowing the use of 0*, 1r, 0*”, 0‘, or any other kind of polarization states of lasers for modulation pur- poses. For example, the same setup can be used to record orientation modulation, in which the polarization state of the pump beam is switched between 0* and 7r, by removing the blocking polarizer (P1), as in Figure 3.4. Also, by removing the Fresnel rhomb, it can be used for orientation modulation, in which the polarization of the pump laser is switched between 0+ and 0" (Figure 3.6). Figures 3.3,3.4,3.6 graphi- cally describe the polarization states of the pump beam under different experimental conditions. A diagram of the modulation part in the alignment modulation experiment is shown in Figure 3.4. It is important to note that the intensity of the pump laser is constant all the time while the polarization state of the laser follows the TTL. This eliminates the pure population pumping effect from the recorded signal. A typical alignment modulated signal is shown in Figure 3.5 along with an intensity modulated signal. The alignment modulated signal is very similar to the typical double resonance signal except that the Gaussian part is suppressed. The same setup is easily converted into an orientation modulated double resonance system by removing the Fresnel rhomb and by using a circularly polarized probe beam (Figure 3.6). The polarization state of the pump beam is now switched between 0+ and 0". It creates a circular optical anisotropy in the sample, which means a different absorption coefficient (Aa = (1+ — 0:") as well as refractive index (An = n+ — n'). A 0+ probe beam, for example, can be used to observe this laser induced optical anisotropy. Another interesting experimental setup takes advantage of the phase changes cre- ated by a circularly polarized pump with a linearly polarized probe beam. A linearly polarized pump beam 0* can be considered as the sum of two circular components: P1 Rhomb CdTe (Iv \ imp-7011 (IPL \ ,1 LJ O M _.|'|_n__n_ I” n” ”ll Trig ’Voltage . . Control z I | | I l l l I JUl—L TTL _fllL_lllL_llL_ Y +2.1kV HV x L__ .-2.1kV LV Figure 3.3: Diagram of the electro-optic switching system. A TTL signal controls the high voltage control circuit and applies either +2.1 kV or -2.1 kV to the CdTe housing. A YX (7r) plane polarized pump beam (PL) is either converted to right circular polarization (0*) or to left circular polarization (0') by the CdTe, depending on the polarity of the high voltage applied to it. A Fresnel rhomb oriented at 45° converts the circularly polarized beams back into either 0* or 1r. A blocking polarizer (P1) whose angle is set parallel to the YX plane blocks the 0* polarization of the pump beam and passes only the 1r polarized state of the pump beam. Since the intensity of the pump beam follows the shape of the TTL signal shown in the picture, this is called intensity modulation in the text. The different polarization states of the pump laser are shown with I (7r), II (0+,0‘), III (7r,0*), and IV (1’). The blocking polarizer (P1) can be rotated to obtain 0* at IV. 48 Rhomb CdT III t [—7 0 11 e c IPL ,4 z_/ 0 l— Intensit y Trig Voltage Polarization-r-L-r-Ll—L . Control 2 f l TTLJ—Ll—Ll—L . Y +2.1kV HV X . . . -2.1kV LV Figure 3.4: Block diagram for alignment modulation between 0* and 7r. Note: The intensities of the two 0*- and r-polarized pump beams do not change. Only the polarization state of the pump beam is switched. Therefore, the pump always creates the same holes and spikes in terms of total population while the alignment of the molecules is different. 49 (Mar/blocked l 1 13050 12970 12890 12810 12730 12650 Figure 3.5: (a) Alignment modulated double resonance signal of the P(6,0), P(6,1), P(6,2), and P(6,3) in the 21/3 4— V3 band of 13CH3F. (b) Power modulated signal. The absolute intensity of the alignment modulated signal was about 1/ 3 of the nor- mal double resonance signal. It is clear that the Gaussian signals are suppressed in the alignment modulation. The z-axis is the microwave frequency in MHz used to generate the sideband laser. When the transition is observed with negative sideband, the numbers are labeled in decreasing order. 50 Intensity Polarization-rm]— Trig —-t , Voltage Control Z I TTLM _1 4.2.11.0 I -2.1kV w . HV LV Figure 3.6: Modulation of the polarization states between 0+ and 0". Again the intensity of the pump beam stays constant, as in alignment modulation. Either a circularly polarized probe beam or a plane polarized beam can be used to observe the optical anisotropy created in this pump scheme. 51 0+ and 0' with the same intensity and no phase difference. The absorption coefficient + component of the probe beam are different and phase change experienced by a 0 from those experienced by the 0' component when a circularly polarized pump beam is used. A 0* probe beam becomes an elliptically polarized beam (due to differential absorption coefficient) whose main axis is tilted (due to phase shift) a little from its original axis (X — Y in the experiment). Although the intensity of the linearly polarized probe beam does not change as the polarization of the pump changes, the direction of the tilt created by the 01' pump is opposite to that created by the 0‘ pump. If a polarizer oriented at 45° is put before the detector, the detector sees a difference in intensity upon changing the polarization state of the pump, because the polarizer selects only the polarization component of the probe beam along its axis. The intensity is proportional to the amount of the phase shift (An = n+ - n'), which is proportional in turn to the interaction between the pump and the sam- ple. The signal recorded in this experiment is related to the previous signal via the Kramers-Kronig relationship and has a dispersion line shape as shown in Figure 3.7. For obvious reasons, no signal is observed when the polarizer before the detector is removed or if its angle is set close to either 0 or 90 ° relative to the 0* plane. Figure 3.8 graphically summarizes the polarization states of the pump and probe beams under variety of double resonance experiments. In this part of the work, all of the double resonance experiments were performed with 1-60 mTorr of 13CH3F while the (1,5,3) 4— (0,4,3) transition was pumped by a flowing CO; gas laser with 1- 5 W/cm2 power. III. Time Resolved Spectroscopy Figure 3.9 shows a diagram of the the spectrometer used for the time-resolved CO; laser-IMSL double resonance study. The spectrometer is essentially the same as the previous setup used for the saturation absorption experiments except for the data recording part. The details of the flowing gas CO; laser, the infrared-microwave sideband laser, and the sample handling are the same as described in the first section of this chapter. The pump beam is essentially 100% amplitude modulated as discussed 52 16380 16360 16340 16320 16300 16280 16260 16240 Figure 3.7: (a) Intensity modulated double resonance signal. of the R(4,3) transition in the V3 band of l3CH3F. (b) Orientation modulated double resonance signal. (c) Single resonance absorption signal. The single resonance absorption signal has a Bennett hole due to the laser pumping. The orientation modulated double resonance signal has dispersion line shape. The horizontal axis is the (negative) microwave offset frequency (MHz). 53 Probe Sample Pump Probe Sample Pump Analyzer (a) alignment pumping (d) orientation Pumping (b) alignment pumping (e) orientation modulation (c) alignment modulation (f) orientation modulation Figure 3.8: Experimental conditions for (a) alignment pumping: x-polarized pump, x-polarized probe; (b) alignment pumping: x-polarized pump, 0*-polarized probe; (c) alignment modulation: x-polarized probe, 0* - 7r polarized pump; ((1) orientation pumping: 7r probe, 0+ pump, 90° polarizer; (e) orientation modulation: 0+ probe, 0"’ -0‘ pump, and (f) orientation modulation: 1r probe, 0+-0' pump, 45° polarizer. For historical reasons (a) and (b) are also called as saturation absorption whereas (d) is called as polarization spectroscopy. Experiment (f) is named circular birefringent measurement because it measures laser-induced circular birefringence. 54 in Figure 3.10. For the time domain experiments, a rate of 100 Hz was used to ensure complete relaxation, while for some frequency domain experiments a 1 kHz rate was used to obtain better S/ N ratio. The sample cell was either a l-m long glass tube, 25 mm in diameter, or a 1-m long White-type cell, operated with either 4-pass or 8-pass. The sample pressure was 10-60 mTorr and the temperature was 297 K. The 9P(32) laser (Laserl) pumped the QR(4,3) transition in the fundamental V3 band. The IMSL radiation (dashed line in Figure 3.9) was directed to an InSb detector (SD) whose output was amplified and then processed by a lock-in amplifier (L1) at the pump laser modulation frequency (F) for steady state experiments or by a LECROY model 6810 transient recorder for time resolved experiments. In the time domain experiments the IMSL frequency was fixed at a frequency selected after observation of the frequency domain spectra. The IMSL absorption was then recorded as a function of time by the transient recorder. Figures 3.11 and 3.12 are frequency- and time-domain spectra recorded in this way. The uniqueness of the described system is that it enables one to observe both the frequency domain and the time domain signal under the same conditions. Therefore, with nominal pumping power ( ~ 1W), the typical double resonance line shape (sum of a Gaussian and spikes) can be recorded in the frequency domain (Figure 3.11) and the time response of each part can be observed separately (Figure 3.12). Since pulses of arbitrary duty ratio can be generated as long as the rate is less than 10 kHz, population increase rates (pump-on) as well as population relaxation rates (pump- ofl) can be studied simultaneously with the same setup by acquiring one complete pump cycle. Usually two complete cycles were recorded and then compared to avoid unpredictable errors such as sudden vibrations or random noise. A. Electra-Optic Switch Unlike the typical Q-switched lasers used for time resolved experiments, which have a spectral bandwidth comparable to or broader than the Doppler profile, the 55 / III I ’ 7f Probe Stab . 3:33] Laser2 \VII [IL]! Laserl \\ n \\ Pump Sample cell P2 @Rhomb CdTe 1 /—7 F—1 _J Stab fl ‘— 5, ,. I \v» \51 F __‘Voltage I I—‘C t l TWTA ion rq Transient L1 I V 13111:] Recorder I , PC +2.1kV Ngcrowave .- ‘ enerator ‘ , IEEE-488 %r— {21104 Printer ‘ . SUN 4W— (Data processing and Plotter Internet communication) Ethernet Figure 3.9: A schematic of the time resolved double resonance system used in this study. The flowing gas laser (Laserl) was used to pump QR(4,3) transition in the V3 band. The beam paths of two CO; lasers and the high voltage cables are drawn with thick lines. The dashed line represents the IMSL beam path. Details of the operation are described in the text. 56 JUUL % IV—n—n—n— IV / III II I I II" II" IIII P2 P1 3 Rhomb CdTe - . .............. -.\, I - ’ 70 I PL SL/ .\ \ ’1 L1 0 ' v @ ------- I - - - -7/ 71;]: ,Voltage Control JL—L mm. ‘ I Transient L1 TTL [1 n n . _. Recmder z X _Jl|LJ|JI_lll_ +2.1kV Hv Y .-2.1kv LV Figure 3.10: Diagram of the electro-optic switching system used for time resolved measurement. A TTL signal controls the high voltage control circuit and applies either +2.1 IN or —2.1 kV to the CdTe housing. A YZ(1r) plane polarized pump beam (PL) is either converted to right circular polarization (0*) or to left circular polarization (0‘) by the CdTe, depending on the polarity of the high voltage applied to it. A Fresnel rhomb oriented at 45° converts the circularly polarized beams back into either 0* or 7r. A blocking polarizer whose angle is set parallel to the YZ plane blocks the 0* polarization of the pump beam and passes only the 1r polarized state of the pump beam. The amplitude of the final pump beam (IV) follows the shape of the TTL signal that is applied. A 0* polarized sideband laser (SL) interacts with the sample, reflects off P2, and is monitored by the detector (SD). 