ULTRABROAD FEMTOSECOND PULSES FOR COHERENT
ANTI-STOKES RAMAN SCATTERING SPECTROSCOPY
By
Paul J. Wrzesinski

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Chemistry
2011

ABSTRACT
ULTRABROAD FEMTOSECOND PULSES FOR COHERENT
ANTI-STOKES RAMAN SCATTERING SPECTROSCOPY
By
Paul J. Wrzesinski

This dissertation focus on the use of sub-ten femtosecond pulses applied to
coherent

anti-Stokes

Raman

scattering

spectroscopy.

The

use

of

such

a

broadbandwidth pulse coupled with adaptive pulse shaping has provided a method to
impulsively excite all vibrational modes within the bandwidth of the pulse. Furthermore,
this method using only a single beam eliminates many of the experimental difficulties
associated with the typical multi-beam CARS methods.
The generation of supercontinuum has allowed for high energy, amplified pulses
to reach the same time duration/bandwidth as lower energy femtosecond oscillators.
This significant increase in pulse energy has allowed the single-beam CARS method to
be extended beyond microspectrocopy, which requires the tight focusing conditions
afforded by a microscope objective in order to reach the necessary pulse energy. This
extension has opened single-beam CARS to fields such as remote sensing and
combustion diagnostics. This dissertation presents the evolution of single-beam CARS
in the context of these fields.
Remote sensing is demonstrated at distances of 12 m for solids, liquids, and
gases in a retro reflective set-up with signal to noise levels high enough for molecular
identification. Single shot measurements are also made, along with direct backscatter
measurements.

CARS gas phase measurements are made on several atmospheric gases, as
well as mixtures of gases. Mode-selective CARS excitation is used to excite a single
Raman mode, creating a contrast mechanism that allows for direct visualization of a
CO2 jet. Several gases were also measured in various pressure regimes to determine
the number density relationship.
Lastly, the group velocity dispersion of several combustion gases was measured
to illustrate the temporal broadening that occurs when femtosecond pulses propagate in
combustion environments. The ability to manipulate the axial resolution of a nonlinear
optical

process

when

using

adaptive

pulse

shaping

is

also

discussed.

ACKNOWLEDGMENTS
During my time at Michigan State University, there have been numerous people
who have been instrumental in my academic growth and development.
First, I would like to thank the members of my committee including Professors
Greg Swain, Gary Blanchard, and Chong-Yu Ruan.

I also extend my thanks to

members of the Dantus group past and present. In particular, I would like to thank Drs.
Ahmasi Harris and Tissa Gunaratne for all the time and energy they spent teaching me
how to get the most out of the instruments and understand everything I was doing. I
would also like to thank Dr. Dmitry Pestov for all of the knowledge and insight he
provided regarding CARS spectroscopy and all of the feedback.
In addition, thank you to my friends and family for their support and
encouragement, particularly my wife Katrina for understanding that science doesn’t
always happen between 9 am and 5 pm and that 30 more minutes really means a
couple more hours.
Lastly, I would like to thank my advisor Professor Marcos Dantus for the chance
to perform world class research, in a world class facility. His guidance and support has
afforded me the opportunities that I have available to me today.

iv

TABLE OF CONTENTS
LIST OF TABLES ........................................................................................................... vii
LIST OF FIGURES ........................................................................................................ viii
KEY TO SYMBOLS AND ABBREVIATIONS ................................................................ xiv
INTRODUCTION ............................................................................................................. 1
CHAPTER 1
CONCEPTS AND EXPERIMENTAL TOOLS .................................................................. 3
1.1. Ultrashort laser pulses and spectral phase .................................................... 3
1.2. Femtosecond laser systems .......................................................................... 6
1.3. Pulse shapers ................................................................................................ 8
1.4. Multiphoton intrapulse interference phase scan (MIIPS) ............................. 12
1.5. Conclusions ................................................................................................. 15
CHAPTER 2
COHERENT ANTI-STOKES RAMAN SCATTERING ................................................... 17
2.1. Theory of Raman spectroscopy ................................................................... 17
2.2, Comparison of Raman and CARS ............................................................... 20
2.3. Resonant and Nonresonant contributions ................................................... 22
2.4. Frequency Domain CARS methods............................................................. 23
2.5. Single-beam CARS ..................................................................................... 27
2.6. Conclusions ................................................................................................. 30
CHAPTER 3
SINGLE-BEAM CARS FOR REMOTE SENSING ......................................................... 31
3.1. Single-beam CARS for Remote Sensing ..................................................... 31
3.2. Experimental Setup ..................................................................................... 32
3.3. Pulse Shaping for Single-beam CARS ........................................................ 35
3.4. Results and Discussion: Neat Samples ....................................................... 35
3.5. Results and Discussion: Selective Excitation and Backscatter .................... 38
3.6. Results and Discussion: Selective Excitation and Backscatter .................... 42
3.7. Conclusions ................................................................................................. 48
CHAPTER 4
SELECTIVE EXCITATION OF GAS PHASE MOLECULES ......................................... 49
4.1. Selective Excitation ..................................................................................... 49
4.2. Binary Phase Shaping for Selective Single-Beam CARS ............................ 50
4.3. Experimental................................................................................................ 57
4.4. Results and Discussion ............................................................................... 59
4.5. Conclusions ................................................................................................. 65

v

CHAPTER 5
MULTI-METHOD SELECTIVE CARS ........................................................................... 66
5.1.Multiphoton intrapulse interference (MII) ...................................................... 66
5.2. Modeling MII ................................................................................................ 71
5.3. Modeling the Excitation Efficiency .............................................................. 75
5.4. Experimental setup ...................................................................................... 77
5.5. Measurements of Excitation Efficiency ........................................................ 78
5.6. Multi-method CARS in liquid and gas phase ............................................... 79
5.7. Results and Discussion ............................................................................... 84
5.8. Conclusions ................................................................................................. 86
CHAPTER 6
GROUP VELOCITY MEASUREMENTS OF COMBUSTION GASES ........................... 88
6.1. Group Velocity Dispersion ........................................................................... 88
6.2. Experimental................................................................................................ 90
6.3. GVD Measurements .................................................................................... 92
6.4. Dispersion and Raman scattering efficiency .............................................. 101
6.5. Conclusions ............................................................................................... 103
CHAPTER 7
CONCLUSIONS .......................................................................................................... 104
REFERENCES ............................................................................................................ 106

vi

LIST OF TABLES

Table 1. CARS intensity of the Raman transitions of Toluene for each type of phase
modulation..................................................................................................................... 81
Table 2. Second- and third-order dispersion values at 800 nm for each gas at a
pressure of 1 bar, along with the standard error in fitting and the statistics of the linear
fit. . ................................................................................................................................ 98
Table 3. Simulated pulse durations (fs) due to changes in dispersion as a function of
pressure for a 0.15-m path .......................................................................................... 100

vii

LIST OF FIGURES
Figure 1.1. The effect of spectral phase on temporal intensity of the pulse (second
column) and second harmonic spectrum (third column). The first column shows
fundamental spectrum (solid line) and the applied phase (dashed line). a) Corresponds
to quadratic phase distortion, b) is for cubic phase distortion, and c) is for sinusoidal
phase modulation. In columns two and three, the solid line corresponds to TL pulses
and the dashed corresponds to applied phase distortion. ............................................... 5
Figure 1.2. Regenerative amplifier schematic. (a) Grating stretcher, which stretches the
time duration of the seed pulse, (b) regenerative amplifier, (c) grating compressor where
the amplified pulses are recompressed. F1: Faraday Isolator, G1 and G2 gratings, Pc1
and Pc2: Pockel cells…………………………………………………………...………………8
Figure 1.3. Schematic of “4-f” pulse shaper, where each optical component is
separated by the focal distance f. The input beam is spectral dispersed into frequency
components and then focused by a lens. The SLM is place at the focal plane (Fourier
plane). The SLM allows for individual manipulation of each frequency with respect to
spectral phase, amplitude or polarization. After passing through the SLM the frequency
components are recombined creating a shaped, collimated output. ............................. 10
Figure 1.4.. Schematic of an all reflective, folded “4-f” pulse shaper. The output beam
follows the same path as the input, but is vertically displaced. OM: Output mirror, CM:
Curved mirror, FM: Folding mirror, and BM: Back mirror............................................... 11
Figure 1.5. Figure 1.5 Cartoon of various pulse compression methods. (a) Prism/grating
compressor, (b) Optimization algorithm using integrated SHG signal, (c) FROG/SPIDER
characterization methods (d) MIIPS method. ................................................................ 13
Figure 1.6. MIIPS principles. (a) The unknown phase (φ′′) is mapped using a reference
grid composed of linear chirp phases. (b) The SHG signal corresponding to the places
where the reference phase and the unknown phase intersect. (c) Mapping the unknown
phase using a sinusoidal reference phase. (d) The SHG signal corresponding to the
intersection of the sinusoidal reference phase with the unknown phase. ...................... 15
Figure 2.1. Energy level diagram of the Rayleigh and Raman scattering processes .... 18
Figure 2.2. Vibrational modes for CO2: The symmetric and asymmetric stretching
modes are Raman active due to the change in polarizabilty, whereas the bending mode
is IR active due to the change in dipole moment. .......................................................... 19
Figure 2.3. Single and group vibrations of peaks common to Raman scattering. The
stars indicate the frequency of the Raman signal in gas phase molecules (CO2, O2,
N2)………………………………………………...………………………………………….…20

viii

Figure 2.4. Cartoon showing the signal accumulation over an active sample volume for
a) CARS and b) Raman. Notice how the signal for CARS is phase-locked, compared to
random for Raman. This phase-locked accumulation results in the large signal
enhancement in CARS.. ................................................................................................ 22
Figure 2.5. Energy level diagrams for four wave mixing processes (ω1/ ω2;red, ω3;
blue, and ω4; orange a) resonant contribution to the CARS process and b) for
nonresonant contributions. For interpretation of the references to color in this and all
other figures, the reader is referred to the electronic version of this dissertation. ......... 23
Figure 2.6. Figure 2.6 Schematic diagrams of frequency domain CARS methods. a)
Narrowbeam CARS, b)Multiplex CAR, and c) Hybrid CARS ......................................... 26
Figure 2.7. Schematic illustrating the phase and polarization shaping method used for
single-beam CARS and a representative CARS response. The right insets show a
closer view of the probe region, and left inset shows temporal profile of the pump/Stoke
and probe components.................................................................................................. 28
Figure 3.1. a) Supercontinuum spectrum (grey) and the phase measured using MIIPS
(dashed black). (b) Measured SHG spectra (black) from the compensated pulses
(spectrometer limited at 300 nm). The experimental SHG spectrum has a bandwidth of
73nm (FWHM), which agrees well with simulations for transform-limited pulses based
on the measured spectrum. The supercontinuum pulses were compressed to 4.8 fs by
MIIPS phase compensation (see inset). (c) Residual phase on the laser after
compensation…………………………………………………………………………………..32
Figure 3.2. Setup and performance of the single-beam CARS. a) The experimental
setup. b) The spectrum, phase and polarization of components of the shaped laser
pulse. The pump and Stokes (red) components have vertical polarization (y) while the
probe (green) and CARS signal (blue) have horizontal polarization (x). The inset shows
a diagram for the CARS process. c) Spectra of six consecutive single shot spectra of
toluene collected at a standoff 12 m distance.. ............................................................. 34
Figure 3.3. Single-beam CARS spectra from liquid, gaseous and solid state samples. a)
CARS spectra from liquid toluene, o-nitrotoluene and m-nitrotoluene; b) CARS spectra
from liquid ortho, meta and para-xylene. c) CARS spectra from CS2, CH2Cl2 and CHCl3
vapors; d) CARS spectra from solid polycarbonate, polystyrene and PMMA. ............... 37

ix

Figure 3.4. 4 Single-beam CARS illustration of sensitivity and discrimination against
background signals. a) Unprocessed spectra of m-xylene collected at a standoff 12 m
distance with (black) and without (red) phase distortion compensation using MIIPS; note
the presence of a large nonresonant contribution (compared to the resonant signal) in
both cases. b) The red phase is designed to optimize excitation of the ν1 breathing
mode at 725 cm

-1

and the blue phase is designed to optimize excitation of ν 12 in-plane
-1

bending mode at 1000 cm . The lower panel shows the calculated temporal profiles
corresponding to red and blue phases. c) Unprocessed CARS spectra from m-xylene
with two specially designed binary phases. Note that the nonresonant contribution is
successfully suppressed eliminating the need for data processing. The designed binary
phases control the ratio between the two Raman peaks with an overall two order-ofmagnitude discrimination from 7:1 to 1:12. d) Integrated intensity for different binary
phases (optimized for different Raman shifts) applied in the pulse shaper……………..39
Figure 3.5. Single-beam CARS spectra with back scatter signal detection. a)
Unprocessed spectrum of o-xylene. b) Processed spectra of o-xylene and toluene. .... 42
Figure 3.6. CARS measurements of o-xylene and p-xylene mixture; a) is a 50:50
mixture, b) is a 1:99 mixture. ......................................................................................... 43
Figure 3.7. Double logarithmic plot of the relative CARS intensity for o-xylene and pxylene as a function of o-xylene concentration.. ............................................................ 44
Figure 3.8. Schematic diagram of the single-beam CARS instrument for detection of
gas-phase measurements... .......................................................................................... 45
Figure 3.9. Nitrogen CARS signal as a function of pressure. Symbols represent the
data points, while the solid lines are the power curves, fit to the data. Each plot contains
three sets of data, illustrating the reproducibility of the measurements. ........................ 46
Figure 3.10. Carbon dioxide CARS signal as a function of pressure. Symbols represent
the data points, while the solid lines are the power curves, fit to the data ..................... 47
Figure 4.1. Selective excitation of Raman-active vibrational modes via BPS: a) binary
phase mask design for ∆Ω ps < 2Ω R ; b) binary phase mask design for ∆Ω ps ≥ 2Ω R .
Here ∆Ω ps is the bandwidth of the pump-Stokes part of the laser spectrum; Ω is the

R

transition Raman shift.................................................................................................... 52
Figure 4.2. Phase-and-polarization shaping for multi-mode and selective single-beam
CARS measurements. a) Polarization mask encoded onto the laser spectrum, shown on
the background by the gray line; b) Phase mask for multi-mode CARS measurements,
when all Raman modes within the laser bandwidth are excited. c,d) Pseudorandom
-1
phase masks used for selective single-beam CARS from O2 (1550 cm ) and N2 (2330
-1

cm ), respectively......................................................................................................... 55

x

Figure 4.3. Calculated excitation spectra, η (Ω R ) , for a TL pulse (no phase modulation)
-1

and waveforms, produced by pseudorandom BPS for selective excitation at 1280 cm ,
-1

-1

-1

1380 cm , 1550 cm , and 2330 cm . ......................................................................... 57
Figure 4.4. Schematic diagram of single-beam CARS experimental setup. SLM, spatial
light modulator. Inset: a typical pulse spectrum at the sample.. .................................... 59
Figure 4.5. Selective single-beam CARS from O2 and N2 vibrations in ambient air..... 60
Figure 4.6. Selective single-beam CARS of a 1:1 N2/CO2 mixture at 1 atm pressure . 61
Figure 4.7 Selective single-beam CARS of pure CO2 at 1 atm. The target Raman shift

Ω R of the pseudorandom binary phase is tuned through the two resonances with CO2
Fermi dyads at ~1280 cm

-1

-1

-1

and ~1380 cm . CARS signal intensities at 1280 cm ,

-1

1380 cm , and integrated over 625-2125 cm as a function of Ω R .. ............................ 62
-1

-

Figure 4.8. Experimental CARS spectra acquired for Ω R equal to 1200 cm , 1280 cm
1
-1
-1
-1
, 1330 cm , 1380 cm , and 1500 cm The multi-mode single-beam CARS spectrum

of CO2 (no BPS) is shown as a reference. The other CARS spectra are scaled in
intensity by a factor of 6 ................................................................................................ 63
Figure 4.9. Imaging of a CO2 gas jet with a) no BPS and b) BPS excitation at 1280 cm

