SHINING LIGHT ON THE EXCITED STATE DYNAMICS OF MEROCYANINE-540: AN APPLICATIONS OF PUMP-PROBE TWO-DIMENSIONAL SPECTROSCOPY

By

JORGE ISRAEL MEDINA

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2017

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© 2017 Jorge Israel Medina

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To my parents, whose personal sacrifices and support allowed me to grow into the person I am—the days you went hungry so I could eat, worked late to provide

opportunities for me, and nurtured me after you got back from work despite being exhausted were not in vain.

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ACKNOWLEDGMENTS

I thank my advisor Professor Valeria D. Kleiman for having the patience to mold

me into a scientist. She taught me the difference between being an expert at an

experimental method (skilled technician) and a scientist. My committee also helped by

burning me down so I could rise stronger from the ashes with their help (though that

was tough on me).

I also wish to acknowledge my family, who were there for me the whole way

cheering me on and supporting me when things got hard and I wanted to quit. My

brothers especially motivated me to not quit, because I didn’t want to disappoint them–

being the middle child is hard.

There are many people who made this possible: educators who believed in me

and pressured me to apply myself; administrators who refused to suspend or expulse

me from school despite my many actions that warranted such responses, because they

saw the potential I had if I only took education seriously; mentors who guided me to

paths that are hidden to those without a guide; and friends and partners who helped me

grow as a person.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 7

LIST OF FIGURES .......................................................................................................... 8

LIST OF ABBREVIATIONS ........................................................................................... 13

ABSTRACT ................................................................................................................... 14

CHAPTER

1 INTRODUCTION .................................................................................................... 15

Background ............................................................................................................. 18

What is Coherence? ......................................................................................... 18 Phase ......................................................................................................... 20 Ultrafast optical pulses ............................................................................... 21

Coherent Mixing On A Detector ........................................................................ 25 Photoisomerization ........................................................................................... 27

Triplets and electro-vibrational coupling ..................................................... 28 Ultrafast photoisomer formation ................................................................. 31

Ultrafast Optical Pulses .................................................................................... 32

Pulse characterization ................................................................................ 32

Controlling ultrafast pulses ......................................................................... 37

2 TWO-DIMENSIONAL SPECTROSCOPY ............................................................... 40

History of Two-Dimensional Spectroscopy ............................................................. 40

Diagrammatic Perturbation Theory ......................................................................... 41 Pump-Probe Geometry Two-Dimensional Spectroscopy ........................................ 47 Experimental Introduction ....................................................................................... 52

Two Pump Pulses ............................................................................................ 54 Noncollinear optical parametric amplifier ................................................... 54 Pulse shaping ............................................................................................ 58

One Probe Pulse .............................................................................................. 60

Broadband Detector ......................................................................................... 61 Making Raw Data Meaningful ................................................................................. 62

Optical 2D-S Pump-Probe Spectroscopy is a Differential Spectroscopy .......... 63

A Slice of Pump-Probe 2D-S Data Corresponds to a TA experiment ............... 64

3 IMPLEMENTATION AND TROUBLESHOOTING .................................................. 73

NOPA Generation ................................................................................................... 74

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Pulse Shaping ......................................................................................................... 78 Tilted 4-f Compressor ....................................................................................... 78

Phase and Amplitude Control Using SLM-640 ................................................. 88 Pump pulse compression ........................................................................... 89 Double pulses ............................................................................................ 97

Broadband Seed/Probe Pulse ................................................................................ 99 Pump-Probe Overlap ............................................................................................ 101

Sample Holder ...................................................................................................... 101 Measuring Signal .................................................................................................. 102

Instrument Control .......................................................................................... 103 Data Collection ............................................................................................... 103 Improving Signal-to-Noise .............................................................................. 105

Data Processing and Management ....................................................................... 108

Expectation Versus Reality ................................................................................... 109

4 MEROCYANINE-540 ............................................................................................ 111

Overlapping Signals .............................................................................................. 112

Method .................................................................................................................. 113 Results .................................................................................................................. 116

Steady-State ................................................................................................... 116