57 l L l 1 12785 12755 12725 12695 12665 12635 Figure 3.11: Double resonance spectra of the QP(6,3) transition. Soft inelastic AJ = 1 collisions with a large impact diameter result in the sharp spike marked S whereas the Gaussian marked G comes from the vibrational swapping mechanism. With sub- Doppler resolution, the two processes in the same transition can be time resolved separately. 58 I I I I I If.” l l l 0 100 200 300 400 500 600 700 800 Time /ps Figure 3.12: Time resolved spectra of the QP(6,3) transition. G represents the signal from the Gaussian whereas S is from the spike. At time 0, the pump laser is turned off and relaxation is observed whereas at time 570ps the pump laser is turned on, and an increase in signal was observed. The difference between G and S can be seen at early time (< 10ps) where the AJ = 1 process dominates. 59 electro-optic switch system provides a soft pulse with a spectral bandwidth compara- ble to that of our steady state double resonance system. One of the main difficulties in building the system shown in Figure 3.9 was the need to switch the high voltage (:1: 2.1 kV) applied to the CdTe housing within less than 1 us. This required nu- merous tests of home made transformers by M. Rabb, who designed the high-voltage switching circuit used. Due to the heat generated by the high voltage switching, the maximum modulation frequency was limited to 10 kHz. B. Data Acquisition The time constant of the recording system and the electro-optic switching was checked using a Honeywell Model LK146C8 HngTe photovoltaic detector (100 MHz band width) with scattered light from the pump laser. The total system time constant measured was better than 1 us, which was the limit of the electro-optic switch. An Infrared Associates Model HG-lOO InSb photoconductive detector with matched pre-amplifier with 350 kHz cutoff frequency was used to record the spec- tra in this study. The pre-amplified detector signal was sent to a LECROY model 6810 transient digitizer and to a Stanford Research Associates SRS-510 lock-in am- plifier at the same time in order to monitor the intensity while recording in the time domain as shown in Figure 3.9. Since the (transferred) spikes have very narrow spec— tral width, a frequency shift of the probe and / or the pump laser was easily noticeable by monitoring the output voltage level of the lock-in amplifier. Care was taken to ensure that the frequencies of both lasers were constant by monitoring the voltage level. The LECROY model 6810 transient digitizer, which was controlled by an IBM-AT compatible microcomputer through an IEEE—488 interface, had a maximum acquisi- tion rate of 5 MHz with single channel acquisition. The IEEE-488 interface board was an IO-tech Model 488 that was controlled by a National Instruments GPIB driver. By using the program supplied by LECROY, after some modifications, it was possible to obtain 1000 scans of 4096 data points in less than one hour. The acquired data were sent to a SUN 4-60 workstation through an Ethernet at the speed of 1 Mbit / sec, 60 where they were either converted into ASCII format for processing or archived. Due to the large size of the data set only interesting time intervals were extracted and then processed by either of two computer programs, GNUPLOT134 or MATLAB.135 Chapter 4 Results and Discussion 61 62 2.4.3) ( 4| Imus) Transferred spike 3-level 4-level probe probe Gaussian Bennett spike . \ Rotational / Energy 1,J,3) Transfer ( J\’\__ _/Il,\_(1.s.3) Vibrational ,,,,,,,,,,,, Energy Transferred hole Bennett hole 4:. ‘ .. T fer Figure 4.1: Graphical illustration of velocity distribution of molecules involved in the pump and probe. The Bennett hole can by studied by probing either the QP(4,3) or the QQ(4,3) transition while the Bennett spike can be done by using the QP(5,3) transition in 21/3 «— V3 band. The Bennett spike is collisionally transferred into different rotational levels and probed by four-level double resonance. It is not clear whether there exist transferred holes or not. Pump v I. Introduction Figure 4.1 is a graphic illustration of collisional energy transfer paths and their results on the velocity distribution of 13CH3F molecules perturbed by a pump laser. A CO; 9P(32) laser depopulates molecules in a selective velocity group from the (v, J, K) = (0,4,3) level to the (1,5,3) level, thereby creating a Bennett hole in the lower level and a Bennett spike in the upper level. The QP(5,3) transition in the 21/3 4— 1/3 band was used to probe molecules excited by the pump in a 3-level double resonance. Molecules excited by the pump experience collisions that can change their rotational and/or vibrational levels, which are then probed in a four level double resonance. Sharp transferred spikes observed in the K = 3 levels are the result of collisions 63 that change the rotational quantum number J by 1 (AJ = i1; dipole interaction, parity changed) or by more than one (AJ = 21:2; quadrupole interaction, parity un- changed, AJ = i3; octopole interaction, parity changed). Due to the large impact parameters for majority of these collisions, molecules conserve many of their charac- teristics such as velocity, alignment, and orientation even after a number of collisions. These molecules are responsible for the sharp spike observed in the power modulation and a dispersion shape in the circular birefringence measurement. The widths of the transferred spikes increase as IAJ I = IJMOI.e — qumpl since collisionally induced large changes in J either require several collisions or collisions with small impact parameter, either of which smear out the characteristics of the molecules. CH3F(1, 5, 3) + CH3F _. CH3F(1, J, 3) + CH3F In the vibrational swapping collisions where the vibrational quantum numbers are exchanged between two collision partners, molecules probed in the four level double resonance originate from the ground vibrational level that had a nearly Gaussian velocity distribution. Therefore those molecules that contribute to the broad Gaussian lineshape observed in the double resonance do not show any sign of photo selection of their alignment or their orientation. CH3F(1,5, 3) + CH3F“), J, K) _., CH3F“), JI, KI) + CH3F(1, J”, K”) Another collision path that follows AK = 3n was observed in K = 0, 3, 6, 9 levels as a broad spike in the lineshape of the double resonance. Although directly pumped molecules are responsible for the absorption skewed to the spike direction, they do not conserve their alignment or their orientation as well as AK = 0 process, probably because the change in the K quantum number requires a hard collision which destroys the photo selected alignment and/or orientation. CH3F(1, 5, 3) + CH3F -* CH3F(1, J, 3n) + CH3F, n = integer Our main concern in this chapter is about the sharp spike observed only from K = 3 levels in 13CH3F or from K = 9 in 12CH3F. A lineshape study of transferred spikes in “CH3F is discussed first. Then the lineshapes of intensity modulated or 64 polarization modulated double resonance of 13CH3F and its time resolved observation are described subsequent sections. In all of the spectra shown in this chapter the horizontal axis is the microwave frequency offset from the frequency of laser line used to generate the sidebands. The laser and the sign of the sideband is given in Table 4.1, for 12CH3F and in Table 4.5 for 13CH3F. II. Lineshape Study of Transferred Spikes in 12CH3F“ A. Three-Level Double Resonance Three-level double resonances were observed while pumping either the QQ(12,2) or the QR(11,9) transitions in the V3 band with probe transitions in both the V3 fundamental band and in the 2V3 «— V3 hot band. Examples of three-level double resonances for the two pump transitions with probe transitions in the fundamental band are shown in Figs. 4.2 and 4.3, while a three-level double resonance for the QR(11,9) pump and a hot-band probe transition is shown in Fig. 4.4. Comparison of Fig. 4.2 and 4.3 demonstrated that pumping the QR(11,9) transition is more effective than pumping the QQ(12,2) transition for comparable laser power. This was not unexpected, because the linestrength is greater and the offset in frequency is smaller for the QR(11,9) than for the QQ(12,2) transition (Table 1.1). In addition, although strong three-level double-resonance spectra could be obtained for either system, the combination of pump and probe transitions for the QQ(12,2) double resonances at- tainable with our system was such that no usable information about the pump power density could be obtained from the lineshapes. This was a result of the relative fre- quencies of the pump and probe transitions as well as the pump power available and is explained elsewhere.ll Finally, because the separation in frequency is greater for larger K, the probe transitions were well separated when the QR(11,9) transition was pumped, whereas there was strong overlapping with the QQ(12,2) pump. In fact, with the QQ(12,2) pump, transferred spikes are seen as a result of the simultaneous pumping of the QQ(12,1) transition. For all of these reasons, we chose to concentrate on double resonances obtained with the QR(11,9) pump. Analysis of the lineshapes 65 WWW l l J I 13900 13866 13832 13798 13764 13730 Figure 4.2: Three-level infrared-infrared double-resonance spectra of the QP(12,2) transition in the V3 band of 12CH3F; the QQ(12,2) transition in the same band was pumped by the 9P(20) 12CmO; laser. The horizontal axis is the (negative) microwave frequency (MHz) offset from the 9R(12) 13le’O; laser. The lower trace is the single + double resonance and the upper trace is the double resonance. 66 —— 'I“ I I -"~ lm l l I 11250 11290 11330 11370 11410 11450 Figure 4.3: Three-level Infrared-infrared double resonance spectra of the QQ(11,9) transition in the V3 band of 12CH3F; the QR(11,9) transition in the same band was pumped by the 9P(22) 12C130; laser. The horizontal axis is the microwave frequency (MHz) offset from the 9P(20) 12C160; laser. The lower trace is the single + double resonance and the upper trace is the double resonance. The broad line was recorded after the first demodulation. For simplicity, the term single resonance signal is used to indicate this part in the text, since it is the average value of the single resonance and the double resonance. The spectrum with a sharp spike was recorded after the second demodulation. This part is called the double resonance signal in the text; it is the double resonance minus the single resonance. The area of the Bennett hole measured in the single resonance signal was ~ 1% of the total area, which implies that ~ 2% of the molecules in the ground state are excited by the laser pumping. 