1

-

. ................................................................................................................................... 65

Figure 5.1. Simulation of MII using two chirped pulses with a rectangular spectrum.
(2)
-1
φ = 1000 fs, the divider is pixel 319, and ΩR=1500 cm a) Pulse spectrum (red,
solid), probe spectrum (blue, solid), and pulse shaping (blue, dashed) used in the
wavelength domain b) frequency domain pulse spectrum (red, solid) and relative phase
delay (blue, dashed) c) temporal profiles of the pump/Stokes (red) and probe (blue).. . 68
Figure 5.2. Simulation of MII sinusoidal phase modulation,with a rectangular spectrum.
-1
α=2π, ωc=770 nm, ΩR=1500 cm and δ=1 a) Pulse spectrum (red, solid), probe
spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength domain
b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue, dashed)
c) temporal profiles of the pump/Stokes (red) and probe (blue) .................................... 69
Figure 5.3. Simulation of MII sinusoidal phase modulation, with a rectangular spectrum.
N=13. a) Pulse spectrum (red, solid), probe spectrum (blue, solid), and pulse shaping
(blue, dashed) used in the wavelength domain b) frequency domain pulse spectrum
(red, solid) and relative phase delay (blue, dashed) c) temporal profiles of the
pump/Stokes (red) and probe (blue).............................................................................. 71

xi

Figure 5.4. Simulation of MII using two chirped pulses and an experimental spectrum.
(2)
-1
φ = 2000 fs, the divider is pixel 319 and ΩR=1500 cm a) Pulse spectrum (red, solid),
probe spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength
domain b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue,
dashed) c) temporal profiles of the pump/Stokes (red) and probe (blue).. .................... 72
Figure 5.5. Simulation of MII sinusoidal phase modulation, using an experimental
-1
spectrum. α=2.25π, ωc=770 nm, ΩR=1500 cm and δ=1 a) Pulse spectrum (red, solid),
probe spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength
domain b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue,
dashed) c) temporal profiles of the pump/Stokes (red) and probe (blue).. .................... 73
Figure 5.6. Simulation of MII using binary phase modulation, and an experimental
spectrum. N=37 a) Pulse spectrum (red, solid), probe spectrum (blue, solid), and pulse
shaping (blue, dashed) used in the wavelength domain b) frequency domain pulse
spectrum (red, solid) and relative phase delay (blue, dashed) c) temporal profiles of the
pump/Stokes (red) and probe (blue)…………………………………………………………74
Figure 5.7. Simulation of autocorrelation data for a) two chirped pulses, b) sinusoidal
modulation, and c) binary phase shaping. ..................................................................... 76
Figure 5.8. Experimental autocorrelation data for a) two chirped pulses, b) sinusoidal
phase modulation, and c) binary phase modulation. ..................................................... 78
Figure 5.9. 2D plot for two chirped pulses. The measured CARS spectrum for toluene is
along the y-axis, and the scan parameter for the selective excitation is along the x-axis.
...................................................................................................................................... 79
Figure 5.10. 2D plot for sinusoidal phase modulation. The measured CARS spectrum
for toluene is along the y-axis, and the scan parameter for the selective excitation is
along the x-axis. ............................................................................................................ 80
Figure 5.11. 2D plot for binary phase (BPS) modulation. The measured CARS
spectrum for toluene is along the y-axis, and the scan parameter for the selective
excitation is along the x-axis. ........................................................................................ 81
Figure 5.12. 2D plot for two asymmetric chirp pulses. The measured CARS spectrum
for toluene is along the y-axis, and the scan parameter for the selective excitation is
along the x-axis. ............................................................................................................ 83
Figure 5.13. Two-dimensional plots showing the scan parameter ( R) vs. the measured
CARS response for a) asymmetric chirp b) chirp (c) sinusoidal and (d) BPS phase
modulation methods in carbon dioxide. ......................................................................... 84
Figure 5.14. a) Two-dimensional plot for two chirped pulses with the integration scheme
highlighted, b) integrated spectra for the various phase functions as a function of the
scan parameter. ............................................................................................................ 85
xii

Figure 6.1. a) Broadband spectrum produced by the Venteon oscillator; b) Diagram of
experimental setup. ....................................................................................................... 91
Figure 6.2. Measured GVD at 800 nm as a function of pressure in low (1–4 bar)
pressure regimes for several atmospheric and combustion-related gases.................... 92
Figure 6.3. Measured GVD at 800 nm as a function of pressure in high (1–50 bar)
pressure regimes for several atmospheric and combustion-related gases.................... 93
Figure 6.4. Measured GVD at 800 nm as a function of gas density for nitrogen, oxygen,
carbon dioxide, and ethylene along with linear fitting of the data. ................................. 94
Figure 6.5. Measured dispersion for nitrogen (raw data) over the entire pressure range
(data for some pressure values have been eliminated for clarity of presentation)......... 95
Figure 6.6. Dispersion of nitrogen normalized on path length and pressure, along with
the linear fit. The intercept value provides the second-order coefficient, while the slope
provides the third-order dispersion. The carrier frequency, ω0 , is set to 2.3526 rad/fs (

λ0 = 800.65 nm). .......................................................................................................... 96
Figure 6.7. Dispersion normalized on the path length and pressure for all the gases,
along with the linear fit. For oxygen, nitrogen, and air, dispersion data from both
pressure ranges are used; for all other gases only the low-pressure data, exhibiting
linear pressure dependence, are used. ......................................................................... 97
Figure 6.8.

-1

Simulated Raman scattering efficiency at 1285 cm
-1

as a function of

propagation distance CO2 with a density of 2.24 mol·L .The inset figure is a schematic
example of how this improved spatial resolution can be used to select a region of
interest to acquire data in a combustion process ........................................................ 102

xiii

KEY TO SYMBOLS AND ABBREVIATIONS

α

a parameter used to define the amplitude of the sine function

BPS

binary phase shaping

CARS

coherent anti-Stokes Raman Scattering

CPA

chirped pulse amplification

δ

a parameter used to define the phase of the sine function

E

electric field

φ(ω)

phase (as a function of frequency)

f(ω)

reference phase used in MIIPS

FROG

frequency-resolved-optical-gating

FWHM

full-width-at-half-maximum

GVD

group velocity dispersion

IR

infrared

L

propagation length

LC-SLM

liquid crystal spatial light modulator

LN

liquid nitrogen

MII

multiphoton intrapulse interference

MIIPS

multiphoton intrapulse interference phase scan

η (Ω R )

normalized excitation efficiency spectra

ñ

complex index of refraction

PCF

photonic crystal fiber

SHG

second-harmonic generation

SLM

spatial light modulator
xiv

SPIDER

spectral phase interferometery for direct electric-field reconstruction

SRS

stimulated Raman scattering

Ti:Sa

titanium:sapphire

TL

transform-limited

UV

ultraviolet

ω

frequency

ΩR

Raman transition

xv

Introduction
-6

Ten femtoseconds, the time it takes light to travel 3.0x10 m, is the approximant
width of a human hair. This is also the same time scale on which the atoms that
compose molecules twist, turn, wiggle, and if provided with enough energy, break apart.
This short time scale, where the electric field is present, is the defining characteristic of
femtosecond lasers. As the field is present for such a short time, it allows power
densities greater that 10

12

2

W/cm to be reached by the focusing of amplified

femtosecond pulses. This high power density is sufficient to induce nonlinear optical
effects, such as second harmonic generation, two photon fluorescence, molecular
ionization, and other various nonlinear spectroscopies. One of these spectroscopies,
coherent anti-Stokes Raman scattering (CARS), is the focus of this dissertation.
The first chapter is written to provide insight into the concepts and characteristics
of femtosecond pulses that make them such a unique and powerful experimental tool. It
also discusses the experimental apparatuses that are critical for the production of
amplified femtosecond pulses and the manipulation of spectral phase, amplitude, and
polarization.
The second chapter discusses the fundamental concepts behind Raman
spectroscopy and the correlation between traditional Raman spectroscopy and CARS.
Furthermore, this chapter discusses some of the typical CARS methods and their
applications. The single-beam CARS method is also introduced.

1

Chapter three highlights the adaptation of the single-beam CARS method from
microspectroscopy to performing CARS measurements at distances >10 m. This
chapter also examines CARS measurements on mixtures of gases and liquids.
The fourth chapter presents mode selective single-beam CARS on gas phase
molecules based upon Binary Phase pulse shaping (BPS). BPS uses a broadbandwidth
pulse to excite only a single Raman mode, rather than impulsively excite all modes
within the bandwidth of the pulse.
Chapter five focuses on examining several different methods of performing mode
selective excitation applied to the single-beam CARS methodology. The theory, in the
context of multiphoton intrapulse interference (MII), and application of double chirped
pulses, sinusoidal modulation, and BPS are highlighted through the use autocorrelation
and CARS measurements.
The last chapter discusses the use of a broadbandwidth pulse to measure the
dispersion of gases that are related to combustion. As the use of femtosecond-laser
sources for the diagnostics of combustion and reacting-flow environments becomes
more common, detailed knowledge of optical dispersive properties of the medium
interacting with the laser beams is required. Here, the second-order and third-order
dispersion values within the 700–900 nm range are reported, along with the pressure
dependence of the chromatic dispersion. The effect of dispersion on axial resolution
when applied to nonlinear spectroscopy with ultrabroadband pulses is also discussed.

2

Chapter 1
Concepts and Experimental Tools
This first chapter discusses the critical concepts and various experimental tools
that are used in the work presented in this dissertation. In particular, ultrashort laser
pulses, femtosecond laser systems, and pulse shaping are highlighted.
1.1 Ultrashort laser pulses and spectral phase
Lasers are typically thought of as narrowband, monochromatic light sources.
However, ultrashort lasers, particularly those with pulse durations on the order of
femtoseconds, are composed of numerous optical frequencies. Ultrashort pulses are
ideal for inducing non-linear optical processes due to the short time duration, resulting in
very high peak powers.
An ultrashort pulse is simply an oscillating electric field, ߝሺ‫ݐ‬ሻ. This field cannot be
monitored electronically due to the short time duration. This results in measurements
that are typically performed in the frequency domain. ߝሺ‫ݐ‬ሻcan be Fourier transformed to

get ߝ̃ሺ߱ሻ, which describes the field in the frequency domain. A practical definition for

ߝ̃ሺ߱ሻ is as follows:

ߝ̃ሺ߱ሻ ൌ Aሺωሻexp ሾiφሺωሻሿ

(1.1)

Aሺωሻ is the spectral amplitude and φሺωሻ is the spectral phase that contribute to the
pulse shape. As the spectral domain is the most common, ultrashort pulses can be
represented by:

ܵሺ߱ሻ ‫̃ߝ| ן‬ሺ߱ሻ|ଶ
3

(1.2)

which can be easily measured using a spectrometer. However, the spectral phase is
much more difficult to measure. The combination of spectral amplitude and phase is all
the information that is needed to completely characterize an ultrashort pulse.
The spectral phase is simply the relative phase of each of the frequency
components. Non-linear optical processes induced by ultrashort pulse are highly
sensitive to the spectral phase of the ultrashort pulse. To achieve the shortest pulse
duration, the spectral phase of the laser pulse must be a flat function. When an
ultrashort pulse achieves the shortest possible duration, it is said to be transform limited
(TL).
Spectral phase distortions arise from different frequencies of the laser pulse
1

experiencing different refractive indices as the pulse propagates. This results in
different frequencies traveling with different velocities. Optical components such as
lenses, windows, or cuvettes all induce phase distortions. Nearly all materials induce a
distortion that is quadratic in nature along with several higher order distortions. Optical
prism and grating compressors have been designed to correct for quadratic distortions,
but do not correct for higher order distortions. In fact, these compressors often introduce
additional higher order distortions. The impact of the phase distortions are best see by
the examination of a non-linear optical process. Second harmonic generation (SHG) will
be used to illustrate the effect of various phase distortions. The SHG can be defined as:

ܵሺ2߱ሻ ൌ |‫ ܧ ׬‬ଶ ሺ‫ݐ‬ሻ expሾ݅߱‫ݐ‬ሻ ݀‫|ݐ‬ଶ

4

(1.3)

The effect of various phase distortions on SHG and time duration of an ultrashort (10 fs)
pulse are highlighted in Fig. 1.1. Linear phases are not examined as they have no effect
on the second harmonic and, and simply shift the pulse in the time domain.

Figure 1.1. The effect of spectral phase on temporal intensity of the pulse (second
column) and second harmonic spectrum (third column). The first column shows
fundamental spectrum (solid line) and the applied phase (dashed line). a) Corresponds
to quadratic phase distortion, b) is for cubic phase distortion, and c) is for sinusoidal
phase modulation. In columns two and three, the solid line corresponds to TL pulses
and the dashed corresponds to applied phase distortion.

5

From Fig. 1.1, the effects of the phase distortions are dramatic. The quadratic phase
distortion, or chirp as it commonly referred to, significantly increases the duration of the
pulse in the time domain as well as reduces the intensity of the non-linear, second
harmonic signal. This is contrasted with the third order, or cubic phase distortion, which
actually generates a train of pulses in the time domain, while spectrally narrowing the
second harmonic. Sinusodial phase modulation also results in the generation of a pulse
train in the time domain and narrowing in the second harmonic signal. The ability to
correct for phase distortions, regardless of the optical components, results in highly
reproducible experimental data. The use of the Multiphoton Intrapulse Interference
Phase Scan (MIIPS) method has demonstrated the ability to accurately correct for all
orders of phase distortion. MIIPS will be discussed in more detail in the following
chapter.
1.2 Femtosecond Laser Systems
More than a decade after the first experimental laser use, sub-picosecond pulses
2

were generated using dyes as gain media. Until the late 1980’s and the arrival of solid
state gain media, these dye-lasers were the primary source of ultrashort pulses,
3

generating pulses as short at six fs. However, the use of solid state gain media,
titanium-doped sapphire (Ti:Sa) in particular ended the dominance of dye lasers due to
their ability to support broad gain bandwidths and provide long term stability.

4,5

regenerative amplifier described in the following section was employed for the
experiments presented in this dissertation.

6

6

A Ti:Sa

The regenerative amplifier is used for laser pulse amplification. Amplification is
achieved by the pulse making multiple passes through a gain medium (Ti:Sa). In the
regenerative amplifier, the Ti:Sa crystal is placed in an optical resonator with an optical
switch that allows the pulse to exit after a desired number of passes through the gain
medium. During this amplification process, the peak intensity of the pulse can become
so high that it becomes possible to induce high order, non-linear effects that may distort
the laser pulse or damage optical elements. To avoid this, a chirped pulse amplification
7

(CPA) method is used. In CPA, pulses are temporally stretched, typically from
femtoseconds to picoseconds, using a highly dispersive optical element before
amplification. This results in a significant reduction in the peak intensity during
amplification. The stretched pulses enter the amplification gain media where after
several passes (4-50), the pulse energy increases by several orders of magnitude. After
amplification, the pulses enter a compressor, typically built with a grating pair that
recompress the pulses to a duration similar to before amplification (<100 fs), resulting in
femtosecond laser pulses with very high peak intensities.

8

The regenerative amplifier (Legend USP, Coherent), seeded by a Ti:Sa oscillator
(Micra, Coherent), used for the experiments described in this dissertation is presented
in Figure 1.2. This system produces pulses of ~35 fs with energies of ~1 mJ/pulse at a 1
kHz repetition rate.

7

Figure 1.2. Regenerative amplifier schematic. (a) Grating stretcher, which stretches the
time duration of the seed pulse, (b) regenerative amplifier, (c) grating compressor where
the amplified pulses are recompressed. F1: Faraday Isolator, G1 and G2 gratings, Pc1
and Pc2: Pockel cells.