Long Lived Isomer .......................................................................................... 119 Two-Dimensional Spectroscopy ..................................................................... 122

Early time 2D-S ........................................................................................ 124 Later time 2D-S ........................................................................................ 125

Transient Absorption ...................................................................................... 128

SVD / MCR-ALS ...................................................................................... 129

Time evolution .......................................................................................... 133 Discussion ............................................................................................................ 135

Ultrafast Formation of Cis-isomer Spectral Signature .................................... 136

Triplet State .................................................................................................... 138

5 CONCLUSION ...................................................................................................... 140

Merocyanine-540 Excited State Kinetics ............................................................... 142

Zwitterion Evidence?............................................................................................. 146

APPENDIX: CONSTRAINING SVD ........................................................................ 148

LIST OF REFERENCES ............................................................................................. 153

BIOGRAPHICAL SKETCH .......................................................................................... 157

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LIST OF TABLES

Table page 2-1 List of optics used in the NOPA. ......................................................................... 71

4-1 Lifetimes and amplitude percentages of SVD/MCR-ALS components of MC540. ............................................................................................................. 135

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LIST OF FIGURES

Figure 1-1 Merocyanine-540 chemical structure .................................................................. 15

1-2 Selective staining of leukemia cells by MC540 results in emission in the dark field, with no emission from healthy cells ............................................................ 17

1-3 Cosine oscillation over time that restarts after an interruption ............................ 19

1-4 Cosine oscillation over time with points at different phase. ................................ 21

1-5 Damped (decaying) cosine oscillation with a phase of 𝜋/2. ............................... 21

1-6 Phase dependence on wave mixing and illustration of phase of a pulse ............ 22

1-7 Carbon bond isomerization represented by both a simple free rotor potential and a more complicated model for a restricted rotor. ......................................... 29

1-8 Isomerization of stilbene induced by photo absorption with corresponding fluorescence quantum yield. ............................................................................... 29

1-9 Spin-Orbital mixing leading to forbidden intersystem crossing. .......................... 30

1-10 Franck-Condon overlap between two vibrational wave functions, can couple electronic states as IC, or optical transitions ...................................................... 30

1-11 Wave-packet dynamics involved in ultrafast formation of retinal rhodopsin isomerization involving a conical intersection ..................................................... 31

1-12 Frequency-Resolved Optical Gating (FROG) diagram ....................................... 33

1-13 Linear chirp of frequency components result in a pulse that appears to sweep frequencies ......................................................................................................... 34

1-14 Optical path length difference for two wavelengths in a dispersive medium ....... 36

1-15 Chromatic dispersion of two wavelengths because of travel in a dispersive medium ............................................................................................................... 36

1-16 Co-propagation of two different wavelengths inside a medium can be achieved by adding an external angle to the propagation of the beams. ............ 36

1-17 Simplified illustration of coherent mixing for OPG and OPA ............................... 38

2-1 Time assignment of the 4-wave interaction given as a difference in time between pulses. .................................................................................................. 43

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2-2 Single ket side electric field interaction represented by DPT .............................. 43

2-3 Interactions with two electric fields represented by DPT. ................................... 44

2-4 Three-wave interaction represented by DPT. ..................................................... 44

2-5 Three-wave interaction with third order response represented by DPT. ............. 45

2-6 Four non-degenerate four-wave mixing paths for a two-level system represented by DPT. .......................................................................................... 45

2-7 A ket side response is the complex conjugates of the bra side response ........... 46

2-8 Illustration of four-wave mixing in the pump-probe geometry and the corresponding third order response signal directions ......................................... 48

2-9 Three level system with two consecutive bra interactions in the same direction represented by DPT. ............................................................................ 48

2-10 Four-wave mixing with the first two fields not having the same magnitude ........ 49

2-11 Example of four-wave mixing where the system changes states between two field interactions depicted by DPT. ..................................................................... 51

2-12 Simplified diagram of a pump-probe geometry experimental setup. ................... 52

2-13 Depiction of angles involved in NOPA phase matching ...................................... 55