67 I I I I l J :===d‘4 9440 9420 9400 9380 9360 9340 Figure 4.4: Three-level infrared-infrared double-resonance spectrum of the QQ(12,9) transition in the 2V; 7— V3 band of 12CH3F; the QR(11,9) transition in the V3 band was pumped by the 9P(22) 12C180; laser. The horizontal axis is the (negative) microwave frequency (MHz) offset from the 9P(36) 12C160; laser. for the QR(11,9) double resonances showed that the area of the Bennett hole pro- duced in a fundamental band probe transition was of the order of 2% of the area of the single-resonance transition, which gives an indication of the extent of pumping for the experiments reported here. The QR(11,9) was also more favorable for the experiments here because the pump and probe transitions of interest (those with I: = 9) were well resolved. For low I: in CH3F, the transitions are so close together that the QQ(12,1) transition is also pumped when the QQ(12,2) is pumped. The three-level lineshapes were analyzed as described in the previous section (and more thoroughly elsewhere") in order to obtain a value for the width of the Bennett spike produced in the pumped level in the v3 = 1 state. For these experiments, the pump laser power was typically 1 W and the beam diameter was ~ 10 mm. The resulting spike in the upper state population was essentially Lorentzian with a halfwidth at halfheight that was ~ 1.4 MHz. 68 B. Four-Level Double Resonance Four-level double resonances were observed for each of the three pump transitions — QR(11,9), QQ(12,2), and QR(31,4) — but for the high-J pump only one four-level effect, on the QP(30,4) fundamental transition, was strong enough to be observed easily. Although many four-level effects could be seen with the QQ(12,2) pump, for the reasons given in the previous section, I report results of lineshape analyses only for experiments with the QR( 11,9) pump transition. Fig. 4.5 is a plot of the four—level effects on some QP(14,K) transitions caused by pumping the QQ(12,2) transition. The simultaneous pumping of the K = 1 and 2 transitions is clearly seen. Fig. 4.6 shows the four-level effects, recorded by the double-modulation procedure, on the Q(9,3) - Q(9,9) and Q(12,3) - Q(12,9) hot band transitions observed with the QR(11,9) pump. These transitions occur in the same sweep because one set absorbs the negative sideband and the other absorbs the positive sideband. Although four-level effects are seen for all of the transitions, obvious transferred spikes are seen only for the Q(12,9) and Q(9,9) lines. In addition extra intensity enhancement is apparent for the transitions with K: 6 and K = 3 showing again the Al: = 3n selection rule for direct transfer of rotational energy by collision. The four-level effects on the transitions for which K 96 9 :i: 3n are attributed to V - V energy transfer (vibrational energy swapping). A series of transferred spikes for both fundamental and hot band probes were observed with the QR(11,9) pump and analyzed by means of the four-level double- resonance lineshape equation given above. The lasers used for the probing in these experiments are shown with the calculated center frequencies and microwave offsets in Table 4.1. Examples of the lineshapes are shown in Figures 4.7 and 4.8 and an example of the result of the fitting is shown in Figure 4.9 assuming single spike and in Fig- ure 4.10 assuming two spikes. They show that while the transferred spike part of the double-resonance lineshape cannot be fit satisfactorily with one K-S function, a sum of two K-S functions provides a very precise representation. The fitted values of the r.m.s. change in velocity that results from collision(s) that bring the molecules 69 l l I 15800 15500 15200 14900 14600 14300 Figure 4.5: Four-level infrared-infrared double-resonance of the QP(l4,0)—QP(14,5) transitions in the 2V3 +— V3 band of 12CH3F. The QQ(12,2) and QQ(12,1) transitions in the V3 band, were pumped simultaneously by the 9P(20) 12CmO; laser. The horizontal axis is the (negative) microwave frequency (MHz) offset from the 9P(12) 1301602 laser. Transferred spikes are seen on both the QP(14,2) and QP(14,1) transitions. (The QP(14,1) and QP(14,0) transitions are almost completely overlapped.) 70 l Jhriil s» all) 7. least 9000 9500 10000 10500 11000 11500 12000 12500 Figure 4.6: Four level infrared—infrared double resonance of the QQ(9,3)-QQ(9,9) and QQ(12,3)-QQ(12,9) transitions in the 2V3 4— V3 band of 12CH3F. The QQ(12,K) tran- sitions are the result of absorption of the negative sideband while QC.2(9,K) transitions are the result of absorption of the positive sideband, both of which are present in the probe radiation. The horizontal axis is the microwave frequency (MHz) offset from the 9P(36) 12C160; laser, negative for QQ(12,K), positive for QQ(9,K). The QR(11,9) transition in the V3 fundamental band was pumped by the 9P(22) 1"’CmO; laser. Cal- culated frequencies and relative intensities for normal single resonance spectra are plotted below the recorded spectra with + for J =9 and with O for J =12. 71 T I I 1 4L 18070 18030 17990 17950 17910 17870 Figure 4.7: Four-level infrared-infrared double-resonance spectrum of the QR( 13,9) transition in the 2V3 ‘— V3 band of 12CH3F; the QR(11,9) transition in the V3 band was pumped by the 9P(22) 12C160; laser. The horizontal axis is the (negative) microwave frequency (MHz) offset from the 9P(36) l"’CmO; laser. into the states probed are shewn in Tables 4.4 and 4.3 for hot band (2V3 «— V3 band) and fundamental (V3 band) transitions, respectively. The values for the hot-band transitions are plotted in Figure (4.11) against AJ, where AJ is the difference be- tween the J value for the lower state of the probe and the upper state of the pump transition. In view of the relatively slow rate of direct vibrational energy transfer, the r.m.s. changes in velocity for the hot band probes reflect the changes as a result of collisionally-induced rotational transitions in v3 = 1. The values given in Table 4.4 and plotted in Figure 4.11 parallel the values obtained earlier for 13CH3F.28 They increase monotonically as A] increases in absolute value. The ratio of the area of the broad component to the narrow component of the transferred spikes also increases as AJ increases (shown in Figure 4.13). If the broad component is interpreted as resulting from collisions with small impact parameter, this is indication that a greater proportion of hard collisions is required for rotational energy transfer with larger AJ. Finally, the ratio of the areas of the Gaussian to spike contributions also increases as AJ increases, which indicates that the time required 72 l l I 9990 9950 9910 9870 9830 9790 Figure 4.8: A typical double resonance spectrum in the fundamental band. (QR(11,9) transition in the V3 band is shown.) L l l I 12360 12388 12416 12444 12472 12500 Figure 4.9: Comparison of observed (noisy line) and calculated (smooth line) four- level double-resonance spectrum for the QQ(9,9) transition in the 2V3 4— V3 band of 12CH3F; theQR(11,9) transition in V3 band was pumped by the 9P(22) 12CIBO; laser. The horizontal axis is the microwave frequency (MHz) offset from the 9P(36) 12C160; laser. The calculated curve is the best fit to a single Keilson-Storer function + Gaussian. 73 L l l I 12360 12388 12416 12444 12472 12500 Figure 4.10: Comparison of observed (noisy line) and calculated (smooth line) four- level double-resonance spectrum for the same pump-probe combination and horizontal axis as shown in Fig. 8. Here, the calculated curve is the best fit to a sum of two Keilson-Storer function + Gaussian. 50 T I I I I I 45 - ‘ <> . 40 - . 35 - <> 1 A 30 I o <> 0 0 I um. 25 - o - 20 - <> - 15 - - 10 - -( P o I l l l L l .4 -2 o 2 4 6 8 10 AJ Figure 4.11: Plot of the ratio of the area of the wide spike to that of the narrow spike vs. AJ for the four-level double resonances listed in Table 4.2. 74 200 I l I I I I O 150 - O 1 O O O O O AIL-""100 "' -I O 50 h- .4 0 I l l l l I -4 -2 0 2 4 6 8 10 A] Figure 4.12: Plot of the r.m.s. change in speed vs. AJ for the molecules that contribute to the broad spike for the four-level double resonance transitions listed in Table 4.2. for rotational energy transfer increases as A] increases. Contrary to our perception about transferred holes and spikes, the Avrm, values calculated for the fundamental probes in Table 4.3 depend on the upper state of the probe transitions, which implies that there may be no transferred holes or that the contribution of the transferred holes to the observed signal may be small. Considering that the sharp spikes originate from directly pumped molecules, this is reasonable since it is highly improbable that only molecules in the selected velocity group fill up the burned hole in the collisional process. This question could probably be answered by probing transitions in diflerent vibrational modes such as V3 while pumping the same QR(4,3) transition in the V3 band. Unfortunately our IMSL system does not cover the V3 band frequency region. In principle, it should be possible to make a quantitative comparison of rate con- stants for collisional rotational energy transfer and V — V processes by comparison of the intensities of the double resonance effects. We show in the Appendix that by comparison of relative intensities of three-level and four-level double resonance effects 75 5 I I f I r I O 4 - ... 3 I- .7 Ratio 0 2 O P o O o O 1 - O .. 0 I l l l J I -4 -2 0 2 4 6 8 10 AJ Figure 4.13: Plot of the ratio of the area of the wide spike to that of the narrow spike vs. AJ for the four-level double resonances. under the same experimental conditions that it is possible to determine the ratio of the effective rate constant for collisional energy transfer from the upper level of the pump to the lower level of the probe, either directly or through some other level, to the effective rate constant for loss of population from the lower level of the probe by any mechanism. If the QR(11,9) transition in the V3 band is pumped, the three-level double res- onance effect on the QQ(12,9) transition and the four-level effects on the Q(2(9,9) and QQ(13,9) transitions, all in the 2V3 «— V3 band, can be recorded without chang- ing laser lines. Furthermore, the intensity-stabilization system in our IMSL source insures that the intensity of the sideband used to monitor these lineshapes remains constant. Thus, by taking appropriate ratios of the narrow spike, broad spike, and Gaussian contribution of each of the two four-level double-resonance lineshapes to the intensity of the three-level lineshape recorded under the same conditions, the corresponding ratios of rate constants can be determined. For the transitions studied, the ratios at sample pressure 20 mTorr and ~ 297K 76 are 0.183, 0.110, and 0.0044 for the narrow spike, broad spike, and Gaussian, respec- tively, for the QQ( 13,9) transition and 0.116, 0.195, and 0.0064 for the corresponding components of the QQ(9,9) transition, respectively. The uncertainty in these ratios is rather large, perhaps 10—15 %. i The lower level of the QQ(13,9) transition can be reached from the upper level of the QR(11,9) pump by a single AJ = +1 collisionally-induced transition, while the lower level of the QQ(9,9) transition requires AJ = -3 from the upper level of the pump. The population ratios show that the effective rate constant for production of the sharp spike is more than 50 % larger than the rate constant for production of the broad spike for the QQ(13,9) transition, whereas the reverse is true for the QQ(9,9) transition. This provides additional evidence for either more collisions or harder collisions required to cause a IAJ I = 3 than a IAJI = 1. At a pressure of 20 mTorr, the Gaussians are only 1.5 % and 2.1 % as intense as the overall spikes for the QQ( 13,9) and QQ(9,9) transitions, respectively. The sum of the population ratios is slightly larger for the QQ(9,9) than for the QQ(13,9) transition (0.32 vs 0.30), which would be expected for thermal equilibration of the populations of the rotational states in v3 = 1. However, comparison of these ratios for different transitions requires the assumption that the rate constants for effective loss of population from these levels is the same, which is probably not the case. C. Summary As expected, there is a strong parallel between the results obtained for 12CH3F in this work and those obtained for 13CH3F in a previous study from this laboratory.”3 The principal results are as follows: 1. Transferred spikes are seen in the double-resonance probe transitions in CH3F only when the quantum numbers for the pump and probe transitions obey the collisional selection rule AI: = 3n where n is a positive or negative integer. Sharp spikes are seen only for AI: = 0. 2. Transferred spikes are seen for all values of J for which the selection rule in (1) is satisfied. For fundamental pump and hot band probe the change in velocity 77 on collision increases monotonically as the J of the lower state of the probe gets further away from the J of the upper state of the pump in either direction. For fundamental pump and probe the change in velocity generally increases as the difference in the J values of either the lower or upper states of the transition increase. 3. The lineshapes of the transferred spikes are very well represented by a theoret— ical equation based on a collision kernel that is the sum of two Keilson-Storer functions. 4. The area of the broad component of a transferred spike increases relative to the area of the narrow component as AJ increases. 