1.3 Pulse Shapers
Pulse shapers are optical devices that allow for the user to control attributes of
the laser pulse such as spectral phase, amplitude, or polarization. These can be
designed in several ways with varying levels of complexity. For example, the use of
optical components such as a grating or prism based compressor allows for the
application of quadratic phase. However, more complex phase functions require the use
of programmable pulse shapers. The use of programmable pulse shaping with ultrafast

8

lasers covers a wide variety of applications ranging from pulse characterization
11,12

non-linear microscopy

9,10

,

13,14

, to control of photochemical processes.

There are two separate approaches taken for the application of pulse shaping.
The first is based upon manipulation in the time domain. This is typically done through
the use of an acousto-optic device. In this device, a time dependent acoustic signal is
driven in a crystal through which the laser pulse propagates. This allows for control of
both the phase of the pulse and the amplitude.

15

The second approach uses

manipulation in the frequency domain, with Fourier-transform pulse shapers. Fouriertransform shapers work by applying a spatial mask to the spatially disperse frequency
16

spectrum of the pulse.

This allows for manipulation of individual frequencies of the

laser pulse. This type of pulse shaping is used throughout the research that is decribed
in this dissertation.
The pulse shaping apparatus highlighted in Figure 1.3 is the typical optical
design of a frequency domain pulse shaper. It is constructed from two diffraction
gratings and two lenses arranged in a “4-f configuration” and a spatial light modulator
(SLM). The input beam is spectrally dispersed from the first diffraction grating (or prism)
and is focused into a spectral disperse line by the first lens (or curved mirror). The focus
of this lens is the Fourier plane, where the SLM is placed. After passing through the
SLM, the frequency components of the beam are recombined, generating a single,
collimated output beam. This arrangement is also known as a “zero dispersion pulse

9

compressor”, due to the fact that if the SLM was removed, the output pulse would be
identical to the input in terms of spectral phase.

Figure 1.3 Schematic of “4-f” pulse shaper, where each optical component is separated
by the focal distance f. The input beam is spectral dispersed into frequency components
and then focused by a lens. The SLM is place at the focal plane (Fourier plane). The
SLM allows for individual manipulation of each frequency with respect to spectral phase,
amplitude or polarization. After passing through the SLM the frequency components are
recombined creating a shaped, collimated output.
The SLM used for the experiments performed in this dissertation uses liquid
crystal technology (LC-SLM). This device is composed of a thin layer of nematic liquid
crystals that are placed between two glass windows. The inside surface of the glass
windows are coated with a thin, transparent material that is electrically conductive. This
creates the SLM mask, which is composed of numerous pixels. When an electric field is
applied to each pixel, the liquid crystal molecules rotate, which results in a change in
refractive index for that pixel. Depending on the polarization of the input light, this
17,18

change allows for the introduction of phase retardation, or polarization rotation.

There are two different types of LC-SLM. One type is phase only, and the second type
is phase and amplitude. In the phase only LC-SLM, a single mask is used, and the
polarization of the input light is such that only phase retardation is introduced. In the LC-

10

SLM capable of phase and amplitude shaping, there are two liquid crystal masks. In this
LC-SLM, the masks are oriented with perpendicular optical axes which are rotated 45
degrees from the polarization of the incoming light. These two masks, along with the
combination of a polarizing optical device allow for the shaping of phase and amplitude;
the polarizing optic can be removed, and phase and polarization shaping can be
performed. The ability to vary transmission of light dependent on polarization is utilized
for the calibration of the various LC-SLMs used.
In the work performed in this dissertation, a 128 pixel phase only LC-SLM (CRi)
was used, along with a 640 pixel phase and amplitude shaper (CRi). The 128 pixel
shaper was placed between the oscillator and the regenerative amplifier, the 640 pixel
shaper was place after the regenerative amplifier. These shapers were configured in an
alternate, fold geometry, highlighted in Figure 1.4.

Figure 1.4 Schematic of an all reflective, folded “4-f” pulse shaper. The output beam
follows the same path as the input, but is vertically displaced. OM: Output mirror, CM:
Curved mirror, FM: Folding mirror, and BM: Back mirror.

11

This folded, all reflective design was chosen because it reduces the amount of space
needed for the shaping device, and it doubles the amount of phase retardation the LCSLM can apply, since the beam passes through the device twice.
These pulse shaping devices were used for several applications discussed
throughout this dissertation. Pulse shapers were used for pulse characterization and
compression, the generation of phase and polarization mask the acquisition of coherent
anti-Stokes Raman scattering (CARS) data, and for the application of phases to
selectively excite individual CARS modes.
1.4 Multiphoton intrapulse interference phase scan (MIIPS)
For ultrashort pulses, the measurement and characterization of spectral phase
distortions is essential. Accurate measurement and correction of phase distortions
prevents any experimental ambiguity that may result from unknown phase distortions,
making experimental results highly reproducible. This is particularly critical for sub 30 fs
pulse durations. The use of multiphoton intrapulse interference phase scan (MIIPS),
developed by the Dantus group

19

provides a highly accurate method to both measure

and correct spectral phase distortions.
There are several different approaches that have been used to perform pulse
compression. These methods include the use of prism or grating compressors, which
was the initial method of choice for pulse compression. In this method the SHG signal is
observed as the compressor is adjusted to achieve an optimal SHG si,gnal. A second
method for characterization involves the use of a computer controlled pulse shaper and

12

an optimization genetic algorithm. Here the integrated SHG signal provides feedback to
the algorithm, which then modulates the phase applied by the pulse shaper in order to
maximize the integrated SHG signal. The downfall of these methods is that they are
limited by the noise level of the measurement. A very stable laser source will fluctuate
on the order of 1-3%, which means that the pulse to pulse stability of the SHG is 2-6%.
This level of noise is insufficient for measurements that require very accurate
knowledge of the phase distortions.
Retrieving spectral phase using a method based upon autocorrelations and/or
interferometery is a a third approach used to perform pulse compression. Frequency
20-22

resolved optical gating (FROG)

23,24

field reconstruction (SPIDER)

and spectral phase interferometry for direct electic-

are two of these methods. Figure 1.5 is a cartoon

demonstrating these approaches, along with the MIIPS method.

13

Figure 1.5 Cartoon of various pulse compression methods. (a) Prism/grating
compressor, (b) Optimization algorithm using integrated SHG signal, (c) FROG/SPIDER
characterization methods (d) MIIPS method.
The MIIPS method works by applying a set of well defined reference phases, -f(ω), is
applied to the pulses with an unknown phase distortion, φ(ω), while measuring a SHG
spectra or other non-linear optical spectra. This results in a total second derivative of
the phase being φ(ω)-f(ω). When φ(ω)-f(ω)=0, there will be a maximum in the SHG
signal. By creating a grid in the second derivate space using -f(ω), the unknown phase
φ(ω) can be mapped out. The simplest way to do this is to use a function in which the
second derivative is a constant, which corresponds to a linear chirp function. This
approach is shown in Figure 1.6 a). The unknown phase (solid line) is measured using
the reference phases (horizontal dashed lines). When the reference phase intersects
with the unknown phase a maximum is generated in the SHG signal as show in figure
1.6(b). This sample method can be applied using a sinusoidal reference phase and is
shown in Figure 1.6 c) and 1.6 d). In each of these methods, the φ′′(ω) is measured for
the unknown and then double integrated to obtain φ(ω). The - φ(ω) is then introduced
by the pulse shaper eliminating the phase distortion. The time to scan the reference
phase is on the order of 10 to 30 seconds, and an interative routine can be used to
obtain the best possible accuracy.

14

Figure 1.6 MIIPS principles. (a) The unknown phase (φ′′) is mapped using a reference
grid composed of linear chirp phases. (b) The SHG signal corresponding to the places
where the reference phase and the unknown phase intersect. (c) Mapping the unknown
phase using a sinusoidal reference phase. (d) The SHG signal corresponding to the
intersection of the sinusoidal reference phase with the unknown phase.
Each of these methods are described in great detail elsewhere, but these
methods are used experimentally thoughout this dissertation for measurement and
correction of spectral phase distortions. This ensures the use of TL pulses and allows
for highly accurate phase shaping to be performed.
1.5 Conclusions
This chapter has presented several key concepts related to the use of ultrafast
laser pulses and phase shaping, including the effect of spectral phase on ultrashort
pulses examined in second harmonic generation and in the time domain. The 4f- pulse

15

shaper is also described in detail regarding the set-up of the devices as well as the
functionality. Multiphoton Intrapulse Interference Phase Scan (MIIPS) is also described
with its application to phase measurement and correction.

16

Chapter 2
Coherent anti-Stokes Raman Scattering (CARS)
The majority of the work addressed in this dissertation involves or is related to
coherent anti-Stokes Raman Scattering (CARS). CARS is a non-linear method that
provides information analogues to that of Raman spectroscopy that provides rich
spectroscopic information. An introduction to the basic theory of Raman spectroscopy
will be given followed by a discussion of the principles of CARS and how it compares
and contrasts with Raman spectroscopy. Lastly, several CARS methods will be
highlighted to provide a frame of reference for the work discussed in chapters 3-6 of this
dissertation.
2.1 Theory of Raman spectroscopy
The interaction of light with matter has long been a field of interest and study for
the scientific community. When light interacts with a material, the material may
absorbed, scattered, or not interact with the light. This interaction is the phenomena
behind all spectroscopic methods, independent of wavelength. Raman spectroscopy is
a scattering technique in which the light interacts with a molecule to distort the electron
cloud surrounding the nuclei. This distortion, or induced polarization, creates a short
lived, unstable virtual state from which photons are quickly reradiated. As Raman is a
vibrational spectroscopy, molecular motion is required, so photons that only distort the
electron cloud are scattered with small frequency changes or elastically scattered. This
process is known as Rayleigh scatter, is the dominate process. However, if nuclear
motion is induced an inelastic scattering occurs and energy may transfer from the

17

photon to the molecule (Stokes) or from the molecule to the photon (anti-Stokes).

25-27

This inelastic scatter results in a frequency shift in the scattered photon is known as the
Raman process. Fig 2.1 highlights this process for a single vibration.

Figure 2.1 Energy level diagram of the Rayleigh and Raman scattering processes.
Molecular vibrations can result in a change in dipole moment or a change of
polarization. Infrared absorption spectroscopy (IR) is highly sensitive to changes in
dipole, while insensitive to changes in polarization, the opposite of Raman scattering.
Therefore, vibrations which cause the largest change in the polarizability are those
which produce the greatest Raman scattering. These are typically symmetric molecular
vibrations. The number of vibrations that a molecule contains is 3N-5 for linear
molecules and 3N-6 for all others, where N is the number of atoms. However, not all of
these modes are Raman active. Some modes result in only in a change of dipole
moment, others a change in polarizablity, and some change both the dipole moment
and polarization. To illustrate this CO2, is examined in Fig 2.2. As CO2 has three atoms,
there are 4 vibrational modes: symmetric stretching, bending and asymmetric
stretching. There are two degenerate bending modes, where the spectroscopic

18

signature is identical. Of these modes, the symmetric and an overtone of twice the
bending mode are Raman active, while the bending mode and asymmetric stretch
results in a change in the dipole moment making it active to infrared absorption.

Figure 2.2 Vibrational modes for CO2: The symmetric stretch and overtone of twice the
bending mode are Raman active, whereas the bending mode and asymmetric stretch
are IR active.

While the modes for small molecules are easy to predict and to model it becomes
much more complicated for large molecules. For example, toluene (C7H8) has 39
vibrational modes, far too many to approximate as was done for CO2. This also makes
in very time consuming to computational model each molecule to predict the Raman
signal. Spectroscopists typically consider single vibrations and group frequency
vibrations when using Raman for identification. Fig 2.3 illustrates the approximate
position of Raman features for some of the more common vibrations. The solid, vertical
lines represent the approximate range for the observation of the Raman response, while
the stars indicate the position of the Raman response for gas phase molecules
discussed later in this dissertation.

19

Figure 2.3 Single and group vibrations of peaks common to Raman scattering. The
stars indicate the frequency of the Raman signal in gas phase molecules (CO2, O2, N2)
While only vibrational Raman scattering has been discussed, rotational
transitions are also commonly observed for gas phase measurements. For the work
presented in the following chapters only vibrational scattering is examined.
2.2 Comparison of Raman and CARS
Raman spectroscopy is a linear spectroscopy and is typically performed with a
single CW laser source. CARS is a nonlinear, four wave mixing process which
traditionally requires three lasers beams. The first two beams, pump(EP) and
Stokes(ES) serve to coherently drive the molecular vibrations, which are then probed by
a third beam (EPR) to generate the CARS signal (ECARS= EP –ES+ EPR).

20

28-31

This is

highlighted in the energy level diagram, Fig 2.1. Taking this into consideration, the
Raman signal can be approximated as SRam.α ILN x eff., where IL is the laser intensity,
N is the number density of the sample and eff. is the detection efficiency. The CARS
2

2

response is proportional to SCARS α N IP/S IPR x eff., where N is the number density,
IP/S is the intensity of the pump/Stokes component, IPR is the intensity of the probe and
eff. is the detection efficiency. From this we can see that in order to perform CARS
spectroscopy high intensity pulses are desired. This makes pulsed laser sources the
ideal choice.
While, experimentally CARS is more complex than traditional Raman
spectroscopy, it has several advantages. First, the CARS signal is coherent and
emerges as a directional beam, not scattered over free space as traditional Raman.
This allows for a much higher efficiency in signal collection. Second, the CARS signal is
blue shifted, making it free from background fluorescence which typically plagues
Raman measurements. Third, CARS signals are typically orders of magnitude stronger
that those of Raman. This enhancement of the CARS signal vs. Raman has been
5

determined to be ~10 . This significant enhancement is the result of phase-locked
signal accumulation over the active sample volume.

21

32,33

Figure 2.4 Cartoon showing the signal accumulation over an active sample volume for
a) CARS and b) Raman. Notice how the signal for CARS is phase-locked, compared to
random for Raman. This phase-locked accumulation results in the large signal
enhancement in CARS.

2.3 Resonant and Nonresonant contributions
For CARS the Raman response is due to the change in the third order polarization
due to the pump, Stokes and probe pulses. This response contains both a resonant and
a nonresonant portion. The nonresonant contribution is due to the instantaneous
electronic response of the molecule, while the resonant response can be attributed to
the Raman transitions of the molecule. In the frequency domain we can consider the
third order polarization, ܲ

ሺଷሻ ሺ

߱ሻ as follows:

ܲሺଷሻ ሺ߱ሻ ൌ ܲேோ ሺ߱ሻ ൅ ܲோ ሺ߱ሻ
ሺଷሻ

ሺଷሻ

However, the CARS response of the sample is proportional toหܲ

ሺଷሻ ሺ

ଶ

߱ሻห

, which

results in complex spectra due to the interference of the resonant Raman transactions
and the nonresonant background. As a result, numerous methods have been developed
with the goal of reducing or eliminating the nonresonant contribution. Figure 2.5 is a
schematic diagram highlighting the different contributions to the CARS process.

22

Figure 2.5 Energy level diagrams for four wave mixing processes (ω1/ω2;red, ω3; blue,
and ω4; orange a) resonant contribution to the CARS process and b) for nonresonant
contributions. For interpretation of the references to color in this and all other figures,
the reader is referred to the electronic version of this dissertation.
2.4 Frequency Domain CARS methods
While, spectroscopic CARS methods have existed since the early 1970s, advances
in ultrashort laser technology and availability have lead to resurgence in CARS
applications. As a result, the evolution in ultrafast sources has lead to the development
of a variety of methods for CARS spectroscopy.
The first approach makes use of two narrowband pulses (ps/ns). One of the
pulses serves as the pump/probe while the other serves as the Stokes. This allows for
acquisition of the CARS signal at a single frequency. To obtain a full spectrum the
Stokes pulse must be scanned in frequency. Narrrowband CARS using picoseconds
34-38

pulses has traditionally been the dominate method for CARS microscopy
diagnostic method for combustion and reacting flows.