2-14 NOPA spectrum dependence as a function of phase matching angle in BBO ... 55

2-15 Comparison of NOPA spectrum generated with anamorphic focusing and spherical focusing ............................................................................................... 57

2-16 Optimized spectrum of the NOPA with an output energy of 2.0 𝜇J/pulse. .......... 58

2-17 Illustration of how individually controlling SLM pixels for a pulse in the Fourier plane can alter the phase and amplitude ............................................................ 59

2-18 Tilted folded 4-f compressor diagram. ................................................................ 60

2-19 Typical white light spectrum generated in sapphire with different fluence .......... 61

2-20 Simplified caricature of 2D-S data to explain on-diagonal and off-diagonal signals. ............................................................................................................... 63

2-21 Raw 2D-S data for DASPI scanning 𝜏 at constant 𝑇 = 30 𝑓𝑠 .............................. 65

2-22 Raw 2D-S data for DASPI scanning 𝑇 and constant 𝜏 ........................................ 66

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2-23 Processed 2D-S data for DASPI at two different 𝑇 values shown in Δ𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 ................................................................................................... 67

2-24 Processed 2D-S data for DASPI at two different 𝑇 values shown in

Δ𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛. ...................................................................................................... 67

2-25 Published TA DASPI data .................................................................................. 68

2-26 A slice of pump-probe 2D-S data for a given excitation wavelength correspond to an equivalent TA experiment at the same excitation wavelength ......................................................................................................... 70

2-27 NOPA schematic ................................................................................................ 72

3-1 Simplified diagram of a pump-probe geometry experimental setup. ................... 73

3-2 Some typical NOPA spectrum achievable day-to-day with energies between 1.5 to 1.8 𝜇J/pulse. ............................................................................................. 74

3-3 Spatial chirp from anamorphic focusing NOPA generation is the result of a large sweep of phase matching angles inside the crystal ................................... 76

3-4 Spatial chirp of NOPA beam measured by imaging first order diffraction on a CCD .................................................................................................................... 77

3-5 Simplified illustration of pulse shaping ................................................................ 78

3-6 Tilted folded 4-f compressor design .................................................................... 79

3-7 Spatial aberrations introduced by the SLM-640 when a cylindrical mirror is used .................................................................................................................... 82

3-8 Spectral bandwidth of the pump pulse allowed through the SLM-640 array, with the 4-f compressor design used .................................................................. 82

3-9 Phase matching bandwidth for SFG between NOPA beam and 800 nm beam at various phase matching angles for 100 𝜇𝑚 thick BBO ................................... 84

3-10 X-FROG traces of the NOPA pulse + 800 nm generated piecewise at different BBO angles .......................................................................................... 86

3-11 Simple illustration to explain how we know the SLM-640 adds positive dispersion from an X-FROG Trace. .................................................................... 87

3-12 Simple illustration of why temporal chirp in a white light probe leads to blue TA signals arriving before red signals in time. .................................................... 87

3-13 Crosscorrelation of Pump pulse + 800 nm pulse before and after a compression mask obtained with a GA using SFG in BBO is applied ................ 90

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3-14 Phase matching acceptance bandwidth of KDP compared with BBO at a single crystal phase matching angle ................................................................... 91

3-15 X-FROG and cross correlation of pump + 800 nm pulse before and after compression mask obtained with a GA using SFG in KDP is applied ................ 93

3-16 Mixing compression mask can allow for pulse with better temporal profile than that achievable directly ............................................................................... 95

3-17 X-FROG and crosscorrelation of pump pulse + 800 nm pulse before and after compression mask obtained with a GA using two-photon absorption is applied ................................................................................................................ 96

3-18 Interferogram generated by generating pulse pairs with the SLM-640 to generate a convolution spectrum ........................................................................ 97

3-19 Difference in intensity of a pulse pair measured by X-FROG because of SLM array leakage ...................................................................................................... 99

3-20 Typical white light spectrum generated in sapphire with different pump fluence ................................................................................................................ 99

3-21 Effects of truncating data and Hamming windows on the resulting FFT ........... 104