5. A Gaussian-shaped component, centered at the resonance frequency of the tran- sition and with the expected Doppler width, is observed as a double-resonance effect for all fundamental and hot-band transitions. For transitions with both spike and Gaussian components, the area of the Gaussian increases relative to the spike as AJ increases. As mentioned in the previous study,28 the transferred spikes for |AJ| > 1 do not obey dipole selection rules, so there is a question as to whether these effects occur as a series of dipole-allowed collisionally-induced transitions or as one or more transitions with IAJ I > 1. Arguments have been presented for both possibilities, but as of yet we do not have direct evidence for either mechanism. Recent time-resolved infrared- millimeter wave results have been interpreted by means of a computer simulation that included both mechanisms with the result that for IAJ I > 2 or 3, the effects of single collisions with large AJ dominate. This is a question that could in principle be answered by time-resolution of the transferred spikes and some preliminary time resolved experiments are described in section 3. III. Saturation Absorption Spectroscopy in 13CH3F The famous QR(4,3) transition in the V3 band of 13CH3F, whose transferred spikes were studied by Matsuo and Schwendeman,28 can be pumped with a 12CO; gas laser 78 unlike the QR(11,9) transition of 1"‘CH3F which requires an isotopic 12C180; gas laser. Therefore, we could pump this transition with our flowing gas laser which can deliver moderately high power (1-5 W). The fate of the molecules pumped in the QR(4,3) transition is the subject throughout the last portion of this dissertation. A. Three-level Double Resonance Lineshape Difference in the lineshape of three-level double resonance spectra was observed be- tween parallel (0* / 0*) and perpendicular (0* /1r) configurations. When the QP(5,3) 2V3 +— V3 hot band was recorded with a 1r probe while a 0* polarization pumps the QR(4,3) V3 transition, its linewidth is narrower than the one recorded with both 0* pump and probe (Figure 4.14). Contrary to the previous report by Leite et al.62 where a wider linewidth was observed in 0* /1r configuration, a broader lineshape was observed in the 0* /0* configuration (thick line) compared with the spectrum with 0* / 7r (thin line) under the same condition. The different observation is attributed partly to the fact that our energy levels are in a cascade system whereas a folded three level (two in terms of energy levels) system was studied by Leite et al., but mainly to the fact that saturation broadening is dominant in our experiment, whereas collision broadening is dominant in Leite’s experiment. A surprising observation is that the absolute intensity from the parallel configuo ration experiment is smaller than from the perpendicular configuration one (Figure 4.15) contrary to a three-level calculation.13‘ It is possible, even after careful con- trol of the experimental conditions, that some experimental errors such as intensity difl'erence in the two experiments or phase settings in the lock-in amplifier led to the discrepancies. Or, since the three-level calculation did not consider m changing collisions this may imply the m changing collisions are important in the theory, as pointed out by Leite et al.62'53 At low pressure, where the effect of phase-changing collisions is small, a dip (or a splitting depending on the point of view) appeared at the center frequency of the spike as others have reported."""""13""""u The dip recorded under the 0* / 0* configuration is wider, as shown in Figures 4.16 and 4.17. It is obvious in each of the figures that 79 14605 14601 14597 14593 14589 14585 Figure 4.14: Three-level double resonance spectra of QP(5,3) transition in the 2V3 «— V3 band while the QR(4, 3) transition in the V3 fundamental band was pumped. The intensities of both peaks were normalized. (a) 0* probe and 0* pump is broader than (b) 7r probe and 0* pump. Sample pressure was 19 mTorr. l 1 1 14605 14601 14597 14593 14589 14585 Figure 4.15: Three-level double resonance spectra of the QP(5,3) transition in the 2V3 «— V; band while the QR(4, 3) transition in the V3 fundamental band was pumped. (a) 0* probe and 0* pump is weaker than (b) 7r probe and 0* pump. Sample pressure was 19 mTorr. 80 J 14605 14601 14597 14593 14589 14585 1 l Figure 4.16: Pump/ probe polarization dependence of three-level double resonance observed in the QP(5,3) transition, recorded with 3 mTorr sample. the lower trace, recorded with the parallel configuration, is wider in the splitting and broader in width than the upper trace obtained with the perpendicular configuration. These observations agree with the three-level calculation considering the m se- lection rules (Am = 21:1 for perpendicular configuration and Am = 0 for parallel configuration) and appropriate rotational line' strengths. The calculated results are plotted in Figure 4.18. Due to the inhomogeneous beam profile of the pump laser as a result of the rapid divergence after the electro-optic modulator, only qualitative comparisons were made. As the pressure increases, phase changing collisions become important and the dip decreases as shown in figure 4.19. Based on the pressure dependence the dip seems to be the result of velocity selective optical pumping for reasons similar to those explained by Liao et “1.32.31 81 l l I 14605 14601 14597 14593 14589 14585 Figure 4.17: Pump / probe polarization dependence of threelevel double resonance observed in the QP(5,3) transition, recorded with 1.5 mTorr sample. l l , - -605 -600 -595 -590 -585 Figure 4.18: Calculated three level double resonance lineshape under (a) thin line: 0* /0* (b) thick line: 0* /1r configurations, respectively. 82 rnTbmr lrnTbmr l l l I 14605 14601 14597 14593 14589 14585 Figure 4.19: Pressure dependence of three-level double resonance observed in QP(5,3) transition. To suppress relatively slow four-level contributions, the pump laser is optically modulated at 1 kHz. B. Four-Level Double Resonance Lineshape Although the absolute intensity of the four-level double resonance signal is stronger in the perpendicular configuration than in in the parallel configuration, as in three- level double resonance, their lineshapes after intensity normalization are practically the same, as shown in Figure 4.20. The slight mismatch in the baseline most likely results from the difference in pump laser intensity for the two configurations. At low pressures, at which a dip was observed in the three-level double resonance signal of the QP(5,3) transition, a similar dip was observed in four-level double reso— nance when the probe laser was tuned to the QR(4,3) and QR(6,3) transitions under parallel configuration. Observed four-level dips are shown in Figures 4.21 and 4.22 for QP(6,3) and QP(4,3) in the 2V3 +— V3 band, respectively. In Figure 4.21, the dip disappears as pressure increases, probably because collision broadening becomes an important factor. The observed signal is extremely weak and requires hours of data averaging. An attempt to reproduce this observation failed and no further attempt has been tried as yet. The dip was observable only under parallel configuration but not 83 12750 12740 12730 12720 12710 12700 Figure 4.20: Four-level double resonance lineshape of the QP(6,3) transition recorded with 0* pump and (a) 0* probe (thick line) (b) 1r probe (thin line). The two peaks had different intensity values and were normalized for comparison. Sample pressure was 21 mTorr. with perpendicular configuration, in accordance with the report by Zou and Bloem- bergen.138 The four-level dip was not observed in the qP(7,3) transition, however. (Figure 4.23). By comparing Figures 4.21 and 4.19, two differences are noticeable between three- and four-level dips. Unlike the three-level dip, the peak at higher frequency is stronger in the four-level dip. The width of the dip in the four-level is experiment larger than the one in the three-level experiment. Although the cause of the dip is yet to be investigated theoretically and experimentally, it is possible that the same physical phenomena that create the dip in the three-level lineshape, namely either an optical Antler-Townes effect or velocity selective optical pumping, or both, have caused this observation. If the off-diagonal terms of the two pumped levels (p33) in a density matrix representation are coupled into the four-level scheme via elastic collisions, the dip may be calculated in the same way that the three-level calculations were calcu- lated. That is to say the coherence is transferred via collision (collisional coherence transfer). Knowing that elastic collisions partially thermalize the velocity distribution 84 l l l I 12740 12736 12732 12728 12724 12720 Figure 4.21: Four-level double resonance lineshape observed in the QP(6,3) transition at various pressures. I T U I J l l 1 16230 16226 16222 16218 16214 16210 Figure 4.22: A clip observed from the QP(4,3) transition. Sample pressure was 1.5 mTorr. The skewed direction and its width are similar to the dip observed from the QP(6,3) transition. 85 r I I I I 1 l 1 f 10635 10631 10627 10623 10619 10615 Figure 4.23: Four-level double resonance lineshape observed in the QP(7,3) transition. Sample pressure was 1.5 mTorr. The peak is symmetric at the top and does not show any sign of dip. while spreading out the coherence coupling, if the coherence transfer exists at all, the wider and reversed intensity of the splitting in the four-level dip agrees with our view of the collisional processes. C. Simultaneous Measurements of Spikes for Co- and Counter-propagating Beam Geometry. The sub-Doppler resolution of saturation absorption spectra has been widely used for accurate measurement of transition frequencies, as in the laser Stark Lamb dip and conventional absorption experiments. When transitions are heavily overlapped or when the molecules cannot be trapped in a Stark cell, alternative methods are required. Measurement of spikes and transferred spikes whose frequency can be ac- curately measured to better than 0.1 MHz is an ideal alternative, especially when the desired transitions are in a hot band overlapped with strong fundamental transitions. To obtain accurate transition frequencies, however, separate double resonance experi- ments under co- and counter-propagating conditions are necessary for each transition, 86 which requires more effort and is usually avoided in practice. We have found that by simply reflecting the pump beam back into a sample cell, using an aperture with a tiny hole (d =~ 1mm) or a mirror with a small hole in it, separate spikes for co- and counter-propagating conditions can be recorded simultaneously by pumping and probing the QR(4,3) transition (Figure 4.24). The offset between the pump laser and the center frequency of the transition can be calculated from the separation in frequency of two spikes without relying on the exact value of the laser frequency or on any applied field, such as used in Stark experiments. The offset of 24.2 :l:0.l MHz measured in this experiment is more ‘39 measured in a laser Stark experiment accurate than the previously known 25.8 MHz largely because the lasers used in the present experiment were stabilized against a fluorescence Lamb dip. A number of different transitions were recorded in this way and all of them show consistent values after correcting for the Doppler effect. For example, the distance between the two spikes in Figure 4. 25 observed in the QP(5, 3) transition in the 21/3 1— V3 is 47. 0 MHz, which becomes 48. 5 MHz after Doppler correction to the QR(4, 3) frequency. A similar measurement performed for the Q(102,9) transition in the 21/3 «- 113 band of 12CH3F was used to determine that the offset between the QR( 11,9) transition and the 9P(20) line of a 12C1802 laser is 24.8 :1: 0.1 MHz. (Figure 4.26) A second unusual feature is that the heights and widths of the resonances depend upon the propagation directions.“140 A peak obtained for counterpropagating beams is narrower with a much higher maximum in the cascade three level system, whereas the opposite case was observed in a folded three level system?