23

39-41

and as a

For CARS microscopy the

intrinsic chemical selectivity afforded by narrowband CARS provides a high contrast
ratio, without the need for labeling. Phospholipids are among the molecules most often
targeted in cells, due to large signal they provide, that enables visualization of even a
single lipid bilayer. The advances in narrowband CARS have allowed for microscopy to
become a method that is capable of producing video rate images with sub-cellular
resolution. This same narrowband approach has also been a choice method for
diagnostic measurements of combustion and reacting flows due to the ability to extract
temperature and species information. Methods to detect two or three species
simultaneously have been developed along with those that allow for measurements to
be made at high temperatures and pressures. This has resulted in narrowband CARS
becoming the most widely used method in the diagnostics of combustion and reacting
flow environments.
Another approach combines a narrowband source and a broadband (fs) source,
in a method know as multiplex CARS.

42-45

In this approach the narrowband source

again serves as the pump/probe and the broadband as the Stokes. Rather than
excitation at a single frequency, this allows for the acquisition of several frequencies,
determined by the bandwidth of the Stokes pulse. This allows for spectroscopy to be
performed without any wavelength tuning. However this method only provides a single
photon pair for excitation at each frequency. Multiplex CARS has been primarily applied
for microspectroscopy of biological samples. For these applications a photonic crystal
fiber (PCF) pumped by a femtosecond oscillator is used to generate broadband
supercontinuum with bandwidth in excess of 2500 cm

24

-1

to serve as the Stokes pulse.

The pump and probe are typically generated from output of the oscillator, but are
spectrally narrowed. Much like the narrowband method this method has evolved to
collect video rate images with subcellular resolution, with the advantage of observing
several Raman transitions simultaneously.
A third method that has evolved is a hybrid CARS. In hybrid CARS two
broadband sources provides the pump and Stokes and a narrow band source is used to
provide the probe. Like the multiplex approach this method provides signal at several
frequencies, however as two broadband sources are used to provide the pump/Stokes,
there are several frequency pairs. These frequency pairs result in much higher
efficiency than the multiplex method as there are several photon pairs that contribute to
the Raman response. One example which illustrates this method is the work by Scully,
et al. In this work they use a hybrid CARS approach to identify bacterial endospores that
are stimulants for hazardous materials such as anthrax.

46-48

The ability of this method
-1

to cover a large portion of the fingerprint region (200-1800 cm ) allows a complex
spectrum to be obtained which may contain several Raman transitions.
Figure 2.6 is a cartoon illustrating these three different methods used for
frequency domain CARS. There are numerous adaptations of these methods, and the
examples given are simply samples of the body of work that has been performed.
However, some insight into these methods is necessary as a frame of reference of the
CARS method used in this work.

25

Figure 2.6 Schematic diagrams of frequency domain CARS methods. a) Narrowbeam
CARS, b)Multiplex CAR, and c) Hybrid CARS.

One common characteristic for each of these approaches is the ability to delay
the probe pulse in time with respect to the pump/Stokes. This allows for the nonresonant response to decay, and the CARS signal to be acquired nearly background
free. However, these methods are not without limitations. First, the hybrid and multiplex
method may not be capable of collecting a full spectrum, due the limited bandwidth of
the pulses used. For the narrowbeam CARS method ΩR must be tuned through various
frequencies in order to require a full Raman spectrum. This is both time consuming, as
well as, experimentally unfavorable due to the instabilities which may occur and the
broad tuning range required to obtain a full spectrum. Secondly, as this method requires
up to three individual beams, from two or three lasers sources, they must be overlapped
both spatial and temporally. This makes this type of CARS measurements unpractical
for applications which are highly turbulent and can cause the beams to wander, or
require the beams travel large distances, such as a standoff detection application.

26

2.5 Single-beam CARS
Single-beam CARS represents a drastic shift in the schemes that for CARS
spectroscopy, as these methods require multiple beams. The single-beam CARS
makes use of a single broadband pulse to both provide the excitation and probe the
system. This method was first demonstrated for microscopy by the group of Silberberg
in 2002.

49

This initial work in 2002 used coherent control techniques, via pulse shaping

in order to examine Raman transitions in the 400-800cm

-1

range. The spectral phase of

the broadband pulse is modulated periodically, where the period of the oscillation
matches the vibrational energy level of the sample. While this method does not provide
a spectrum and requires different spectra phases to examine different transitions, it has
shown that it is possible to eliminate the multibeam setups and perform CARS
microscopy using a single-beam.
Single-beam CARS like all CARS methods has undergone numerous advances.
Following the initial single-beam CARS work, the next step was to use a single pulse to
acquire a CARS spectrum. This was again accomplished by the use of pulse shaping.
For this work a pulse shaper capable of providing both phase and polarization
modulation is used. The broadband pulse is shaped as two components, one to serve
as the pump/Stokes, the other the probe. For the probe pulse, a narrow spectral region,
typically corresponding to a couple of pixels on the SLM is selected. A spectral phase
of 0 is applied to half of these pixels, while a phase of π is applied to the others.
Additionally, the polarization of this narrow region is also rotated to be orthogonal to the

27

polarization of the incoming beam. For the pump/Stokes component the polarization is
maintained and a flat spectral phase is applied across the bandwidth of the pulse. The
combination of both phase and polarization has been shown to nearly suppress the
50-53

entire nonresonant contribution.

A schematic of the spectral pulse shaping in the

wavelength and time domain is shown in Fig 2.7.

Figure 2.7 Schematic illustrating the phase and polarization shaping method used for
single-beam CARS and a representative CARS response. The right insets show a
closer view of the probe region, and left inset shows temporal profile of the pump/Stoke
and probe components.
This method allows for impulsive excitation of all Raman modes within the bandwidth of
the pump/Stokes pulse. This means that a fairly standard femtosecond oscillator
capable of producing 10 fs pulses would allow for impulsive excitation of approximately

28

-1

2000 cm . This allows for coverage of the entire fingerprint region, which is highly
useful as it contains numerous Raman transitions.
In addition to the work by the group of Silberberg, the groups of Leone and
Motzkus also developed various single-beam approaches for applications to CARS
microscopy, based upon the single pulse approach utilizing pulse shaping. The group of
Leone used different phase functions on the probe portion of the pulse to acquire a
CARS spectra for each phase.

54-57

The use of an imaging spectrometer also allows the

collection of two polarizations (±45 ), enabling simultaneous measurement of the real
and imaginary components of the CARS signal. The imaging capabilities of this method
were demonstrated on the imaging of 200 nanometer poly(methyl methacrylate)
(PMMA) beads and the collection of chemical images of thin films containing PMMA and
polystyrene.
The Motzkus group has taken a slightly different approach with the single beam
method and works primarily in the time domain, rather than the frequency as well as use
a heterodyne method where the CARS signal is mixed with a local oscillator field.

58-61

To achieve this a periodic phase function is used to create two pulses from a single
broadband pulse. The first pulse serves as the pump/Stokes; the second serves as the
probe. The time delay of the probe pulse is then scanned while the signal is measured
as a function of delay. This signal can then be Fourier transformed from the time
domain back to the frequency domain and the CARS data extracted. This same data
processing method was also used with two pulses of two different colors. These pulses

29

were created again by phase shaping. For theses pulses, a broadband pulse was split
into two sections by the use of linear phase, which can shift the pulse forward or
backward in time. These methods have been used to image microcapsules filled with
1,4-diiodobenzene and bromoform at attomole concentration levels.
2.6 Conclusions
While in existence since the early 1970’s, spectroscopic CARS methods have
advanced as rapidly as the laser technology that enables them. The laser-like
directionality of the CARS signal, low signal absorption, spectral selectivity, and
excellent spatial resolution provide an optical method that is flexible and robust enough
for applications ranging from video rate microspectroscopy, combustion diagnostics,
and remote sensing. This chapter has highlighted several typical CARS methods along
with the underlying principles related to CARS and Raman spectroscopy.

30

Chapter 3
Single-beam CARS for Remote Sensing
As the previous chapter has discussed CARS in great detail, this chapter will focus on
the authors’ contribution to the field of single-beam CARS spectroscopy, particularly for
the application to standoff or remote sensing. The following is reproduced with
permission from H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus,
Coherent mode-selective Raman excitation towards standoff detection," Optics Express
2008, 16, 5499-5504. Copyright 2008. Optical Society of America.

3.1 Single-beam CARS for Remote Sensing
Ultrashort pulses have made possible the development of powerful spectroscopic
tools that rival conventional high-resolution approaches.

62

Their ultra-broad bandwidth

makes them ideal for impulsive excitation of vibrational modes, which evolve in time
coherently. When pairs or trains of such pulses are used, large amplitude molecular
motion can be achieved.

63,64

These capabilities were recently combined to achieve

single-beam coherent anti-Stokes Raman scattering microscopy,

49,53,60,65

a modality

that is sensitive to molecular composition. Here we present a method for remote
sensing of films and residues located on solid targets tens of meters from the laser
based on single-beam CARS. In contrast to its implementation in microscopy, this
development requires amplified (six-orders of magnitude) ultra-broad bandwidth pulses.
As well as, phase and polarization pulse shaping to deliver optimally coherent pulses

31

tens of meters from the laser source. The resulting method is capable of selective
vibrational mode excitation to provide molecular discrimination and to eliminate the nonresonant contribution. The single-beam CARS method eliminates the need for crossing
three separate laser pulses (pump, Stokes, and probe) as used for arms-length
identification of anthrax spores,

46,48

making it more practical for standoff detection 50-

100 m from the laser and detection unit.

Figure 3.1. a) Supercontinuum spectrum (grey) and the phase measured using MIIPS
(dashed black). (b) Measured SHG spectra (black) from the compensated pulses
(spectrometer limited at 300 nm). The experimental SHG spectrum has a bandwidth of
73nm (FWHM), which agrees well with simulations for transform-limited pulses based
on the measured spectrum. The supercontinuum pulses were compressed to 4.8 fs by
MIIPS phase compensation (see inset). (c) Residual phase on the laser after
compensation.

3.2 Experimental Set-up
Femtosecond laser pulses from a Micra oscillator (Coherent) are shaped by a 4f
reflective pulse shaper using a 128-pixel phase-only programmable liquid crystal spatial
light modulator (SLM) (CRi). The shaped pulses are then amplified by a regenerative

32

amplifier (Legend USP, Coherent) and focused by a 1 meter focal length curved mirror
into an argon-filled hollow waveguide that is 0.39 m long and has a 500 µm inner
diameter. By adjusting the incident laser power, argon pressure and chirp of the input
laser pulse, a continuum broadened spectrum is generated.

66,67

An argon pressure of

0.15 MPa with input pulse energy of 340 µJ is found to generate 200 µJ of hollow
waveguide output from 750 to 870 nm. Optimum continuum generation is obtained
when high-order dispersion is eliminated by the pulse shaper using multiphoton
19,9

intrapulse interference phase scan (MIIPS)

2

and a linear chirp of -500 fs is then

added to the input pulse. The broad bandwidth output laser beam is collimated by a
0.75 m focal length curved mirror and shaped by a second 4f pulse shaper with a 640pixel, phase and polarization SLM (CRi).
The supercontinuum output spectrum is shown in Fig. 3.1 a); the spectral phase
68

of the output laser beam is measured and compensated by using remote MIIPS , as
shown in Fig. 3.1 c). The compensated, 4.8 fs pulses, are found to generate very broad
second harmonic generation (SHG) spectrum, shown in Fig. 3.1 b).
For the CARS measurements, wavelengths shorter than 765 nm are blocked at
the Fourier plane of the pulse shaper. The laser beam is reflected by a beam splitter
and loosely focused on the target 12 m away by a home-built Newtonian telescope
consisting of a negative 0.2 m focal length lens and a 0.75 m focal length spherical
curved mirror (see Fig. 3.2 a)). The energy at the sample is 10 µJ/pulse, and the beam
diameter is 2 mm. This laser power is well below the damage threshold of all the

33

samples studied. For most of the measurements presented here, a mirror is placed
behind the sample to retro-reflect the CARS signal for detection through the same
telescope. After the signal passes through a horizontal polarizer and a 740 nm low pass
filter (Omega Optical), a compact QE65000 spectrometer (Ocean Optics) is used to
record the CARS spectrum. For other measurements, we remove the mirror behind the
target and applied liquid samples (toluene and o-xylene), which form a thin film, to a
scattering surface.
Figure 3.2

34

Figure.3.2. Setup and performance of the single-beam CARS. a) The experimental
setup. b) The spectrum, phase and polarization of components of the shaped laser
pulse. The pump and Stokes (red) components have vertical polarization (y) while the
probe (green) and CARS signal (blue) have horizontal polarization (x). The inset shows
a diagram for the CARS process. c) Spectra of six consecutive single shot spectra of
toluene collected at a standoff 12 m distance.
3.3 Pulse Shaping for Single-beam CARS
As previously mentioned, the second pulse shaper uses MIIPS to compensate
the dispersion introduced by the hollow waveguide, telescope optics and propagation in
”

2

69

air (k air = 20.1 fs /m)

, ensuring transform-limited pulses at the target. It is also used

to control the phase and polarization of different components of the laser pulse in a way
that minimizes the non-resonant contribution and improves resolution. The nonresonant CARS signal increases with the bandwidth of the laser, which in our case is
-1

1800 cm . In order to reduce the considerable background in single-beam CARS
microscopy Oron et al. use a π phase gate.

50

In other work, they have also introduced a
53

polarization gate to the probe to further improve the resolution.

We incorporate both of

these strategies in our approach. The probe pulse is defined by keeping 6 out of 640
pixels (about 1.5 nm bandwidth, centered at 770 nm) horizontally polarized while using
the SLM to rotate the rest of the pulse to vertical polarization. A π phase gate (3 out of
640 pixels) is also used.
3.4 Results and Discussion: Neat Samples
Single shot spectra obtained from a liquid toluene sample are shown in Fig. 2(c)
to illustrate the speed, reproducibility and sensitivity of the system. The single-beam

35

CARS spectra of several liquid, gaseous and solid state samples obtained at a distance
of 12 m are shown in Fig. 3. For these spectra, the non-resonant broadbandwidth
contribution is fitted and removed by subtraction. Figures 3.3 a) and 3.3 b) present
CARS spectra for a number of liquid samples including different isomeric species, which
are easily distinguishable by this technique. Spectra from carbon disulfide (CS2), 1,2dichloroethane (C2H4Cl2) and chloroform (CHCl3) vapors (0.11 m sample path length
with vapor pressures of 40, 12, and 21 kPa respectively) were also recorded, and are
shown in Fig. 3.3 c). The spectra for several solids including polycarbonate, polystyrene
and polymethyl methacrylate (PMMA) are displayed in Fig. 3.3 d). We have observed
similar signal levels for condensed phase samples of 0.1 to 10 mm thickness, leading
us to believe that the majority of signal generation occurs within a thin region of the
sample where phase matching is satisfied.

36

Figure 3.3. Single-beam CARS spectra from liquid, gaseous and solid state samples. a)
CARS spectra from liquid toluene, o-nitrotoluene and m-nitrotoluene; b) CARS spectra
from liquid ortho, meta and para-xylene. c) CARS spectra from CS2, CH2Cl2 and CHCl3
vapors; d) CARS spectra from solid polycarbonate, polystyrene and PMMA.
To illustrate the necessity for compensation of phase distortions, the
unprocessed CARS spectrum of m-xylene is presented in Fig. 3.4 a) before and after
elimination of spectral phase distortion using MIIPS, which results in a significant (order
of magnitude) increase in the CARS signal. Note that despite polarization shaping, the
non-resonant contribution (broad feature spanning the whole spectrum) is more intense

37

-1

than the resonant CARS features at 725 and 1000 cm . The ability to isolate the
desired signal from a complex chemical background is a critical requirement for
molecular sensing. In particular, for CARS it is important to eliminate, as much as
possible, contributions from the non-resonant contribution. These improvements are
achieved by phase, amplitude and polarization shaping.
3.5 Results and Discussion: Selective Excitation and Backscatter
In addition to affecting the non-resonant signal, spectral phase can also provide a
method for achieving molecular selectivity. Silberberg and coworkers used a sinusoidal
phase function to control the single-beam, broad bandwidth CARS process and
achieved molecular selectivity.

52

Also, maximum intrapulse interference can be used to

achieve selectivity in nonlinear optical processes using binary phase functions.

70,71

When using binary phases, the laser pulse spectrum is partitioned into discrete regions,
each receiving a phase retardation value of zero or π. The CARS signal at each
frequency Ω is given by the sum of discrete contributions from all the frequencies in the
pulse whose difference is Ω according to the equation: E(Ω) = Σω E(ω)E*(ω- Ω),
where the electric field E can only take the value of (+1) when the phase is zero and
(−1) when the phase is π The goal becomes finding the binary phase function that
causes the sum to reach a maximum for the desired Ω, and zero elsewhere.
Fortunately, this problem has been solved in the field of mathematics. The type of
72

functions that we are looking for are known as Galois fields , or minimum correlation

38

73

sequences.
63,74

trains

Pseudorandom binary sequences have been used to create pulse

and to control nonlinear optical processes.

Figure. 3.4

39

71

Figure. 3.4 Single-beam CARS illustration of sensitivity and discrimination against
background signals. a) Unprocessed spectra of m-xylene collected at a standoff 12 m
distance with (black) and without (red) phase distortion compensation using MIIPS; note
the presence of a large nonresonant contribution (compared to the resonant signal) in
both cases. b) The red phase is designed to optimize excitation of the ν1 breathing
mode at 725 cm

-1

and the blue phase is designed to optimize excitation of ν 12 in-plane
-1

bending mode at 1000 cm . The lower panel shows the calculated temporal profiles
corresponding to red and blue phases. c) Unprocessed CARS spectra from m-xylene
with two specially designed binary phases. Note that the nonresonant contribution is
successfully suppressed eliminating the need for data processing. The designed binary
phases control the ratio between the two Raman peaks with an overall two order-ofmagnitude discrimination from 7:1 to 1:12. d) Integrated intensity for different binary
phases (optimized for different Raman shifts) applied in the pulse shaper.
Here, we use optimal discrimination based on Galois fields synthesized using
binary phase functions to achieve selective excitation of individual vibrational modes,
and at the same time eliminate the non-resonant contribution. One of the reasons why
the non-resonant signal is greatly reduced is that the complex binary spectral phase
causes the creation of a train of pulses in the time domain (see Fig. 3.4 b)). The
temporal profiles of the pulses corresponding to red and blue binary phases show
oscillation periods ~46 fs and ~33 fs, which match the vibration frequency of ν 1
breathing and ν 12 in-plane bending modes of m-xylene, respectively. By spreading the
peak intensity of the ultrashort pulse into several sub-pulses, the non-resonant
contribution is essentially eliminated. This type of pulse shaping allows for CARS data
to be collected with high selectivity despite the ultrabroad bandwidth. The unprocessed
75

spectra in Fig. 3.4 c) show selective excitation of the ν 1 or ν 12 modes of m-xylene ,
with the elimination of non-resonant contribution. We point out that selective vibrational
excitation of two different molecules in a mixture was reported recently using feedback
40

controlled optimization in a three beams (two colors) setup with a special crossed-beam
geometry.

76

Frequency selective excitation, as shown here, gives single-beam CARS a

means to discriminate between different compounds in a complex mixture, making it
ideal for applications in complex environments. By collecting the integrated CARS signal
for each binary phase, single-beam CARS spectroscopy can be achieved without a
spectrometer, as shown in Fig. 3.4 d).
Up to this point, the data obtained made use of a mirror placed behind the
sample to retroreflect the CARS signal. In Fig. 3.5, we show data obtained from backscattered signal. For this experiment, we apply a drop of toluene or o-xylene on a
surface covered with transparent polymer beads. The signal is collected by imaging the
surface on the detection fiber placed at an arms-length distance. The characteristic
Raman signatures can be easily identified. As we contemplate the application of this
method to standoff detection of explosives at 50-100 m, we plan to increase the energy
per pulse from 10 µJ to 100 µJ, increase the diameter of the telescope used for
excitation and signal collection, and to use a photon counting, spectrally dispersed
signal detector. Overall, we expect these changes should result in up to three orders of
magnitude increase in signal. By using the time-gated detector, we will be able to obtain
time-of-arrival information of the CARS signal and to further discriminate against
ambient light. With these enhancements, we believe that this approach will have a
significant impact in the standoff detection of films and residues located on solid targets
which scatter or reflect the incident light.

41

Figure 3.5 Single-beam CARS spectra with back scatter signal detection. a)
Unprocessed spectrum of o-xylene. b) Processed spectra of o-xylene and toluene.
3.6 Results and Discussion: Mixtures and Concentration measurements.
The following section contains excerpts which are reproduced in part with
permission from H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M.
Dantus, Coherent mode-selective Raman excitation towards standoff detection," Optics
Express 2008, 16, 5499-5504. Copyright 2008. Optical Society of America.
In addition to the measurement of neat samples, mixtures of liquids and gas
samples were also examined. A binary mixture of molecular isomers, o-xylene and pxylene, was studied at various concentration ratios ranging from 50:50 to 1:99 volume to
volume. These measurements were made using the standoff detection set-up described
previously. Figure 3.6 a) displays the CARS spectra for both molecules in the 50:50
mixture, while Fig.3.6 b) displays the 1:99 ratio.

42

Figure 3.6. CARS measurements of o-xylene and p-xylene mixture; a) is a 50:50
mixture, b) is a 1:99 mixture.
-1

In Fig. 3.7, the relative intensity of the o-xylene (735 cm ) with respect to p-1

xylene (825 cm ) is plotted as a function of o-xylene concentrations ranging from 110% on a double logarithmic scale. The linear fit results in a slope of ~1.4. The CARS
response should result in a value of 2.0 for the slope, while the non-resonant should
result in a value of 1.0. The 1.4 value suggest that the measured CARS response is not
purely resonant and contains some interference from the non-resonant contribution to
the signal.

43

Figure 3.7. Double logarithmic plot of the relative CARS intensity for o-xylene and pxylene as a function of o-xylene concentration.
In addition to performing measurements on liquid samples, several gas phase
samples were examined. The experimental set-up varied slightly in that the experiments
were made using a pressure cell for the various gases and the CARS signal collected in
transmission mode. The experimental setup for the gas phase measurements is
highlighted in Fig. 3.8.

44

Figure 3.8 Schematic diagram of the single-beam CARS instrument for detection of gasphase measurements.
Two different gases were examined: nitrogen, with a single resonance at 2330
-1

-1

cm , and carbon dioxide, with two resonances at 1285 and 1388 cm . Nitrogen was
first examined as a function of pressure, up to 8 bar. These plots are shown in Fig 3.9.
For each data point, the intensity of the CARS signal for nitrogen was integrated over a
narrow spectral region. Fig. 3.9 a) displays the range for pressures up to 2 bar, while b)
displays the pressures from 2-8 bar for nitrogen.

45

Figure 3.9. Nitrogen CARS signal as a function of pressure. Symbols represent the data
points, while the solid lines are the power curves, fit to the data. Each plot contains
three sets of data, illustrating the reproducibility of the measurements.
The CARS signal dependence on number density was also examined in CO2. These
measurements were performed under the same conditions as the nitrogen experiments.
Each vibrational mode, 1285 cm

-1

(B in Fig. 3.10) and 1388 cm

-1

(A in Fig. 3.10), is

plotted as a function of pressure and fit with a power curve as shown in Fig 3.10.

46

Figure 3.10. Carbon dioxide CARS signal as a function of pressure. Symbols represent
the data points, while the solid lines are the power curves, fit to the data.
In the low pressure regime for nitrogen, the CARS signal depends on the number
density squared, as one would expect; however, for the higher pressure region (2-8
bar), the CARS signal is linearly dependant on the number density. In carbon dioxide,
the signal from each mode does not show the expected number density relationship,
with a saturation point appearing around 5 bar. The saturation effects and non-quadratic
dependence may be due to nonlinear optical effects such as self-phase modulation or
77

additional multiphoton processes, collisional line mixing , pressure effects on the
78

coupling constants between the CO2 Fermi resonances , saturation of the Raman
transitions, or interference between the resonant and nonresonant responses.

47

79

3.7 Conclusions
Single-beam CARS using amplified femtosecond pulses has demonstrated its
ability to be in several different fields. The additional energy provided by the amplified
pulses allows for the single-beam method to be readily extended to distances much
larger than those of the initial microspectroscopy applications. The ability to operate at
larger distances along with the additional advantages provided by the single-beam
CARS method highlight the applicability of this method for remote sensing. Additionally,
this method has demonstrated the feasibility to be used for gas phase measurements,
particularly those which may be of interest for the diagnostics of combustion processes
or reacting flows.

48

Chapter 4
Selective Excitation of Gas Phase Molecules
This chapter expands upon the previous work and focuses on the theory and an
methodology for selective excitation. In particular, this work highlights the application of
binary phase shaping (BPS) for selective excitation of gas phase molecules. The
application to gas phase molecules is significant in that CARS methods are one of the
80-85

primary methods for the diagnostic of combustion processes.

The following It is

reproduced with permission from P. Wrzesinski, D. Pestov, V. V. Lozovoy, B. Xu, S.
Roy, J. R. Gord, and M. Dantus, “Binary phase shaping for selective single-beam CARS
spectroscopy and imaging of gas-phase molecules”, Journal of Raman Spectroscopy
2011, 43, 393-398 Copyright (C) 2010 John Wiley & Sons, Ltd.
4.1 Selective Excitation
Selective excitation of Raman modes facilitates nonresonant-background
suppression in the single-beam CARS scheme. Importantly, it also allows for elimination
of multi-channel acquisition of CARS spectra, which is difficult to integrate with highspeed laser beam scanning for imaging applications. Sinusoidal phase modulation,
though conceptually simple, provides a fairly low degree of signal rejection at offresonant Raman frequencies. Better contrast is expected for linearly chirped pulses that
have been utilized extensively in multi-beam CARS setups.

86-88

Another attractive

alternative, discussed in this work, is pseudorandom binary sequences. Using
pseudorandom binary phase shaping (BPS), we have demonstrated previously high-

49

contrast excitation selectivity for second-harmonic generation (SHG), two-photon
excited fluorescence, and stimulated Raman scattering.
for mode-selective CARS with liquid samples.

89

71

We have also applied BPS

Here we extend it to selective excitation

of gas-phase molecules. In particular, we use pseudorandom BPS for selective
-1

-1

excitation of O2 (~1550 cm ) and N2 (~2330 cm ) vibrations in ambient air. We also
show independent excitation of CO2 Fermi dyads at ~1280 cm

-1

and ~1380 cm

-1

in

gas-phase CO2 and CO2/N2 mixtures. Finally, we demonstrate selective single-beam
CARS imaging of CO2 gas jet.
4.2 Binary Phase Shaping for Selective Single-Beam CARS
Coherent vibrations of a molecular ensemble in CARS are established through the
nonlinear interaction with the optical field. The excitation efficiency is, therefore,
dependent on both the amplitude and the relative phase of contributing spectral
components, or rather on multiphoton intrapulse interference (MII) since the excitation is
impulsive.

90

The coherence amplitude at some wavenumber Ω R is proportional to

+∞
∗
(4.1)
∫ E (Ω + Ω R )E (Ω)dΩ,
0
where E (Ω ) ≡ E (Ω ) ⋅ exp(iϕ (Ω )) ∝ S (Ω ) ⋅ exp(iϕ (Ω )) is a complex spectral amplitude of
E (0) (Ω R ) ≡

the field at wavenumber Ω , determined by the spectral field intensity S (Ω) and phase

ϕ (Ω) . Since the pulse shaper operates with a finite number of independent channels, it

50

is insightful to rewrite Eqn. (4.1) for a mesh of N equidistantly spaced points between
Ω

ps
ps
and Ω max :
min
(0)
En ≡

N − n −1

∑

∗
Em + n Em ∝

N − n −1
∑ S m + n S m ⋅ exp(i(ϕ m + n − ϕ m )),
m=0

m=0
n = 0Κ N − 1.
The notations used are:
(0)
E j = E (0) ( j∆Ω N ), E j ≡ E (Ω j ), S j ≡ S (Ω j ), ϕ j ≡ ϕ (Ω j ),
ps
ps
ps
) /( N − 1), j = 0 Κ N − 1.
Ωj =Ω
+ j ⋅ ∆Ω N , ∆Ω N = (Ω max − Ω
min
min
If we now limit the phase values to 0 or

π

(4.2)

(4.3)

(more generally, to two values offset by

and assume that the spectral intensity within the [Ω

π)

ps
ps
,Ω
] -interval remains
min max

constant, we find that the electric field {E j } , subject to proper normalization, can be
presented as a sequence of values +1 and −1. Since all such sequences of length M
M

form a mathematical object known as a Galois field GF(2 ), the problem of selective
excitation can be linked to the number-theory problem of finding sequences of numbers

+1 and −1 with minimal autocorrelation. Indeed, for every given Raman shift
j
( 0)
from Eqn. (4.2), i.e., by
Ω R0 ≡ j0 ⋅ ∆Ω N , the excitation efficiency is determined by E
j0

j
correlation of {E j } and {E j + j } . When the binary sequence is repeated after Ω R0 ,
0
(0)
E j would have a maximum at j = j0 . The use of a minimal-autocorrelation sequence

to modulate the phase, however, ensures that the excitation at nearby frequencies is
suppressed.
51

Following the considerations above, the phase mask across the pump-Stokes
part of the spectrum is built as follows; see the diagrams in Fig. 4.1. We first assign the
minimal, Ω

ps
ps
, and maximal, Ω max , wavenumbers of the pump-Stokes band and
min

ps
ps
, with 2Ω R , where Ω R is the selected
compare its bandwidth, ∆Ω ps ≡ Ω max − Ω
min
wavenumber. Here we assume that the pump-Stokes bandwidth ∆Ω ps exceeds Ω R ,
i.e., the transition can be excited impulsively. If ∆Ω ps < 2Ω R , as shown in Fig. 4.1 a),
the chosen

4.1. Selective excitation of Raman-active vibrational modes via BPS: a) binary phase
mask design for ∆Ω

ps < 2Ω
ps
R ; b) binary phase mask design for ∆Ω ≥ 2Ω R . Here

52

∆Ω ps is the bandwidth of the pump-Stokes part of the laser spectrum; Ω R is the
transition Raman shift.

ps
pseudorandom sequence is stretched over a ( ∆Ω ps − Ω R )-wide interval, from Ω max
down to Ω

ps
ps
ps
+ Ω R , and then repeated between Ω max − Ω R and Ω
, with
min
min

ps
translational symmetry relative to the first interval. The interval between Ω max − Ω R
and Ω

ps
+ Ω R , which does not contribute towards excitation at Ω R , is filled with a
min

high-frequency random binary phase to suppress the background contribution from this
part of the spectrum. If ∆Ω ps ≥ 2Ω R (see Fig. 4.1 b)), the Galois sequence is stretched

ps
ps
ps
over Ω R and encoded from Ω max to Ω max − Ω R , and then from Ω max − Ω R down to
ps
Ω max − 2Ω R . The left-over SLM pixels are again filled with a high-frequency random
binary phase. In principle, one can put in as many sequence copies as can fit in ∆Ω ps ,
i.e. more than two. The extra copies, however, will contribute to higher harmonics of

Ω R as well. At last, it is worthwhile to note here that Galois sequences are best suited
for shaping of flat-top laser spectra. Their minimal-autocorrelation property implies
equally weighted contribution from every term in a sequence, which is not quite the case
for the spectrum provided by our laser source. In practice, it results in inferior
background suppression when compared to the optimal case.