“0 The asymmetric characteristics of the two peaks have been used in a ring resonator to obtain a unidi- rectional laser action as a result of the gain asymmetry“1 or to measure the lifetime of the intermediate states.”'"° 87 l “I L J 16400 16366 16332 16298 16264 16230 Figure 4.24: The QR(4,3) transition in the V3 band of 13CH3F was probed by an IMSL operating on the 9R(26) line of a 13C0; laser while being pumped by another 9R(32) C0; laser. The spike under counter propagating condition is at —16339.0 MHz whereas that at —16290.5 MHz is for the co-propagating condition. The difference between the two spikes is 48.5 MHz which corresponds to 24.25 MHz offset. 88 1 14620 14600 14580 14560 14540 14520 Figure 4.25: The QP(5,3) transition in the 21/3 +— 143 band of 13CH3F was probed by an IMSL operating on the 9P(16) line of a 13C0; laser while the QR(4,3) transition in the V3 band was being pumped by another 9R(32) C0: laser. The center frequencies of the co— and counter-propagating spikes are 14596.0 MHz and 14547 .0 MHz, respectively. 89 Table 4.1: List of transitions of the 2V3 «— V3 band in 12CH3F and their frequencies plotted in this Chapter. Transition frequency intensity laser line 52; - Q Q(2(9,9) 3093534853 0.008558 12C1602 9P(36) 12433.10 QR(10,9) 3147456975 0.001677 12C1602 9P(16) —16867.65 QQ(12,9) 3091352861 0.004959 12C1602 9P(36) -9386.82 QR(12,9) 31558480.46 0.002586 1201604 9P(14) 14451.58 QQ(13,9) 3090494247 0.004128 120160, 9P(36) 47972.96 QR(l5,9) 3167930005 0.002964 12C1602 9P( 8) -17761.38 QQ(16,9) 3087525516 0.002337 12C1602 9P(38) 13357.65 QR(17,9) 3175647503 0.002793 ”01°02 9P( 6) 9991.23 QQ(18,9) 3085219720 0.001565 12C1602 9P(38) -9700.32 QQ(21,9) 3081273791 0.000825 12C1603» 9P(40) 12595.26 Table 4.2: List of transitions of the V3 band in 12CH3F and their frequencies plotted in this Chapter. Transition frequency intensity laser line 9; — Q qQ(11,9) 3139525559 0.983508 120160... 9P(20) 11355.18 QR(11,9) 3199858806 0.365846 ”0180, 9P(22) -26.10 QP(12,9) 3078365450 0.331194 12Cwo2 9P(40) 46488.15 Q11(13,9) 3208176137 0.465245 12C1602 9R( 8) -9891.29 QQ(14,9) 31368401.78 0.564118 1201602 9P(20) 45498.63 QR(14,9) 3212229733 0.484147 1201602 9R(10) 41969.56 QR(15,9) 3216213295 0.487108 ”C1302 9R(12) 43946.54 QR(16,9) 32201268.41 0.477234 1201602 9R(14) 45822.86 QR(l7,9) 3223970400 0.457373 1201602 9R(16) 47599.35 QQ(21,9) 3128201297 0.133864 ”01602 9P(24) 8765.82 90 Table 4.3: Velocity changes upon collision for V3 band transitions in ”CH3F. The QR(11,9) transition in the V3 band was pumped. Probe“ RAfiO k3] c (Avrmsh 1‘32 e (Avrms)2 W129) 1.0 2.2 15 11 74 R(13,9) 1.4 2.8 19 12 81 Q(14,9) 1.3 2.7 18 12 79 R(14,9) 1.7 3.2 27 15 98 R(15,9) 2.4 3.7 24 16 106 R(16,9) 2.6 4.0 27 18 117 R(17,9) 2.8 4.8 32 20 131 Q(21,9) 3.7 7.5 51 23 154 " Probe transition in the V3 band. AK = 0 for all transitions. 5 Ratio of the area of the broad spike to that of the narrow spike. ° Keilson-Storer fl parameter in frequency units (MHz) for the narrow spike. k = the magnitude of the wave vector for the probe transition. ‘ Root-mean-square change in speed (m/s) for molecules that contribute to the narrow spike. ° Keilson-Storer fl parameter in frequency units (MHz) for the broad spike. ’ Root-mean-square change in speed (m/s) for molecules that contribute to the broad spike. 91 Table 4.4: Velocity changes upon collision for 2V3 «— V3 band transitions in the CH3F. The QR(11,9) transition in the V3 band was pumped. Probe“ AJ" Ratioc kfll ‘1 (Av,,,,,)1e 11:5; 3 (Avrm,)29 Q(9,9) -3 1.7 3.5 24 16 107 R(10,9) -2 1.3 3.1 22 13 91 Q(13,9) 1 0.9 2.2 15 10 69 R( 15,9) 3 1.4 3.0 20 14 92 Q(16,9) 4 1.8 3.3 22 15 101 R( 17,9) 5 2.2 3.7 25 16 108 Q(l8,9) 6 2.6 4.0 27 17 120 Q(2l,9) 9 4.7 5.5 37 22 149 “ Probe transition in the 2V3 4— V3 band. AK =. 0 for all transitions. " AJ = J (lower state of probe) — J (upper state of pump). ° Ratio of the area of the broad spike to that of the narrow spike. ‘ Keilson-Storer fl parameter in frequency units (MHz) for the narrow spike. k = the magnitude of the wave vector for the probe transition. ° Root-mean-square change in speed (m/s) for molecules that contribute to the narrow spike. I Keilson-Storer fl parameter in frequency units (MHz) for the broad spike. 9 Root-mean-square change in speed (m/s) for molecules that contribute to the broad spike. 92 Table 4.5: List of transitions and their frequencies (MHz) in 13CH3F plotted in this Chapter. Transition vu v; frequency laser line 0; - (I QR(4,3) 1 0 31042692 I“‘Cwog 9P(32) -25 QR(4,3) 1 0 31042692 130602 9R(26) 46317 QP(4,3) 2 1 30144521 130160, 9P(14) 46198 QP(5,0) 2 1 30092702 1301602 9P(16) 44850 QP(5,1) 2 1 30092732 130160, 9P(16) 44820 QP(5,2) 2 1 30092823 1301302 9P(16) 44729 QP(5,3) 2 1 30092976 1301602 9P(16) 44576 QP(5,4) 2 1 30093194 1301602 9P(16) 44358 QP(6,0) 2 1 30040538 130130, 9P(18) 42990 QP(6,1) 2 1 30040868 1301602 9P(18) 42959 QP(6,2) 2 1 30040661 130130, 9P(18) 42867 QP(6,3) 2 1 30040816 1301304 9P(18) 42712 °P(7,3) 2 1 29988045 130160, 9P(20) 40605 QR( 10,3) 2 1 30843128 130160, 9R( 14) 9116 QI>(22,3) 2 1 29124206 120130, 10R(14) 43529 QP(22,4) 2 1 29124424 1201604 10R(14) 43311 93 9420 9406 9392 9378 9364 9350 Figure 4.26: The QQ(12,9) transition in the 2V3 4— V3 band of 12CH3F was probed by an IMSL operating on the 9P(36) line of a 12C0; laser while the QR(11,9) transition in the V3 band was pumped by another 9P(22) 01803 laser. The spike under counter propagating conditions is at -9409.6 MHz whereas it is at -—9361.7 MHz for co- propagating condition. The difference between the two spikes is 47.9 MHz which corresponds to 24.8 MHz offset in the QR(11,9) after correcting for the Doppler effect. 94 IV. Polarization Spectroscopy Figures 4.27 and 4.28 compare double resonance signals recorded with a 7r (i.e., linearly polarized) probe while a 0+ (i.e., left circularly polarized) laser was used for pumping. The top traces in Figures 4.27 and 4.28, recorded with a 1r analyzing polarizer in front of the detector, are almost identical with normal intensity-modulated double resonance signals for the case in which the 1r probe beam is observed without the analyzing polarizer while the 11‘ pump beam is being mechanically modulated. When the analyzing polarizer is set to the 0* angle, the phase of the sharp spike observed on top of the broad Gaussian is reversed as shown in the middle trace of Figures 4.27 and 4.28. The top trace was subtracted from the middle trace to remove the Gaussian (shown in the bottom trace), or these could be added to each other to remove the spike. This simple demonstration shows that the spike part and the Gaussian part have different polarization characteristics, which can be used to separate them. The 0* pump beam creates a population increase in the upper level (intensity modulation) as well as inducing an optical anisotropy in the excited level. The polar- ization directions of the two signals created are different. The signal from the optical anisotropy has an elliptical polarization tilted away from the probe polarization, as explained in the experimental section, whereas the intensity modulated signal has the same linear polarization as the probe beam. If a polarizer is used in front of the detector to block the original probe polarization, the weak laser-induced anisotropy can be measured. This experimental technique is called polarization labeling. The molecules directly excited by a or" pump are probed as a spike, whereas the laser-induced optical anisotropy shifts the phase of the a+ component of the linearly polarized probe, tilting its polarization axis. This is shown as a negative sign when 0:1: is selected or as positive when 7r is chosen. The Gaussian, as discussed in the pre- vious section, comes from those molecules that underwent vibrational energy transfer collisions with the directly pumped molecules. Therefore molecules originating from that process will be isotropic unless the polarization of a directly pumped molecule transfers during the collision. Therefore the phase of the Gaussian does not depend 95 14620 14600 14580 14560 14540 14520 Figure 4.27: QP(5,3) in 2V3 4— V3 of 13CH3F at 6 mTorr. The QR(4,3) in the V3 funda- mental band was pumped by a 0+ 9R(32) CO; laser. Description of the experimental conditions is given in the text. 14620 14600 14580 14560 14540 14520 Figure 4.28: QP(5,3) in 2V3 +— V3 of 13CH3F at 60mTorr. The QR(4,3) in the V3 funda- mental band was pumped by a 0+ 9R(32) C03 laser. The experimental arrangement is described in the text. 96 upon the polarization axis selected and its phase does not change in the recorded spec- trum. This laser-induced optical anisotropy was not observed when plane polarized light (0* or 7r) was used for pumping for obvious reasons. The observation just described prompted polarization modulation experiments in which the polarization states of the pump beam are modulated between 0* and 7r (alignment modulation) or between 0"” and a' (orientation modulation). V. Polarization Modulation A. Alignment Modulation (oi/1r) Alignment modulated double resonance signals show only a sharp peak located at the usual spike frequency as shown in Figures 4.29 and 4.30. When the polarization of the pump beam is modulated such that the intensities of the pump beams polarized 0* and 1r are the same, the total population difference (AN = N10,”, — NW9") created by the two pump beams are same, even though, as described in the theory section, the alignments of the molecules are different. The recorded signal, therefore, represents the absorption from those molecules that change their alignment as the polarization of the pump beam changes. This may be interpreted as a form of photo-selected linear dichroism in which a differential absorption (Aa = a, — 0,4) of two beams with orthogonal planes of polarization is measured. The observation of our alignment modulated signal in four-level double resonance shows (Figure 4.30) that the J changing inelastic collisions do not completely de- stroy the alignment. As explained above, the Gaussian component of the lineshape originates from ground level molecules that underwent collisional vibrational energy transfer and which therefore do not experience the polarization of the pump beam directly. They should therefore not contribute to the alignment modulated double resonance. Therefore the residual Gaussian background in Figure 4.30 is most likely the result of the intensity difference between the 0* and the 7r pump beams due to the experimental difficulty in obtaining the same intensity after reflection by mirrors. 97 14900 14780 14660 14540 14420 14300 Figure 4.29: The frequency of the 0* polarized probe laser was scanned from the QP(5,0) to the QP(5,4) transitions in the 2V3 4— V3 band of 13CH3F while the polar- ization of the pump laser coincident on the QR(4,3) transition in the V3 band was switched between 0* and 1r. There is no sign of signal other than at the frequency where the ordinary spike is observed, which implies that only the spike changes its orientation to follow the change in polarization of the pump beam. 98 (b)1r/blocked l 1 13050 12970 12890 12810 12730 12650 Figure 4.30: The frequency of the probe laser was scanned from the QP(6,0) to QP(6,3) transitions while (a) the polarization of the pump laser was switched between 0* and 71' and (b) the pump beam was intensity modulated by blocking its 0* component. Signals from the Gaussian part are apparent in (b) intensity modulation, but not in (a) alignment modulation. 