53

To retrieve CARS spectra, we use a polarization-shaping technique.

53,89

The

polarization of a narrow band on the blue side of the laser spectrum (polarization Px in
Fig. 4.2 a), four SLM pixels wide) is rotated by 90° relative to the remaining spectrum.
The polarizer in the acquisition arm is also set along this polarization. Only CARS
photons with polarization Px are detected. The intense Py-polarized signal,
overwhelmed by the nonresonant background produced by the pump-Stokes
component and having poor spectral resolution, is rejected. We also encode a π-phase
step across the Px-polarized band when acquiring multi-mode CARS spectra, as shown
in Fig. 4.2 b). The π step is used to minimize the time overlap between the Py-polarized
pump-Stokes and Px-polarized probe parts, mitigating the contribution due to the
instantaneous electronic response.

54

Figure 4.2 Phase-and-polarization shaping for multi-mode and selective single-beam
CARS measurements. a) Polarization mask encoded onto the laser spectrum, shown on
the background by the gray line; b) Phase mask for multi-mode CARS measurements,
when all Raman modes within the laser bandwidth are excited. c,d) Pseudorandom
-1
phase masks used for selective single-beam CARS from O2 (1550 cm ) and N2 (2330
-1

cm ), respectively.
Two examples of selective-excitation phase masks, based on a 37-bit Galois
sequence, are shown in Figs. 2 c) and 2 d). The phase mask in Fig. 2 c) is designed to
-1

excite the O2 vibrational mode at ~1550 cm . For the given experimental parameters,
the condition ∆Ω ps ≥ 2Ω R is fulfilled; therefore, the Galois binary sequence is stretched
-1

over 1550 cm , and its two copies are stacked together next to the probe band. The
-1

pseudorandom phase mask in Fig. 2 d) targets the N2 Raman transition at ~2330 cm .
Here ∆Ω ps < 2Ω R and the two sequence copies are separated by a random binary
modulation.

55

Using this method, phases for selective excitation of the two Fermi dyads of CO2,
and the Raman modes of O2 and N2 were designed. The normalized excitation
efficiency spectra η (Ω R ) ,
2

η ( Ω R ) ≡ E ( 0) ( Ω R ) / E ( 0) ( 0) ,

(4.4)

for each of the phases as well as for zero phase, which corresponds to a transform
limited (TL) pulse, are shown in Fig. 4.3. From the figure it is clear that BPS is used
most effectively when the condition ∆Ω ps < 2Ω R is fulfilled. When ∆Ω ps ≥ 2Ω R , BPS
eliminates high-harmonic contributions at the expense of the inferior excitation strength.
Raman-shift-dependent excitation efficiencies, both due the limited laser bandwidth and
spectral phase shaping, contributes towards the strength of Raman peaks observed in
CARS spectra. In principle, such dependences might be accounted for experimentally
by the normalization of the CARS signal on the purely nonresonant response from a
reference sample. To predict the measured CARS spectra or use those to retrieve
relative concentrations of contributing species, however, one also needs to account for
the timing between the pump-Stokes and probe fields, Raman cross sections of
transitions being examined, and their coherence dephasing rates. This is currently
under development, along with other possible methods to perform selective excitation in
single-beam CARS.

56

Figure 4.3 Calculated excitation spectra, η (Ω R ) , for a TL pulse (no phase modulation)
-1

and waveforms, produced by pseudorandom BPS for selective excitation at 1280 cm ,
-1

-1

-1

1380 cm , 1550 cm , and 2330 cm .
4.3 Experimental
The experiments were performed with a system based on a Ti:sapphire
regenerative amplifier (Legend, Coherent Inc.); see Figure. 4.4. A pulse shaper (not
shown) was installed between the oscillator (Micra, Coherent Inc.) and the amplifier to
remove high-order phase distortion of laser pulses at the regenerative-amplifier output.
The laser spectrum was then broadened through self-phase modulation in a hollow
91

waveguide (HWG),

constructed from a 39-cm-long glass capillary with a core

57

diameter of ~300 µm and filled with argon at ~2 bar. The HWG output bandwidth was
optimized by varying the input power, pulse chirp, and argon pressure. The typical
spectrum of a pulse reaching the sampled volume is shown in the inset of Fig. 4.4. The
corresponding TL pulse duration is about 7 fs. Phase distortions of the pulse at the
2

sample (primarily linear chirp of ~2000 fs ) were corrected via multiphoton intrapulse
10

interference phase scan (MIIPS) , performed with a 4f pulse shaper located after the
HWG. The same shaper was used for polarization-and-phase shaping as discussed
below. It had a dual-mask 640-pixel spatial light modulator (CRi SLM-640-D) at the
Fourier plane, with the polarizer removed. The beam of shaped pulses was focused in
ambient air or a gas pressure cell using a 75-cm-focal-length curved mirror. A concave
metallic mirror with 25-cm focal length was used for imaging of the CO2 jet. The
generated CARS signal was separated from the input field using a 650-nm short-pass
filter (Omega Optics) and a calcite polarizing cube (Newport), with the transmission axis
set perpendicular to the polarization of the excitation photons. The filtered CARS
photons were either focused into a high-resolution spectrograph with a LN-cooled CCD
camera or fiber-coupled into a low-resolution Ocean Optics QE-65000 spectrometer.
For imaging experiments, we used two motorized translation stages to shift the nozzle
in the focal plane of the laser beam. Spectrally integrated CARS signal over 1460 cm
was recorded as a function of the nozzle position.

58

-1

Figure 4.4 Schematic diagram of single-beam CARS experimental setup. SLM, spatial
light modulator. Inset: a typical pulse spectrum at the sample.
4.4 Results and Discussion
Selective excitation via BPS was examined with several different gases. Initial
experiments were performed with ambient air, whose CARS spectrum is expected to
-1

have two strong Raman lines corresponding to vibrations of O2 (~1550 cm ) and N2
-1

(~2330 cm ) molecules. The experimental multi-mode CARS spectrum (gray shadow in
Fig. 5) indeed features a pronounced N2 line. The O2 line, however, is hidden by the
remaining nonresonant contribution that rises at low wavenumbers. Selective excitation
-1

at 1550 cm , using the phase mask from Fig. 4.2, mitigates the interfering background
and makes the O2 line obvious. The other pseudorandom phase mask highlights the N2
vibrational mode. The slight offset of the spectra from zero is due to the electronic dark
current of the LN-cooled CCD used for detection.

59

Figure 4.5 Selective single-beam CARS from O2 and N2 vibrations in ambient air.
Single-beam CARS measurements with a 1:1 N2/CO2 mixture in the pressure
cell showed similar results. In the multi-mode CARS spectrum, the nonresonant
background due to the instantaneous electronic response interferes with the two CO2
signatures; see Fig. 6. The designed binary phase masks allow exciting all three Raman
lines, including the N2 line and CO2 Fermi dyads at ~1280 cm

-1

independently. They also strongly suppress the nonresonant background.

60

-1

and ~1380 cm ,

Figure 4.6 Selective single-beam CARS of a 1:1 N2/CO2 mixture at 1 atm pressure.
The excitation selectivity contrast can be inferred from Fig. 4.7 a), where the
-1

CARS signal intensities at 1280 cm , 1380 cm
-1

-1

and over the entire spectral region

(625-2125 cm ) from pure CO2 gas at 1 atm are plotted as a function of the design
parameter Ω R .

61

Figure 4.7 Selective single-beam CARS of pure CO2 at 1 atm. The target Raman shift

Ω R of the pseudorandom binary phase is tuned through the two resonances with CO2
Fermi dyads at ~1280 cm

-1

-1

-1

and ~1380 cm . CARS signal intensities at 1280 cm ,

-1

1380 cm , and integrated over 625-2125 cm as a function of Ω R .
Several representative CARS spectra, acquired with Ocean Optics QE-65000
spectrometer while scanning Ω R , are shown in Fig. 4.8. When the 1280-cm
selectively excited, the ratio of CARS intensities between the 1280 cm
lines is 10:1. For selective excitation of the 1380cm
1280 cm

-1

and 1380 cm

-1

-1

-1

-1

line is

and 1380 cm

-1

CO2 line, the ratio between the

lines is 1:24. When the CARS signal is not resolved

62

spectrally, the contrast is limited primarily by the cumulative nonresonant contribution
reaching the detector.

-1

-

Figure 4.8 Experimental CARS spectra acquired for Ω R equal to 1200 cm , 1280 cm
1
-1
-1
-1
, 1330 cm , 1380 cm , and 1500 cm The multi-mode single-beam CARS spectrum
of CO2 (no BPS) is shown as a reference. The other CARS spectra are scaled in
intensity by a factor of 6.
To emphasize the utility of selective BPS, we imaged a jet of CO2 gas, flowing
out a narrow rectangular nozzle, with TL and shaped pulses. In both cases, a 0.6-by-2.2
mm region near the tip of the nozzle was scanned using 0.01 mm vertical steps and
0.05 mm horizontal steps. The spectrally integrated CARS signal from 1060-2520 cm

-1

was recorded at each position in the scan. The image obtained with TL pulses (see Fig.
4.9 a)) exhibits poor chemical contrast, which can be improved, however, by spectral

63

filtering of the CARS signal corresponding to the CO2 lines or by post-processing of
CARS spectra if those are available. Note that the CARS spectra over the observed
range featured N2 and O2 lines from ambient air as well as comparable nonresonant
contribution at lower wavenumbers (longer wavelengths). Selective excitation,
implemented in Fig. 4.9 b) for 1280 cm

-1

Raman transition in CO2, virtually eliminates

the need for signal post-processing, favors single-channel detection, and allows for
straightforward tuning between different Raman resonances. The image in Fig. 4.9 b)
demonstrates excellent chemical contrast and reveals interesting dynamics of the
turbulent CO2 flow. In particular, the intensity modulation seen in the CO2 flow is
reproducible from image to image and is deemed to be characteristic of the imaged jet.

64

-1

Figure 4.9 Imaging of a CO2 gas jet with a) no BPS and b) BPS excitation at 1280 cm .
4.5 Conclusions
We have extended the pseudorandom BPS technique, introduced elsewhere, to
selective excitation of high-wavenumber molecular vibrational modes in the gas phase.
In particular, we have used it to address Raman transitions of O2 and N2 in ambient air
as well as CO2 Fermi dyads in a 1:1 N2/CO2 mixture and pure CO2 gas at atmospheric
pressure. We have shown that pulse phase shaping using pseudorandom BPS allows
for high-contrast selectivity and efficient nonresonant-background suppression in singlebeam CARS measurements, enabling high-contrast spectroscopy and imaging.

65

Chapter 5
Multi-method Selective CARS
This chapter discusses the use of Multiphoton Intrapulse Interference to provide
selective excitation of a single Raman mode. Selective excitation has been previously
shown as a method to dramatically decrease the non-resonant response, providing
large signal to noise levels and high selectivity desirable for applications that require
high data acquisition rates. Various phase shaping methods for performing MII are used
in conjunction with single-beam CARS spectroscopy.
5.1 Mulitphoton Intrapulse Interference (MII)
Numerous applications of Multiphoton Intrapulse Interference (MII) have been
92-95,19, 96-98

demonstrated for the coherent control of atomic and molecular systems.

In MII, the spectral phase of the pulse is used to constructively or destructively interfere
pairs of frequencies within the bandwidth of the laser at a singular desired frequency.
This interference allows for enhancement or suppression to occur at the desired
frequency. In these experiments, various phase shaping approaches were used to
perform selective CARS excitation based upon MII.
Several fundamental phase shaping methodologies were evaluated. Each method
has been adapted to the single-beam geometry using a liquid crystal spatial light
modulator (SLM) based 4f-pulse shaper. The first phase shape is based upon the use of
two chirped pulses. This method has been previously reported for use in a multiple99

100,87,101

beam geometry for control of molecular wave packets , improved resolution

66

,

coherent Raman in highly scattering solids
pulses.

103

102

, and coherent Raman with white-light

In the adaption of this method for the single-beam geometry, the pulse

spectrum is divided into two portions in the frequency domain (at the center pixel of the
SLM), and a uniform chirp phase function is applied to each half using the SLM. The
relative delay between the two portions is then tuned, resulting in a time-domain
waveform that is matched to the frequency of a desired vibrational mode. Continuous
scanning of the delay maps out the entire accessible CARS spectrum. This phase
function is described by equation 5.1, where φ(ω) is the desired phase function.

߮ሺ߱ሻ ൌ ൝

߮஺ ൅ భఝሺమሻ ቀఠିఠವ ାభ
మ
మ

߮஻ ൅ భఝሺమሻ ቀఠିఠವ ିభ
మ
మ

In this phase function, φ

(2)

మ
ೃቁ

௜௙ ఠவఠವ

మ

ೃ ቁ ௜௙ ఠஸఠವ

ൡ

(5.1)

2

is the amount of linear chirp applied (1000 fs ), ωD is
-1

the divider frequency, and ΩR (1500 cm ) is the desired Raman frequency to be
excited. This is illustrated in Fig.5.2 using a rectangular spectrum with a bandwidth of
~200 nm to simulate the effect of the pulse shaping in the time domain. Panel a)
illustrates the pulse spectrum (pump/Stokes and probe) and the applied spectral phase
in the wavelength domain; panel b) shows the pulse in the frequency domain along with
the applied phase with respect to τ (relative delay between frequencies). Finally, panel
c) shows the time domain profiles for both the pump and probe.

67

Figure 5.1. Simulation of MII using two chirped pulses with a rectangular spectrum.
(2)
-1
φ = 1000 fs, the divider is pixel 319, and ΩR=1500 cm a) Pulse spectrum (red, solid),
probe spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength
domain b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue,
dashed) c) temporal profiles of the pump/Stokes (red) and probe (blue).
The second approach makes use of sinusoidal phase modulation to perform MII.
The utility of this type of phase modulation has been demonstrated in numerous
applications relating to coherent Raman.

52,104

When this function is used for mode

selective excitation, a train of pulses with a time interval determined by the sinusoidal
phase period is generated. This period, or integer multiples of the period, coincides with
the period of molecular vibrations that are excited. The sinusoidal phase can be defined

68

as follows:

߮ሺ߱ሻ ൌ ߙ · cos ቀ2ߨ

ఠିఠ೎
ೃ

െ ߜቁ

(5.2)

Here α, ωc, ΩR, and δ are the amplitude (2π), central frequency (770 nm), desired
-1

Raman transition (1500 cm ), and relative shift in period (1) respectively. The values of
each are fixed with the exception of the desired Raman transition. The time domain
profile for this pulse shape is shown in Fig. 5.2.

Figure 5.2. Simulation of MII sinusoidal phase modulation, with a rectangular spectrum.
-1
α=2π, ωc=770 nm, ΩR=1500 cm and δ=1 a) Pulse spectrum (red, solid), probe
69

spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength domain
b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue, dashed)
c) temporal profiles of the pump/Stokes (red) and probe (blue).
A third method using MII for selective CARS excitation with binary phase shaping
is also explored. This method was described in greater detail in chapter 4. Briefly, in
binary phase shaping, two identical N-bit identical sequences (N=13) are separated by a
desired Raman frequency and have phase values limited to zero or π. These
sequences are applied to the pump-Stokes frequencies. Alternating zero and π values
are written onto all other pixels to prevent excitation at non-desired frequencies. The
sequences are chosen based upon minimum autocorrelations at all Raman frequencies
except the desired resonance. Scanning of the frequency separation between the two
sequences allows mapping of the Raman excitation at different vibrational frequencies.