99 B. Orientation Modulation (0'/0+) Generally circular dichroism (CD) is measured by recording the differential ab- sorption of left and right circularly polarized radiation (A0 = 0+ - a‘) in two—step experiments or by polarization modulation in which the polarization of the radiation is modulated between 0+ and 0". This technique can also be applied to the mea- surement of photo-selected vibrational circular dichroism (VCD), in which an intense 0* light is used to select the molecules and the polarization of a weak probe beam is modulated between 0* and 0’. Even those molecules that do not show ordinary VCD exhibit this kind of photo-selected VCD, since the circularly-polarized strong pump beam induces circular dichroism by creating oriented molecules. For experi- mental reasons, the photo—selected VCD was measured by probing a 0+ beam while modulating the pump beam between 0+ and 0’, as shown in Figure 3.6. The three level double resonance signal of the QP(5,3) transition in the 2V3 <- V3 band of 13CH3F was recorded with different configurations while the QR(4,3) tran- sition in the V3 band was pumped by a 9R(32) C03 laser. The pump laser was modulated by switching the polarization between 0+ and 0". In Figure 4.31-(a,b) a circularly polarized probe beam interacts with the molecules and then hits the detec- tor. When a wire-grid polarizer was used in front of the sample cell to create a plane polarized probe beam, the signal almost disappeared, providing firm proof for circular dichroism (Figure 4.31-(b)). If the polarizer was after the sample cell (in front of the detector), a spectrum with half the intensity of the VCD signal was observed (Figure 4.31-(c)). This is expected since circularly polarized light can be considered to be a sum of two plane polarized beams and only half of the probe beam intensity is hitting the detector. The only difference in the experimental conditions between (b) and (c) in Figure 4.31 is whether the wire-grid polarizer is located (b) before or (c) after the sample cell. Therefore, the probe beam is plane polarized in (b) when it interacts with molecules whereas in (c) it is circularly polarized. The experimental test just described ensures that the VCD in Figure 4.31-(a) is not the result of experimental artifacts, such as intensity diflerence between 0* and 0' or an elliptical polarization. The usual picture of circular polarization being the 100 fi-——(a) 0+ probe c) 0* probe b) 0’" probe/ P2 14620 14610 14600 14590 14580 14570 Figure 4.31: Photo-selected VCD observed from QP(5,3) in the 2V3 4— V3 band of 13CH3F while the QR(4,3) in the V3 band was pumped. (a) A 0* probe was used while the polarization of the pump beam was modulated between 0+ and 0". (b) A wire-grid polarizer was put in front of the sample cell to create a plane polarized probe beam. Other conditions were exactly same as in (a). (c) The polarizer used in (b) was moved to in front of the detector. The probe beam is circularly polarized while interacting with molecules but plane polarized at the detector. 101 sum of two orthogonal plane polarized beams is assured from the intensity ratio of (a) and (c) in Figure 4.31. Here we will derive recorded intensities for these three experimental conditions using the Jones calculus explained in Chapter 2. First a 0*(Jat) polarization is converted into 0+ by a quarter wave plate (M ,\ /4) and used for the probe while the polarization of the pump is modulated between 0+ and 0‘. Using the Jones calculus the recorded intensity is I = Inlet-AIA/4'Ia*l2 — ljwor’jllA/ct'lail2 =£-fi- This recorded signal represents laser induced vibrational circular dichroism. If a polarizer (Mo=9o) is put before the sample cell I = |M.,,M9(,M.,,J.,1|2 — |M...114...,114.,,.I.,..|2 = o , which agrees with our experimental observation. When the same polarizer is moved in front of the detector, the recorded signal is I = IMgoMc,,.M;(/4J¢,4|2 — |M90M¢,,.IM,\/4J,,1=I2 = (p? - I’D/2 - It is again a circular dichroism measurement, but its intensity is halved. C. Laser-induced Birefringence In the series of previous experiments, two linear polarizers can be used with a relative 45° angle, one before the sample cell, the other after the sample cell. Then the detector sees I = I1W¢9=451Wor1140:0441/4JatI2 " lM9=45Mor’M0=OMA/4J0*l2 = p,p;sin(26)/2 . This is a pure circular birefringence induced by the optical pumping. This result is confirmed from the approximate method discussed in Chapter 2. In Eq. 2.47 the 102 resulting intensity under similar experimental conditions was [(10) = Io[4 sin 92 - 43in 0cos 9(Ak)L + (Air2 + A042)L2 cos2 9] = o[4 sin 02 + 2sin(20)Ach + (Aka + A02)L2 cos2 0] where 0 is the angle of the linear polarizer referred to the x axis. The effect of polarization modulation is to change the sign of Air. Therefore the difference in signal is I (w) = 2Io[sin(20)Ak — sin(20)(-Ak)]L = 410 sin(20)AkL . Since 0 = 45° in this experiment, the observed signal is 4I°Ach. With this method a dispersion lineshape was observed by probing the QP(5,3) transition in the 2V3 «— V3 band while pumping the QR(4,3) in the V3 band; the spectrum is shOwn in Figure 4.32. Similar spectra were observed for the QP(6,3) transition in the 2V3 +— V3 band, which does not have direct connection to the level perturbed by the pump. As shown in Figures 4.33-4.35 a photo-selected VCD, a dispersion shape, and an intensity mod- ulated signal all show the same tendency when observed by the three-level double resonance. Upon comparison of the three spectra, it is clear that the Gaussian sig- nal observed in the intensity modulation is removed in the polarization modulation completely. Another interesting observation was made when the pressure of the sample was lowered to below 5 mTorr until a splitting was observed in the intensity modulated signal. A number of spectra were recorded under three different conditions with a linearly polarized probe. The first of these was recorded with so-called intensity modulation in which the pump was mechanically chopped. It is shown at Figure 4.36. It shows a splitting at the center of the spike. Then the electro-optic switch system described previously was placed in the pump beam path in addition to the mechanical chopper and the same experiment was repeated with the mechanical chopper. The result is shown at Figure 4.37. It seems that the presence of the CdTe crystal spoils the laser beam profile and results in no splitting. The experiment was then repeated once more without the mechanical chopper. Instead, the polarization of the pump 103 l l l I 14620 14610 14600 14590 14580 14570 Figure 4.32: A dispersion signal observed in the QP(5,3) transition in the 2V3 «— V3 band of 13CH3F while the QR(4,3) transition in the V3 band was pumped. Two polarizers were used for the probe beam (one to generate a plane polarized probe beam before the sample cell, the other after sample cell set to 45° relative to the first polarizer) while the polarization of the pump beam was modulated between 0+ and 0’ . 104 l l I I 12800 12760 12720 12680 12640 12600 Figure 4.33: Photo-selected VCD observed in the QP(6,3) transition in the 2V3 4— V3 band while the QR(4,3) transition in the V3 band was pumped. A 0* probe was used while the polarization of the pump beam was modulated between 0+ and 0". beam was modulated between 0* and 0‘ by the electro-Optic switch system. The result of this experiment is shown in Figure C. It shows a sign of a dip at the center of the dispersion signal. Upon comparing Figures 4.37 and C it is clear that the orientation modulated signal is more sensitive than the intensity modulated signal for observing the splitting. In fact, this can be expected considering that in the intensity modulation the signal is from any population changes that result from collisions, whereas in orientation modulation the signal is 80531113: the mo1ecules that do not change their orientation. In other words, the oriented molecules that underwent no or a few soft collisions are favorably probed compared to intensity modulation, where the history of the molecules does not matter as long as they stay in the same velocity group. All of these observed lineshapes agree at least qualitatively with calculations from our three-level double resonance theory.12 105 l 1 l 1 12800 12760 ' 12720 12680 12640 12600 Figure 4.34: A dispersion signal observed in the QP(6,3) transition in the 2V3 4— V3 band of 13CH3F while the QR(4,3) transition in the V3 band was pumped. Two polarizers were used for the probe beam (one to generate a plane polarized probe beam before the sample cell, the other after the sample cell set to 45° relative to (the first polarizer) while the polarization of the pump beam was modulated between 0+ and 0'. 106 l l l 1 12800 12760 12720 12680 12640 12600 Figure 4.35: Intensity modulated double resonance signal observed in the QP(6,3) transition with the same conditions as in the previous figure. A 0+ probe was used while the power of the 1r pump beam was modulated with a mechanical chopper. l l I 14605 14601 14597 14593 14589 14585 Figure 4.36: Intensity modulated spectrum of the QP(5,3) transition in the 2V3 +— V3 band while the QR(4,3) transition in the V3 band was pumped. 107 L I I 14605 14601 14597 14593 14589 14585 Figure 4.37: Intensity modulated spectrum of of the QP(5,3) transition in the 2V3 4— V3 band while the QR(4,3) transition in the V3 band was pumped. A 11' probe was used with a analysing polarizer (9 = 45) in front of the detector. l 1 L I 14605 14601 14597 14593 14589 14585 Figure 4.38: Orientation modulated spectrum of the QP(5,3) transition in the 2V3 «— V3 band while the QR(4,3) transition in the V3 band was pumped. A 7r probe was used with a analysing polarizer (0 = 45) in front of the detector. 108 VI. Polarization Labeling The assignment of observed transitions can be assisted by polarization labeling experiments based on the phase and the intensity of the signals as explained in the theory. Although intensity modulated signals (modulated-population spectroscopy”) allow a distinction between fundamental band and hot band transitions, the polar- ization labeling experiment provides information about whether the transition is in the P(AJ = -1),Q(AJ = 0), or R(AJ = +1) branch. In practice, however, measuring the birefringence is better than the normal polar- ization labeling experiments for number of reasons. 1. The birefringence measurement results in better signal/noise ratio (S/ N) be- cause the probe beam sees a constant perturbation by the pump in the bire- fringence measurement, whereas, in polarization labeling the probe beam expe- riences a sudden change in pump power in addition to the laser-induced optical anisotropy. Even though the sudden change experienced by the probe gives only a DC signal, it affects the entire detecting system and results in a poorer S/ N ratio compared with the birefringence measurement. 2. It is somewhat easier to determine the center frequency of the dispersion line- shape obtained in the birefringence measurement than the center frequency of the absorption lineshape determined in the polarization labeling experiment. The signs of the polarization modulated dispersion lineshapes show a clear dis— tinction among P, Q, and R branches, as in polarization labeling spectroscopy. Three different transitions are shown in Figures 4.39-b, 4.40-b, and 4.41. Measurement of many other transitions showed that the phase of the dispersion shape changes from positive to negative in P-branch transitions, from negative to positive in R-branch, and no observable signal was recorded in Q-branch transitions, which agrees with the results for polarization labeling spectra. By combining the two double resonance signals (intensity modulation and polarization modulation), observed transitions can be assigned unambiguously to P, Q, or R branches and to fundamental or hot band transitions. The results are summarized in Table 4.6. 109 Table 4.6: Summary of relative signs observed in the population- and orientation- modulated double resonance signals. P, Q, R: Branch of the transition. +, —, and 0 are for positive, negative, and no observable signal, respectively. vum mom, Branch Population Orientation l 0 P - — — 4— + l 0 Q — 0 l 0 R - + +- - 2 1 P + + *- - 2 1 Q + 0 2 1 fl +- -— e- 4- (b) l L l 14630 14614 14598 14582 14566 14550 Figure 4.39: The (v, J, K) = (2,4, 3) 4— (1,5, 3) observed in double resonance: (a) intensity modulated signal; (b) polarization modulated signal; (c) signal recorded after the first demodulation during polarization modulation. 110 l . 