70

Figure 5.3. Simulation of MII sinusoidal phase modulation,with a rectangular spectrum.
N=13. a) Pulse spectrum (red, solid), probe spectrum, (blue, solid) and pulse shaping
(blue, dashed) used in the wavelength domain b) frequency domain pulse spectrum
(red, solid) and relative phase delay (blue, dashed) c) temporal profiles of the
pump/Stokes (red) and probe (blue).

5.2 Modeling MII
MII was also used to model the experimental conditions used for the modeselective CARS measurements. For these models, the three phase shapes, chirp,
sinusoidal, and binary, were all used. Rather than an idealized rectangular spectrum,
the actually spectrum used for the experiments and the actual phase shapes used for

71

collection of the experimental CARS data are presented. Two chirp pulses are
presented in Fig 5.4 in the same format as the MII simulations. The experimental
parameters for these values were selected based upon the experimental limits
presented by the pulse shaper resolution and the measurements of various
(2)

autocorrelations (Chapter 5.4). For the double chirp phase function φ

= 2000 fs, the

-1

divider is pixel 319 and ΩR=1500 cm .

Figure 5.4. Simulation of MII using two chirped pulses and an experimental spectrum.
(2)
-1
φ = 2000 fs, the divider is pixel 319 and ΩR=1500 cm a) Pulse spectrum (red, solid),

72

probe spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength
domain b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue,
dashed) c) temporal profiles of the pump/Stokes (red) and probe (blue).
The same method was also used to examine the Sinusoidal and BPS phase functions
for a typical experimental spectrum. Fig. 5.5 shows the results for a sinusoidal function
-1

where α=2.25, ΩR=1500 cm , ω0=770nm, and δ=0.

Figure 5.5. Simulation of MII sinusoidal phase modulation, using an experimental
-1
spectrum. α=2.25π, ωc=770 nm, ΩR=1500 cm and δ=1 a) Pulse spectrum (red, solid),
probe spectrum (blue, solid), and pulse shaping (blue, dashed) used in the wavelength
domain b) frequency domain pulse spectrum (red, solid) and relative phase delay (blue,
dashed) c) temporal profiles of the pump/Stokes (red) and probe (blue).

73

Figure 5.6 shows the results the MII simulation using BPS functions, where N=37.

Figure 5.6. Simulation of MII using binary phase modulation, and an experimental
spectrum. N=37 a) Pulse spectrum (red, solid), probe spectrum (blue, solid), and pulse
shaping (blue, dashed) used in the wavelength domain b) frequency domain pulse
spectrum (red, solid) and relative phase delay (blue, dashed) c) temporal profiles of the
pump/Stokes (red) and probe (blue).
The comparisons between the temporal profiles of the two different excitation spectra
provide very useful information regarding the relative intensities and duration of the
pulse trains produced by the various phase modulations. For the rectangular spectrum,

74

the pulse train (bottom panel) is always symmetric around time zero, with equal intensity
distribution throughout the time duration. The experimental spectrum is asymmetric,
with unequal intensity distributions. Furthermore, the phase modulation methods can be
compared to one another. For double chirp and BPS, there is nearly the same relative
intensity of the pulse train; however, sinsuodial modulation has a much higher relative
intensity. The intensity distribution and pulse train duration also differ greatly amongst
the pulse shapes.
5.3 Modeling the Excitation Efficiency
Considering the non-interferometric, intensity autocorrelation (Eqn. 5.3) of the
excitation pulse with a specific selective excitation phase provides information about the
pulse in the time domain.

‫ܣ‬ሺ߬ሻ ൌ ‫ ܫ ׬‬ሺ‫ݐ‬ሻ‫ כܫ‬ሺ‫ ݐ‬൅ ߬ሻ ݀‫ݐ‬
ି∞
∞

(5.3)

This time domain information will contain a repetitive oscillation, or beating frequency,
-1

corresponding to a vibrational time period (33.3 fs = 1000 cm ). This function can then
be Fourier transformed to extract the frequency data. According to the Convolution
Theorem (Eqn. 5.4), the power spectrum of the intensity of the pulse I(Ω) is the Fourier
transform of the autocorrelation function:

‫ ܨ‬ሾ‫ܣ‬ሺ߬ሻሿ ൌ |‫ܫ‬ሺ ሻ|ଶ

(5.4)

Stimulated Raman scattering (SRS) measured is proportional to the product of this
spectral intensity (property of the Pump-Stokes light) and cross-section of the Raman
transition (property of the molecules).

75

By autocorrelating each shaped pulse with itself and Fourier transforming the
autocorrelation, the SRS excitation can be generated for that particular pulse shape. By
evaluating a matrix of phase values, a 2D plot can be generated and can be used to
highlight the efficiency at a particular frequency as a function of the excitation phase.
This is illustrated in Fig. 5.7. The diagonal feature illustrates the correspondence
between the expected excitation frequency (ΩR) as a function of phase shaping and the
measured excitation efficiency.

Figure 5.7. Simulation of autocorrelation data for a) two chirped pulses, b) sinusoidal
modulation, and c) binary phase shaping.
From these simulations the following conclusions can be made. First, we expect
the chirp and sinusoidal phase functions to have the highest intensity, particularly in the
lower wavenumber region. Both of these phase functions use the entire bandwidth of
the excitation pulse, unlike BPS which only uses a portion. It is possible to modify the
BPS function to use the entire bandwidth; however, this would result in the production of

76

additional higher frequency contributions such as those seen with sinusoidal
-1

modulations near 2000 cm . Secondly, the BPS is most effective in the middle of the
-1

scan region (1300-1600 cm ), as this is where the binary phase function uses the
largest portion of the excitation spectrum.
5.4 Experimental Set-up
The experimental set-up used in this study has been described in great detail
previously in this dissertation. Briefly, the output from a regenerative amplifier (Legend,
Coherent) was focused into a narrow (300 µm I.D.) capillary filled with Ar gas at 1.5
atm. The 2500 cm

-1

continuum output is then collimated and directed into a reflective 4-

f pulse shaper with a 640 pixel liquid crystal spatial light modulator (640D, CRi) capable
of phase and polarization or phase and amplitude modulation. This allows for the
necessary phase modulation for implementing the various pulse shaping strategies as
well as correction of phase distortions.
The phase distortion correction is performed using mulitphoton intrapulse
interference phase scanning (MIIPS). MIIPS allows the spectra phase distortions to be
directly measured, then implements the opposite function of the measured distortion,
which cancels it. This allows for high accuracy pulse shaping at the target. The beam is
then steered from the pulse shaper and direction into a symmetric, home built
autocorrelator, which is used for the collection of autocorrelation data. The CARS data
is collected using a thin (200 µm) cuvette for liquid samples or a home built pressure

77

cell for gas phase samples. The output signals are recolimated and focused on to an
optical fiber which is coupled into a compact spectrometer (Ocean Optics QE65000).
5.5 Measurement of Excitation Efficiency
The intensity autocorrelation was collected for a matrix of phases with different
excitation scan parameters. Each autocorrelation was then Fourier transformed,
generating a two-dimensional plot indicating the SRS excitation frequency as a function
of a particular scan parameter. These plots should mirror the plot generated by the
modeling of the excitation efficiency. Experimental data for chirp, sinusoidal, and binary
phase shaping methods in the 1000 and 2000 cm

-1

region is shown in Fig.5.8. This

experimental data shows very good agreement with the modeled data. This data is then
used to ensure proper excitation frequencies and to optimize experimental parameters
for collecting CARS from various samples.

Figure 5.8. Experimental autocorrelation data for a) two chirped pulses, b) sinusoidal
phase modulation, and c) binary phase modulation.

78

5.6 Mutli-method CARS in liquid and gas phase
Using the parameters determined from the autocorrelation data, CARS data for
neat toluene in a 200 µm path length cuvette was collected for chirp, sinusoidal, and
binary phase functions. For the chirp function, the phase was split at the center pixel of
2

the SLM, and 2000 fs of chirp was used. The CARS spectrum was measured from
-1

-1

600-2000 cm , and ΩR scanned from 600-1800 cm . The resulting 2D plot is shown
in Fig. 5.9

Figure 5.9. 2D plot for two chirped pulses. The measured CARS spectrum for toluene is
along the y-axis, and the scan parameter for the selective excitation is along the x-axis.

79

For the sinusoidal phase function, the CARS signal was observed in the same region,
while scanning through the same range. The parameters for this function were as
-1

follows: α=2.25π, δ=1, and ΩR=600-1800 cm . Fig. 5.10 displays the 2D plot for this
phase function.

Figure 5.10. 2D plot for sinusoidal phase modulation. The measured CARS spectrum
for toluene is along the y-axis, and the scan parameter for the selective excitation is
along the x-axis.
Lastly, the CARS response from toluene was measured using BPS. For this
phase, the sequence used was N=37; the phase was alternated between 0 and π for all
pixels not in the N-bit sequence. The resulting 2D plot is shown in Fig. 5.11. The
resonant Raman peaks for toluene at 800 and 1000 cm

80

-1

are easily distinguishable

along the diagonal feature. The intensity of the CARS response near 800 and 1000 cm
1

-

for all three phase functions is shown in Table 1.

Figure 5.11. 2D plot for binary phase (BPS) modulation. The measured CARS spectrum
for toluene is along the y-axis, and the scan parameter for the selective excitation is
along the x-axis.

Table 1. CARS intensity of the Raman transitions of Toluene for each type of phase
modulation
Phase
Function
Chirp
Sine
BPS

CARS Intensity
-1
at 800 cm
200 a.u.
900 a.u.
200 a.u.

81

CARS Intensity
-1
at 1000 cm
400 a.u.
1000 a.u.
300 a.u.

In addition to these functions, several other functions were evaluated based upon
modifications of the previous functions. Of the phases examined, only one was
comparable to the previously used phase functions. This is an asymmetric chirp function
in which the low frequency phase is fixed and only the high frequency portion of the
phase is scanned. This is in contrast to the symmetric chirp in which both the high and
low frequency components are scanned. This phase function can be described as
follows:

߮ሺ߱ሻ ൌ ቊ

߮஺ ൅ మఝሺమሻ ሺఠିఠವ ିΩೃ ሻమ ௜௙ ఠவఠವ
భ

߮஻ ൅

భ ሺమሻ
ఝ ሺఠିఠವ ሻమ
మ

௜௙ ఠஸఠವ

ቋ

(4)

The resulting 2D plot for the asymmetric chirp phase functions is shown below for the
neat toluene sample.

82

Figure 5.12. 2D plot for two asymmetric chirp pulses. The measured CARS spectrum for
toluene is along the y-axis, and the scan parameter for the selective excitation is along
the x-axis.
The CARS signal from the asymmetric chirp function is slightly larger than that from the
chirp function with less background signal than is observed with the other pulse shaping
methods.
These same four phase functions were also applied to carbon dioxide in a 125
-1

mm path length pressure cell to examine the resonances at 1280 and 1388 cm . The
data for CO2 is illustrated in Fig. 5.13.

83

Figure 5.13. Two-dimensional plots showing the scan parameter ( R) vs. the measured
CARS response for a) asymmetric chirp b) chirp (c) sinusoidal and (d) BPS phase
modulation methods in carbon dioxide.
5.7 Results and Discussion
In evaluation of the data for the different phase modulations, three different
factors are apparent. The first of these is the signal intensities. The second factor is the

84

off diagonal signal corresponding to non-resonant and off-resonant contributions (in the
case of the sine function). Third is the region of highest excitation efficiency for each
phase function. From the autocorrelation data, it can be seen that sinusoidal has the
highest efficiency in the 800-1000 cm

-1

region, versus BPS which has the highest

-1

efficiently near 1400 cm . In addition to the 2D data sets, integrated plots are
generated for each phase function.
For the integrated plots, one band along the scan parameter axis (light yellow in
Fig. 5.14a) and a region of the CARS spectrum bound by the parameter axis and
spectra resolution (dark yellow in Fig.5.14a) are integrated. The ratio of the two areas
can be plotted as a function of the scan parameter. This allows for closer examination of
the diagonal feature corresponding to the scanned excitation and resonant Raman
transitions. Performing this analysis for each data set allows for direct comparison of the
different pulse shaping methods as shown for toluene in Fig. 5.14 a-b.

85

Figure 5.14. a) Two-dimensional plot for two chirped pulses with the integration
scheme highlighted, b) integrated spectra for the various phase functions as a
function of the scan parameter.
Examining the data in this manner allows for more direct discussion of the observations
made for the 2D data sets. First, sinusoidal and chirp functions have much more
intensity than the BPS function; this is evident in the simulation, autocorrelation, and
CARS data. The signal strength for the sine function and the chirp functions are nearly
equivalent and much higher than the BPS methods. In this situation, the phase function
is applied over the entire spectral bandwidth using all frequencies to contribute to the
signal, whereas with the BPS only the frequencies from the two active regions
contribute, which results in lower signal intensities. Another consideration for the
differences in signal intensities between chirp/sinusoidal modulation and BPS is that the
BPS method is typically reliant on a rectangular shaped spectrum. In this work, the
spectrum is far from this shape, thus reducing the overall effectiveness of the BPS
method. While the sine functions produce more off diagonal signal this is to be expected
as the sine functions are periodic. This results in higher noise levels and less defined
peak structure.
5.8 Conclusions
By comparing the various methods available for mode selective CARS excitation
it can be concluded that no single method is more desirable than another. Each method
has its own advantages and disadvantages. Sinusoidal modulation has very high signal
intensities, but much higher background. The double chirped phase has very low
background, but lowers signal intensities. BPS also has low background, suffers from

86

decreased excitation efficiency. The ideal phase is dependent on the desired transition
to be measured.

87

Chapter 6
Group Velocity Measurements of Combustion Gases
This chapter details the measurement of Group Velocity Dispersion (GVD) for
gases related to the combustion processes. These measurements are very valuable in
that they provide insight into the amount of temporal broadening that will occur as a
short pulse propagates in combustion environments. This understanding allows for
more accurate models and simulations of experimental conditions. The following
chapter is reproduced with permission from P. Wrzesinski, D. Pestov, V. V. Lozovoy, J.
R. Gord, M. Dantus, and S. Roy, “Group-velocity-dispersion measurements of
atmospheric and combustion-related gases using an ultrabroadband-laser source”,
Optics Express 2011, 19, 5163-5170. Copyright 2011. Optical Society of America
6.1 Group Velocity Dispersion
Developments in the optical diagnostics of combustion and reacting-flow
environments have been closely linked to advances in ultrafast-laser technology.
Historically, this field of study has been dominated by the use of nanosecond (10
and picosecond (10

-12

sec) sources. However,femtosecond (10

-15

105-107

108

, and imaging of turbulent gas flows.

109

sec)

sec)-laser sources

have recently been successfully applied for gas thermometry
studies

-9

, pressure

While these experiments reinforce

the numerous advantages of broadband-laser sources and optical diagnostics on the
femtosecond time scale, they also bring attention to an inherent nuance of ultrashort
(spectrally broadband)-pulse propagation--femtosecond pulses are much more
88

susceptible to temporal broadening due to group-velocity dispersion (GVD) than
picosecond and nanosecond pulses.
110-112

The GVD of many solids

113,114

and liquids

have been measured with

several experimental methods. However, GVD information for gas phase molecules is
not as prevalent. In this study we focus on the dispersion properties of common
atmospheric and combustion gases at room temperature and explored their scalability
with gas pressure. We relied on the Multiphoton Intrapulse Interference Phase Scan
(MIIPS) technique

10

to obtain the chromatic dispersion of these gases over the 700–

900 nm range, limited by the spectral bandwidth of our laser. MIIPS directly measures
the second derivative of the pulse spectral phase, φ(ω), at the target. This is
accomplished by scanning a well calibrated reference phase f(ω) and observing
changes in the second harmonic spectrum. When the curvature of this function, f′′( ω)
corrects for the local phase distortion, φ′′(ω), a local maximum appears in the second
harmonic signal, thus allowing φ′′(ω) to be mapped for the entire spectrum. From the
integration of φ′′(ω) the phase distortion can then be corrected. However for this work,
the φ′′(ω) information is sufficient as GVD is defined as
GVD (ω ) ≡

d  1  d 2 k (ω )

=
≡ k ′′(ω ),
dω  V g (ω ) 
dω 2



(6.1)

where V g (ω ) is the group velocity, k (ω ) = (ω / c ) n(ω ) the wavenumber, and n(ω ) the
refractive index of the media, GVD can be obtained from differential MIIPS
measurements performed with and without gas in a pressure cell. For a homogenous

89

gas distribution, the phase difference is proportional to the path length in the cell,
∆φ (ω ) = ∆k (ω ) L , and the GVD

GVD =

′′
gas
∆(ϕ ′′(ω )) ϕ ′′ (ω ) − ϕ vac (ω )
=
,
L
L

(6.2)

where L is the interaction length with the dispersive media. A similar approach was
previously demonstrated to provide GVD in solutions with high precision and
accuracy.