1 ‘ 1 1 1 1 16380 16360 16340 16320 16300 16280 16260 16240 Figure 4.40: The (v, J, K) = (1,5,3) «— (0,4, 3) observed in double resonance: (a) intensity modulated signal; (b) polarization modulated signal; (c) signal recorded after the first demodulation during polarization modulation. l I r 1 l l I 9050 9070 9090 9110 9130 9150 Figure 4.41: The (v,J, K) = (2, 11,3) 4— (1, 10,3) observed in four-level double res- onance under conditions of polarization modulation. The sign changes from positive to negative. 111 A remarkable result is seen in Figure 4.41. Even after the many collisions that must occur in order to be observed from the J = 10 level and the substantial change in angular momentum that is required, the directly-pumped molecules still remember the orientation induced by the pump laser. VII. Backward and Forward Spikes: Revisited As demonstrated earlier in this chapter, center frequencies of transitions and their offsets from the laser frequencies can be measured accurately by measuring the fre- quencies of two spikes occurring under co- and counter-propagating conditions (c.f. Figures 4.24, 4.25, and 4.26). As shown in Figure 4.42, the same experiment with polarization modulation gives two dispersion shaped peaks which allow easy estima- tion of the center frequencies of the spikes without fitting. The dispersion signal can also be used to lock the laser frequency at the center of the dispersion shape, thereby eliminating the intentional frequency modulation that is necessary to lock the laser to the usual fluorescence Lamb dip. , Since the intensity of the pump laser does not change in the polarization modu- lation experiment, the signal recorded after the first demodulation shows the double resonance effect under constant pumping condition. This effect of laser pumping can be simultaneously recorded while the orientation changes are being recorded from the second lock-in amplifier. In Figures 4.43 and 4.44 the lower trace (signal recorded after the first demodulation) shows the pumping effect on the absorption with a very good S/ N. 112 1 14620 14600 14580 14560 14540 14520 Figure 4.42: The (12,], K) = (2,4, 3) 4— (1,5, 3) transition of 13CH3F was probed by an IMSL while (v,J, K) = (1,5,3) 4— (0,4, 3) was pumped (a) by polarization modulation (PM) between 0* and 0" (b) by intensity modulation (IM). In both cases the pump laser was reflected back into sample cell to record both of the spikes occurring under co- and counter-configuration. (b) L2 - - 3 1 (a) L1 1 L I 16400 16366 16332 16298 16264 16230 Figure 4.43: The (1), J, K) = (1,5, 3) 4— (0,4, 3) double resonance signal recorded (a) after the first demodulation from L1 (b) after double demodulation from L2. 113 After PSD2 ———_—_—————-—— After PSDl I I I I 14620 14600 14580 14560 14540 14520 Figure 4.44: The (v, J, K) = (2,4, 3) 4— (1,5,3) double resonance signal. 114 VIII. Time Resolved Spectroscopy A. Measurement of Relaxation rates Since the transferred spikes originate from those directly pumped molecules that underwent J changing collisions with large impact parameters while the Gaussian part is presumed to result from V — V energy transfer, I expected the transferred spikes to have the fastest time response to the pumping. Everitt and De Lucia113 found from their measurements of time-resolved infrared-millimeter wave double resonance spectra, that the directly pumped spike has the fastest time response. In our work, we found that the time response of the transferred spikes becomes slower as the absolute value of AJ ( = “pumped — mebedl) becomes larger as shown in Figure 4.45. Of the transitions studied, the directly pumped QP(5,3) spike had the steepest slope, whereas the QP(7,3) spike had the slowest rise time. For AJ > 0, there is also a delay after the pump laser is turned on, which increases with IAJ I suggesting an increasing effect of multiple collisions. Unlike time-resolved experiments involving rotational transitions where popula- tion changes are the result of transitions into and out of both levels in the same vibrational mode, timeresolved signals from vibrational spectra in a stacked double- resonance configuration may show population changes of only the lower probed level, since population changes of the upper probed level may be negligible. Therefore, by measuring several levels adjacent to the pumped level, it should be possible to find out whether multiple AJ = :hl collisions or single AJ = n, (n = 2,3,4...) collisions are the main collision paths that change rotational energy populations. Also, by mea- suring the spikes and the Gaussian separately, it should be possible to deduce directly the relaxation rates of the three collision processes from recorded signals. From the AJ = 1 collision rate reported by Henry and De Lucia,"3 the calculated rate of growth of the population of the (J, K) = (4,3) or (6,3) levels in the 2V3 «— V3 band at 20 mTorr is 1.32 MHz. Since the recorded signal is the convolved result of the system time response (350 kHz band width) with a population change of the probed level that is the result of dozens of collision channels, direct fitting of the 115 absroption P(7,3) l I 0 10 15 20 Time (#13) Figure 4.45: Time resolved spectra of the (transferred) spike of QP(4,3), QP(5,3), QP(6,3), and of QP(7,3) transitions in the 2V3 4— V3 band. The QR(4,3) transition in the V3 fundamental band was pumped on at 3 psec. The transient digitizer was pre-triggered to record starting values. relaxation rates from the decay curve was not possible. Instead, as reported by Henry and De Lucia,113 a simulation including all of the important collision channels is required to extract relaxation rates from the observed decay curves. Unfortunately, the signal/noise ratio (S/N) of our system is only marginal, so that it was difficult to record more than five transitions, which were not enough for the simulation. The S/ N can be improved by increasing the sample pressure, but at higher pressure the rate also increases above the limit of the LECROY 6810 and puts the probe signal at a level at which it is no longer a linear function of the absorption coefficient. This would require a difficult calibration to locate the baselines. Even though many transitions with good S/ N were recorded with an 8«pass 1-m White type cell, these experiments showed the same non-linearity problem. For these reasons, efforts to obtain the relaxation rates were not attempted any further and only a qualitative description of the observed results will be given. As expected, at higher pressure the rates of the collision processes increase, which leads to faster time response as shown in Figure 4.46. Although I thought that the 116 I I 0 2 4 6 8 10 12 14 16 18 20 Time /ps Figure 4.46: Time resolved signal of the QP(6,3) transition at (a) 20 mTorr (b) 40 mTorr pump-on response and the pump-ofl' response would be the same, since the rates do not change, a faster pump-on increase than pump-of decrease was observed by recording at least one complete pump cycle. This is shown in Figure 4.47. For previously described reasons, the measurement of relaxation rates was not attempted any further. However, it was confirmed that there exist at least three different relaxation paths with different rates as predicted from the lineshape study of four-level double resonance. The results shown in Figure 4.48 represent the AJ = 11, AK = 0 process, the AK = 3n process, and the vibrational energy transfer, respectively. It is summarized with approximate rates; 1. sharp spike, ~ psec, observed only from K = 3 levels, AJ = in, AK = 0 CH3F(v, J, K) + CH3F -+ CH3F(v, J j: n, K) + CH3F 2. broad spike, ~ msec, observed from K = 3n,n = integer levels, AK = 3n CH3F(U, J, K) + CH3F -* CH3F(U, J’,K :1: 3n) + CH3F 3. Gaussian, ~ msec, observed from all of the levels, vibrational swapping CHaF(1, J, K) + CH3F(0, J', K’) 4 CH3F(0, J”, K”) + CH3F(1, J’”, K’”) 117 0 2 4 6 8 10 12 14 16 18 20 Time /ps Figure 4.47: Time resolved signal of the QP(6,3) transition. (a) when the pump laser is turned on; (b) when the pump laser is turned off. The measured ON signal is subtracted from a constant to have common starting level. The on-stage time response is faster and more intense than the off-stage. (a I I 0 100 200 300 400 500 ' 600 700 800 Time /ps Figure 4.48: Time resolved signals of (a) sharp spike (b) Gaussian + broad spike observed in QP(6,3) transition (c) Gaussian observed in QP(6,2) transitions. 118 B. Phase Separation of Ortho- and Para-transitions Even though relaxation rates of the three collision processes were not obtainable, the time resolved data contain useful time domain information. Since Alc # 3n collision-induced transitions require a collision-induced change of the spin, state, pumping a K = 3 transition should lead to faster population changes in other K = 3n transitions than in K 75 3n transitions. It should be possible to observe this difference by varying the phase of the lock-in amplifier that processes the steady state double resonance signal. The spectrum shown in Figure 4.49 includes the steady-state four-level double resonance signals of the J = 22, K = 1...9 transitions in the 2V3 4— V3 band of 13CH3F recorded by using the system shown in Figure 3.9 while the QR(4,3) transition in the V3 band was pumped. At J = 22, the AJ = :1:1 rotational relaxation contribution is almost certainly smaller than (at most comparable to) the other two processes. The only contributions to the double resonance signals of the para transitions (K 95 3n), are from vibrational energy transfer processes whereas both vibrational energy transfer and AK = 3n processes contribute to the signals of the ortho transitions (K = 3n). This is clearly seen when the intensities of the recorded spectrum are compared with the intensities of a calculated spectrum, as in Figure 4.49. Therefore it is reasonable to assume that the ortho- and para-transitions have slightly different time responses. Unfortunately, the time resolved signals of K = 3 and K = 4 shown in Figure 4.50 had so similar time response that when they were normalized they looked almost the same. Nevertheless, the phase difference of the two peaks, if any, could be easily detected by simulating the output of a lock-in amplifier at different phases by using 3(3) = [01 D(t)sin(wt + ¢)dt, (4.1) where w is the modulation frequency, 0 is the phase, S(¢) is the calculated signal at phase 45, and D(t) is the detected signal at time t. The experimental time domain signals and the resulting simulated phase variation are plotted in Figures 4.50 and 4.51. 119 14000 13500 13000 12500 12000 1 1500 1 1000 Figure 4.49: Double-resonance spectrum of °P(22,K) transitions in the 2V3 +— V3 band of 13CH3F upon which calculated frequencies and intensities are superposed. It is clear that the K = 3n transitions are stronger than calculated compared with K # 3n transitions. The pump transition is QR(4,3) in the V3 band and the pump source is a 9P(32) “01°02 laser. The probe source is the negative sideband on the 10R(14) 12CmOg laser; the horizontal axis is the microwave frequency offset. P(22,3 I I I I I I I 500 1000 1500 2000 2500 3000 3500 4000 Time [#3 Figure 4.50: Time resolved spectra of K=3 and K=4 transitions in Figure 4.51. The K=3 transition is stronger and faster than the K=4 transition. 120 I I I I I 6 - H 3 .- 0 -- —————— -3 .. .4 =4 -6 K=3 (ortho) .. -9 1 p 1 1 1 0 30 60 90 120 150 180 Figure 4.51: Calculated output vs. phase setting of the lock-in amplifier for the peak double resonance signal for the QP(22,3) (thin line) and QP(22,4) (thick line) transitions shown in Figure 4.49. From Figure 4.51, it is obvious that the two signals have different phases; other- wise, the two signals would have changed their signs at the same phase. At the phase near 110°, where an arrow is drawn, the absorption of the K = 3 (ortho-transition) occurs in the positive phase while the absorption of the K = 4 (para-transition) oc- curs in the negative phase. In fact, by using this calculated phase in an experiment it was possible to clearly distinguish ortho-transitions (K = 3n) from para-transitions (K # 312) as shown in Figure 4.52. The spectrum shows that the phase of K = 3n transitions are all positive whereas the phase of K 96 3n transitions are all negative, as expected from the simulation. Apparently the AI: = 3n selection rule persists for many J states away from the originally-pumped level(J = 5). The spectrum also shows that the AK = 3n peaks are skewed to lower frequency relative to their center frequencies. This supports the assumption that the I: = 3n populations result primarily from a sequence of rotational transitions that brings the molecules from the originally-pumped level to the lower level of the probe without complete thermalization of velocity. 