115

Note that the MIIPS measurement yields GVD as a function of frequency,

ω , i.e., it contains information concerning several leading orders of dispersion in the
Taylor-series expansion near the carrier frequency ω0

GVD(ω) ≡ k ′′(ω) = k ′′(ω0 ) + k ′′′(ω0 ) ⋅ (ω − ω0 ) + Κ

(6.3)

6.2 Experimental
The dispersion measurements were performed using an ultrabroadband
femtosecond oscillator (Venteon; Pulse 1), operating at 75 MHz with 40 mW of average
power. The spectral bandwidth covers over 400 nanometers, extending from 620 to
1050 nm (see Fig. 6.1). Such a broad spectrum allowed the measurement of dispersion
across the entire 700–900 nm range without wavelength tuning. The output beam
passed through a spatial filter and was then directed into a 4f reflective pulse
16,74

shaper

(BioPhotonics Solutions Inc.; MIIPS Box 640) using a 640-pixel, dual-mask,

liquid-crystal spatial-light modulator (SLM). Upon exiting the pulse shaper, the beam
passed through one of two different pressure cells. One cell, with a path length of 0.90

90

m, was used for measurements in the low
surements
low-pressure regime (1–4 bar) and was double
4
passed, increasing the interaction length. The other cell had a path length of 0.20 m and
was used for measurement in the high
high-pressure regime (10–50 bar). After exiting the
50
pressure cell, the beam was focused onto a thin 10 µm KDP crystal for generation of
eam
10-µm
the second harmonic. The second
second-harmonic-generation (SHG) signal was separated
generation
from the fundamental spectrum and focused into a spectrometer (Ocean Optics;
QE65000).

and
Venteon oscillator; b) Diagram of
Figure. 6.1. a) Broadband spectrum produced by the Ve
experimental setup.

91

Prior to dispersion measurements, the cell was evacuated, and the intrinsic
phase distortions to the system were measured and corrected using MIIPS. The sample
gas was then introduced at the desired pressure, and MIIPS was again employed to
measure the phase distortions produced by addition of the gas. For each gas
measurement a pressure point was randomly selected, and the dispersion was
measured in triplicate. All dispersion measurements were performed at room
temperature (295 K).
6.3 GVD Measurements
The results of low-pressure measurement of dispersion for seven cylinder gases
are summarized in Fig 6.2. For five of those gases, the dependence of dispersion on
pressure was measured in a high-pressure regime as well [see Fig. 6.3].

92

Figure 6.2 Measured GVD at 800 nm as a function of pressure in low (1–4 bar) pressure
regimes for several atmospheric and combustion-related gases.

Figure 6.3. Measured GVD at 800 nm as a function of pressure in high (1–50 bar)
pressure regimes for several atmospheric and combustion-related gases.
We found that for all gases, the dispersion changed linearly with pressure in the
low-pressure regime, as expected due to direct pressure/density relationship (ideal gas
behavior) in this limit. However, two of the measured gases--carbon dioxide and
ethylene--exhibited a nonlinear dependence of GVD on gas pressure in the highpressure regime.
The GVD of materials scales linearly with density. To illustrate this dependence
for gases we obtain the density using the first approximation of the virial equation of
116

state

93

ܲ ൌ ߩܴܶሾ1 ൅ ߚߩሿ

(6.4)

with the first virial coefficient (β), and plot dispersion as a function of gas density in Fig.
6.4. As expected we see the linear dependence on density.

Figure 6.4 Measured GVD at 800 nm as a function of gas density for nitrogen, oxygen,
carbon dioxide, and ethylene along with linear fitting of the data.

For extracting the dispersion values of each gas or gas mixture, the rise of the
second derivative of the phase with pressure within 1–4 bar (with 1-bar step) and for
some gases within 10–50 bar (with 5-bar step) is fitted by a linear function at every
spectrometer wavelength. The measured dispersion is then normalized on the beam
path length in the pressure cell and used to determine the second- and third-order

94

dispersion coefficients by linear fitting of the data in the frequency domain, as shown in
Fig. 6.5 and 6.6 for nitrogen.

Figure 6.5 Measured dispersion for nitrogen (raw data) over the entire pressure range
(data for some pressure values have been eliminated for clarity of presentation)

95

Figure 6.6 Dispersion of nitrogen normalized on path length and pressure, along with
the linear fit. The intercept value provides the second-order coefficient, while the slope
provides the third-order dispersion. The carrier frequency, ω0 , is set to 2.3526 rad/fs (

λ0 = 800.65 nm).
This analysis was performed for all measured gases. The experimental GVD
curves and their linear fits are shown in Fig. 6.7. The retrieved second-and third-order
dispersion coefficients are reported in Table 1 which contains the GVD coefficients for
oxygen, nitrogen, and air that were obtained using the entire pressure range (1-50 bar).
For carbon dioxide and ethylene, only the low-pressure (1–4 bar) data were used

96

because of the nonlinearity at high pressures. The GVD of acetylene and propane was
measured in the low-pressure (1–4 bar) regime only.

Figure 6.7. Dispersion normalized on the path length and pressure for all the gases,
along with the linear fit. For oxygen, nitrogen, and air, dispersion data from both
pressure ranges are used; for all other gases only the low-pressure data, exhibiting
linear pressure dependence, are used.

97

Table 2. Second- and third-order dispersion values at 800 nm for each gas at a
pressure of 1 bar, along with the standard error in fitting and the statistics of the linear
fit.
Standard
SecondThirdCoefficient of
Deviation
Order
Order
Determination
from the
Gas
Dispersion Dispersion
2
Linear Fit
2
3
(R )
2
(k′′-fs /m)
(k′′′-fs /m)
(fs /m)
Oxygen
24.76±0.04
12.5±0.2
0.957
0.66
(O2)
Nitrogen
18.70±0.04
11.8±0.2
0.950
0.67
(N2)
Air
20.05±0.06
11.8±0.4
0.906
0.89
Carbon
Dioxide
30.90±0.05
21.5±0.3
0.977
0.81
(CO2)*
Acetylene
78.20±0.07
43.7±0.4
0.989
1.12
(C2H2)*
Ethylene
102.18±0.08
57.0±0.5
0.992
1.28
(C2H4)*
Propane
111.21±0.08
52.8±0.5
0.990
1.30
(C3H8)*
*Values extracted from low-pressure data only.

To the authors’ knowledge, most of these values have not been reported
previously. The second-and third-order dispersion values of air, measured in
Ref.
2

117,118,69,119

, are in good agreement with our values (from ref. 83: 20.14±0.14
3

fs /m and 18±15 fs /m, respectively). Additional dispersion measurements have been
made on several noble gases as well as nitrogen using interferometry; our measured
2

values for nitrogen are also in agreement with these values (18.04±0.15 fs /m and

98

3

10±10 fs /m in

117

117

). Fitting of refractive index measurements with the Sellmeier
2

2

equation gives GVD values of 19.49 fs /m for nitrogen and 19.87 fs /m for air.
To highlight the role of dispersion in experiments where femtosecond pulses are
used, we have examined the effect of dispersion on pulse-time duration by simulating
the effect of various gas pressures in a 0.15-m-path-length pressure cell. The
simulations were performed using the femtoPulse Master software (BioPhotonic
Solutions Inc.), assuming Gaussian pulses with transform-limited (TL) time durations of
5, 10, and 50 fs. The software uses the input-pulse spectrum along with the secondand third-order dispersion values from Table 2 to calculate pulse durations at various
pressures.

99

Table 3: Simulated pulse durations (fs) due to changes in dispersion as a function of
pressure for a 0.15-m path

Gas

Pressure
(bar)
0

1

2

3

4

5

10

20

30

40

Oxygen Nitrogen
(O2)
(N2)
5
10
50
5.4
11.4
50
6.4
11.5
50
7.9
11.6
50
9.6
11.7
50
20.9
13.6
50.1
40.9
21.2
50.2
61.2
30.6
50.4
81.6
40.5
50.7
101.8
50.2
51

5
10
50
5.2
11.4
50
5.9
11.5
50
6.8
11.5
50
7.9
11.6
50
16.1
12.6
50
30.9
17
50
46
23.7
50.2
61
30.8
50.2
76.4
38.1
50.6

Air

5
10
50
5.3
11.4
50
6
11.5
50
7
11.5
50
8.3
11.6
50
17.2
12.8
50
33.3
17.9
50.1
49.6
25.2
50.2
66
33
50.4
82.4
40.9
50.7

Carbon
Dioxide
(CO2)

Ethylene
(C2H4)

Acetylene
(C2H2)

Propane
(C3H8)

5
10
50
5.7
11.5
50
7.1
11.5
50
9.1
11.7
50
11.2
11.9
50
25.6
15
50.1
50.3
25.8
50.3
75.3
37.8
50.6
100.1
49.9
50.9
125.6
62.4
51.6

5
10
50
9.8
11.7
50
17.5
12.9
50
25.6
15
50
33.8
18.1
50.1
83.7
41.5
50.7
167.6
82.7
52.8
251
124
56.1
334.5
165.3
60.5
418
206.6
65.6

5
10
50
8.1
11.6
50
13.8
12.2
50
19.9
13.4
50
27.8
15.1
50
64.1
32.0
50.4
128.3
63.4
51.7
192.1
94.9
53.7
265
126.4
56.4
320.3
158.3
59.7

5
10
50
10.4
11.8
50
19
13.2
50
27.9
15.7
50
36.9
19.4
50.1
91.6
45.3
50.8
182.9
90.2
53.3
274.4
135
57.2
365.6
180.2
62.2
457.1
225.4
68.1

100

The simulation results indicate a significant temporal broadening of ultrashort
pulses at high gas pressures--even for a 0.15-m path. From the values obtained it is
obvious that the dispersion due to the gas component of an experimental setup is highly
influential for short pulses at pressures typically used for combustion studies and must
be taken into account--even at normal pressure conditions for distances of 0.5 m or
longer. While the data in Table 2 may discourage one from using shorter laser pulses
because of their greater propensity for dispersion, this can also be viewed as an
advantage in the case of nonlinear spectroscopic applications, as discussed below.
6.4 Dispersion and Raman Scattering efficiency
When considering optical spectroscopy or imaging of high-pressure systems, the
volume from which the optical signal emerges determines the spatial resolution of the
measurement. Typically, three-dimensional sectioning capability in CARS diagnostics at
range (i.e., with weakly focused beams) is achieved by crossing of two or more laser
beams at a point of interest. Unfortunately, turbulence in the reacting-flow environment
renders this cross-beam geometry very problematic. Single-beam spectroscopic
89,120

imaging methods that have been developed recently

are much more immune to

the inhomogeneity of the medium; however, another sectioning mechanism must be
used to resolve the structure along the beam path. We have found that by implementing
adaptive pulse compression to pre-chirp the laser pulses, the pulse can be adjusted to
become TL at a specific location and, in turn, can be used to achieve spatial resolution

101

along the weakly focused laser beam. Thus, the laser beam can be scanned to obtain
an in-plane image, and the input pulse chirp can be tuned to adjust the depth.
This effect is examined in Fig. 6.8 for carbon dioxide at 2.24 mol·L

-1

(corresponds to 40 bar at room temperature) by simulating the excitation efficiency of
-1

the Raman-active vibrational mode at 1285 cm . It is assumed that the pulse energy is
sufficiently small that transition saturation effects can be neglected. Pulse durations
greater than 20 fs are not considered since they lack the spectral bandwidth to excite
impulsively the 1285 cm

-1

Raman mode. The input pulse energy is scaled to provide the

same excitation efficiency at the zero Raman shift.

Figure 6.8 Simulated Raman scattering efficiency at 1285 cm
-1

-1

as a function of

propagation distance CO2 with a density of 2.24 mol·L .The inset figure is a schematic
example of how this improved spatial resolution can be used to select a region of
interest to acquire data in a combustion process.

102

From the figure one can observe both the large increase in signal and the highly
improved spatial resolution that results from the use of shorter pulses. The Raman
excitation efficiency is directly related to the signal intensity in single-beam CARS
measurements that employ a short pulse to provide the pump and stokes components
and a long pulse as a probe. This illustrates the advantage of using very short pulses to
perform single-beam CARS measurements. For a 5-fs pulse, one would obtain the full
range of Raman shifts, along with a spatial resolution of ~2.5 mm along the z axis. The
in-plane resolution is determined by the beam focusing and scanning parameters.
6.5 Conclusions
The increasing use of ultrafast laser systems and the greater availability of sub30-fs laser sources have prompted the evaluation of pulse dispersion and its effects on
nonlinear optical spectroscopy. An ultrabroadband laser source was used in this study
to measure the spectral dispersion of a number of gases that are of importance to the
combustion community. MIIPS was shown to be a straightforward approach for both
accurately measuring the dispersion and introducing a pre-chirping phase mask that is
capable of recovering TL pulses. It is suggested that dispersion, especially when using
ultrabroadband laser sources, can provide a high level of axial resolution for singlebeam spectroscopic methods. Such axial resolution is advantageous for obtaining
three-dimensional images of flames.

103

Chapter 7
Conclusions
This dissertation has discussed several applications of various pulse shaping
methods for single-beam CARS spectroscopy. Phase shaping allows for selective
excitation of any Raman active mode of a molecule. Several different methods, binary
phase shaping, double chirped pulses, and sinusoidal phase modulation were all used
to perform selective excitation. The application of this type of pulse shaping was
highlighted as a contrast mechanism that allow for the visualization of a CO2 jet in
ambient air.
A less elaborate pulse shaping method was also used to collect the full CARS
spectrum that results from the impulsive excitation from the broadband femtosecond
pulse. This full spectrum acquisition was used for the measurement of various gas
phase conditions in preliminary work examining the use of single-beam CARS as a
method for combustion diagnostics. In addition to these experiments, another set of
experiments was conducted that examined the use of the single-beam CARS method
for standoff detection. These experiments were conducted at 12m distance and
demonstrated the ability to identify solid, liquid, and gas samples as well examine binary
mixtures of molecular isomers.
These initial measurements have served to establish single-beam CARS as a
viable method for many applications ranging from imaging to remote detection.
Currently, efforts are being continued in to our lab in both fields using the advances and
methodologies discussed in this dissertation.
104

Future work in the field of combustion diagnostics will involve the use of singlebeam CARS to provide the measurement of the temperature of gas phase molecules in
combustion environments along with species information. An ultimate application in this
field would be for the use of selective phase shaping to image the combustion
environment providing real time information for the monitoring of that particular species
as the combustion evolves. This information would provide critical insight to the
chemistry and physics of the combustion process on a time scale fast enough to
measure transients in the combustion process.
Our lab has also continued to push forward the use of single-beam CARS as a
method of standoff detection. Current measurements have been made with a limit of
2

detection below 2.5 µg/cm , and double chirped pulse have been used to perform
selective excitation imaging of thin DNT and PMMA films deposited on to gold
substrates at distances great than one meter. As efforts continue to push forward, the
distances over which measurements are made should increase and actual field
measurements of trace detection of hazardous compounds should become feasible.

105

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