121 I I I I I 14000 13500 13000 12500 12000 1 1500 1 1000 Figure 4.52: Double-resonance spectrum of °P(22,K) (K=0..9, left to right) transi- tions in the 2V3 4— V3 band of 13CH3F observed with the 110° phase. (The calculated spectrum is drawn with vertical bars for comparison.) The pump transition is QR(4,3) in the V3 band and the pump source is a 9P(32) 12C1603 laser. The probe source is the negative sideband on the 10R(14) 12C1603 laser; the horizontal axis is the microwave frequency oflset. 122 The results of the time-dependent spectra confirm the assumptions of the simu- lation of the time dependence of infrared-millimeter wave double-resonance spectra proposed by Everitt and De Lucia.113 They found it necessary to use a larger rate constant for Ak = 3n transitions than for Al: 75 3n transitions. The lineshapes of our infrared-infrared double-resonance spectra confirm their hypothesis that the Air = 3n transitions are collisionally-induced rotational transitions whereas the Al: ¢ 3n tran- sitions result from a V-V energy transfer. The spectra in Fig. 4.52 also demonstrate that the AI: = 3n excitation produced by radiation pumping persists for many J values away from the originally pumped level. Whether this requires many collisions or only a few is not certain. Based on the time delay in the time resolved obser- vation of the transferred spikes (J = 5,6, and 7) and the phase shift observed in the P(22,K) transitions, it is clear that many successive collisions of AJ = 1 and of AI: = 3n, AJ = n exist. Harradine et 01.52 interpret their data in terms of successive AJ = il collisions, whereas the simulation of Everitt and De Lucia113 includes a separate rate constant for AI: = 0, AJ = n collisions which would dominate at the AJ = 17 required for Figure 4.52. IX. Summary 1. The electro-optic switching system was shown to be useful for time resolved infrared-infrared double resonance spectroscopy. With a faster digitizer and a more stable laser system this experiment should give unambiguous answers to many of the current questions about collisional energy transfer. 2. The three collisional processes predicted from the lineshape of four-level infrared-infrared double resonance signals were time resolved and show differ- ent characteristics in the time domain. Time gated frequency domain spectra should be very useful for extraction of relevant information from their line shape. 3. Transitions in ortho and para CH3F were distinguished by the difference in phase, which implies successive collisions in the Air = 3n process. More detailed and extensive experiments are required to confirm this result. 123 4. The laser guiding optics used in the polarization modulation experiments can be used to time resolve the alignment relaxation rates and orientation relaxation rates without modifications. Chapter 5 Conclusion and Future Work I have demonstrated a number of sub-Doppler or Doppler-free double resonance spec- troscopic techniques by tailoring the polarization states of lasers used in double res- onance experiments. They are useful in studying collisional processes of molecules as well as in identifying observed transitions. Through the use of an electro-optic polarization modulation device and a partially transmitting mirror, various of exper- iments were demonstrated that can measure linear dichroism, circular dichroism, and circular birefringence of a laser-induced optical anisotropy. Especially, the measure- ment of circular birefringence is shown to be very useful and easy to implement in experiments. A similar technique can be used to observe a laser-induced dichroism and birefringence, in which a circularly polarized probe beam is recorded, while the polarization state of the pump beam is modulated between t and 0*. If the probe beam is recorded after passing a polarizer set 0° relative to the YZ plane, a pure linear dichroism can be measured, whereas a linear birefringence can be recorded by rotating the polarizer 45°. By taking advantage of the Doppler line profile, it was possible to extract velocity changes of molecules as a result of collisions from the lineshapes of the transferred spike. It should be possible to relate the observed dispersion lineshape to the ori- entation of the molecules, thereby obtaining changes not only of velocity but also of orientation as result of collisions. 124 125 Table 5.1: Summary of identified relaxation paths, lineshapes, relaxation times, and their effects on velocity, alignment, and orientation. Process Lineshape Rate Velocity Orientation AJ = 1, AK = 0 Sharp spike as Yes Yes AK = 3n,n integer Broad spike ms Yes No V-V energy transfer Gaussian ms No No The electro-optic switching system should be very useful for time-resolved infrared- infrared double resonance spectroscopy. The three collisional processes predicted from the lineshape of four-level infrared-infrared double resonance signals were time resolved and show different characteristics in the time domain. Time-gated frequency domain spectra should be very useful for extraction of relevant information from their line shape. If the laser guiding optics are modified, as in the polarization spectroscopy section, the system can also be used to time resolve laser-induced optical anisotropy, in which a photoreaction can be initiated with a laser and its progress can be probed by monitoring the. polarization signals either of the reactants or of the products. Since the polarization information allows a three-dimensional view of molecules, this would be extremely powerful in studies where spatial information is required such as in enzymes or in catalysts. Table 5.1 summarizes the characteristics of the different collisional processes ob- served. The sub-Doppler resolution and spatial resolution of the saturation experiments should be a valuable tool in remote sensing since a spatially fixed probe can be recorded while the pump beam selects different regions as in Figure 5.1. 126 m Pump(f2) Figure 5.1: Application of double resonance in remote sensing. By changing the incident angle of the pump beam, only a selected portion (a, b, or c) of the probe beam path is affected and its signal can be recovered after the double demodulation. Chapter 6 APPENDIX 127 128 APPENDIX The purpose of this Appendix is to develop equations that facilitate the direct comparison of the intensities of three-level and four-level double resonances taken with the same apparatus under conditions of constant pump and probe powers. The basic equation for this purpose is the relation between the spectroscopic absorption coefficient and the imaginary part of the density matrix element that connects the two states most closely involved with the absorption by the probe beam. We use this equation in the form (167;;N 112224.100]: ..(m v.)dv. (Al) in which V is the frequency and E° is the electric field amplitude of the probe beam and pab(m) is the transition dipole moment connecting states a and b of energies E, and E5, respectively, for which V ~ (Eb — Ea) / h. The density matrix factor {a is defined by p1... = (dim + “@643“ (A?) where p5,, is the element of the density matrix connecting states a and b. Also in Eq. A1, c is the speed of light in the sample; N is defined to be the number of molecules per cm3 in the lower level of the pump transition; and a is assumed to be expressible as a sum of absorption coefficients for transitions involving individual m states, where mh is the component of the angular momentum of an individual molecule in the direction of the space-fixed Z axis. For three-level double resonance, we assume a strong pump beam traveling in the Y direction and polarized in the YZ plane, so that Am = 0 selection rules apply for the pump transition. The probe beam is assumed to be polarized in the YX plane for which the selection rules are Am = i1. A further assumption, confirmed by calculation, is that the probe is weak enough that j: 4(m.v.)dv.=z.»(m)a'1:(m) (As) 129 where zab(m) = p¢b(m)E°/ h and d" (m) is independent of 3:31,. Consequently, al- though each pump transition is associated with two double resonances, m—mme—°+bem —1 and m—fm ”Ob—j m,+1 the two probe transitions may be viewed as part of a single double resonance, for which the probe intensity is the sum of two terms. Therefore, we may write 211850") L: dfl,(m,v,,)dv,, = Z [pab(m + l «— m)xab(m + 1 4— m) m + IZW" ‘1 ‘— m)z,,(m - 1 *- mll 1'10")- (A4) For a probe transition in the 2V3 4— V3 band of CH3F, pab(m :l:1 «— m) = p” < J, k,m :1: 1|¢X,IJ, k,m > (A5) in which 14., is the vibrational transition moment for the 2V3 +— V3 band and (fix, is the direction cosine between the space-fixed X and molecule-fixed z axis. Combination of Eqs. A1, A4, and A5 with the definition of 3:05 yields a3= (1———6",:""N )zg(m)d'.'.(m (46) in which g(m) = I < J',lc,m + l|¢x,|J,lc,m > I2 + I < J',k,m —1|¢x,|J,k,m > |2.(A7) The density matrix factor Jifa is calculated by solving the density matrix equa- tions for a 3-level system. The form of the equations used in this work is described in detail elsewhere11 and is essentially equivalent to other published forms (e.g., Refs. 121,142,143). In our calculation, we assume a three—level system with ener- gies E, < E. < E5. By setting N in Eq. Al to the number of molecules in state 9 at thermal equilibrium, the thermal equilibrium values of the diagonal elements of the density matrix are each calculated relative to p3,, = 1. Therefore, for example, for a single m component of level 0, p2. = em-hvp/ka'r) (AS) 130 in which V, is the center frequency of the pump transition, k3 is the Boltzmann con- stant, and T is the temperature. The absorption coefficient in Eq. A6 has been written as 03 to identify it as the absorption coefficient for three-level double resonance. To obtain the counterpart of Eq. A6 for four-level double resonance, we begin again with Eq. A1 in which V is the center frequency, an), is the transition moment, and 1’, is the off-diagonal density matrix for the probe transition (E9 < E, are the pumped levels and E. < Eb are the probed levels.). In this case, /°° a7..(mw.)dv. = human. (49) where zab(m) is still pab(m)E°/h, but now 3,6,0 is independent of m since we assume that the probe power is non—saturating. Therefore, in this case of four-level double resonance, 16 2 2N , a. = (fife—wash. (A10) in which [(J.+1)’ - k’]/3(J +1) for J +1 «— J 5.1:. = (2J +1)k2/3J(J +1) for J c— J (All) (J2 — k3)/3J for J -14— J The 51;, defined here differ from those often seen (e.g. Ref. (144)) because they include summation over m, but exclude summation over the directions of the space-fixed axes, which is just the reverse of the usual formulation. For both 3-level and 4-level double resonance in the work described here, the probe beam power, sample pressure, and optical path length are sufficiently low that absorption by the probe is not only non-saturating but also may be considered to be optically thin, so that the spectrometer signal may be written S = Glola (A12) where l is the path length, I, is the incident intensity of the probe, and G is an instrument gain factor. As a result of the amplitude modulation of the pump and the coherent detection, the observed signal is in fact, as '= 5., — 0,, = 01.1mm. - am) (413) 131 in which 50,. and am, are the spectrometer output and the absorption coefficient with the pump beam on and So” and a,” are corresponding values for the pump beam ofl. For three-level double resonance, substitution from Eq. A6 into Eq. A13 gives A53 = CV3 Zg(m)Ad-’b’¢(m) (A14) where C is the quantity in parenthesis in Eq. 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