3-22 Effect of collecting unneeded data past the signal decay on the FFT signal-to-noise ............................................................................................................. 105

3-23 Phase cycling data ........................................................................................... 106

4-1 Chemical structure of Merocyanine-540 in trans-isomer configuration ............. 111

4-2 Spectral signature of long lived transients ........................................................ 113

4-3 Steady state spectra collected for MC540 in methanol ..................................... 117

4-4 Excitation Spectrum of MC540 in methanol ...................................................... 118

4-5 Dilution study of MC540 absorption prepared in atmospherically wet methanol ........................................................................................................... 119

4-6 Transient signal detected before time-zero when the sample is not refreshed between pump pulses ....................................................................................... 120

4-7 Transient signal observed before “time-zero” when adequately refreshing sample between consecutive excitation pulses ................................................ 121

4-8 Solvent flow difference between home build flow cell and commercial flow cell used ........................................................................................................... 122

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4-9 2D-S signal for MC540 at 𝑇 = 0.3 ps ................................................................ 124

4-10 Snap shots of the time evolution of the 2D-S signal of MC540 in methanol at early times ........................................................................................................ 126

4-11 2D-S data for later times of MC540 in methanol ............................................... 127

4-12 TA data collected for MC540 in methanol with excitation at 480 nm ................ 128

4-13 Singular Value Decomposition values of TA data for MC540 in methanol excited at 555 nm ............................................................................................. 129

4-14 Spectral components and spectra from MCR-ALS for TA data collected at three different excitation wavelengths .............................................................. 131

4-15 Residuals from TA data excited at 555 nm fit using the SVD/MCR-ASL results ............................................................................................................... 132

4-16 Composition of spectral signitures of SVD/MCR-ASL components .................. 134

4-17 Normalized cis-isomer component amplitude kinetics ...................................... 138

5-1 Transient data for a model merocyanine which shows spectral signatures like those observed for merocyanine-540 ............................................................... 143

5-2 VB structure used to assign transition from work by Haas on the MCM system .............................................................................................................. 144

5-3 Reproduction of plots shown in Figure 4-15. .................................................... 145

A-1 Example of a decaying exponential signal with noise ....................................... 151

A-2 Two unconstrained fits of MC540 TA data that fit the data well, but have no physical meaning .............................................................................................. 152

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LIST OF ABBREVIATIONS

BBO 𝛽-Barium Borate

BOA Born-Oppenheimer approximation

CCD Charged Coupled Device

DPT Diagrammatic Perturbation Theory

FWHM Full-Width and Half-Max

FROG Frequency Resolved Optical Gating

GA Genetic Algorithm

KDP Potassium Dihydrogen Phosphate

MCR-ALS Multivariate Curve Resolution Alternating Least Square

MC540 Merocyanine-540

NOPA Noncolinear Optical Parametric Amplifier

SFG Sum-Frequency Generation

SHG Second Harmonic Generation

SLM Spatial Light Modulator

SVD Single Value Decomposition

TA Transient Absorption

2D-S Two-Dimensional Spectroscopy

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Abstract of Dissertation Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

SHINING LIGHT ON THE EXCITED STATE DYNAMICS OF MEROCYANINE-540: AN

APPLICATIONS OF PUMP-PROBE TWO-DIMENSIONAL SPECTROSCOPY

By

Jorge Israel Medina

May 2017

Chair: Valeria D. Kleiman Major: Chemistry

The anionic molecular dye Merocyanine-540 is soluble in a variety of solvents;

has an environment dependent fluorescent yield making it a good molecular probe; and

forms an isomer and triplet upon visible light absorption. MC540 has been extensively

studied because it selectively binds to leukemia cells, killing the cells after irradiation

with visible light. Though many of its properties are well known, the excited state

dynamics that lead to isomerization and triplet formation are still not well understood

and there are conflicting conclusions in the literature. We present 2D-visible

spectroscopy as a new tool to resolve the dependence of the excited state dynamics on

excitation wavelength. Combined with Transient Absorption to help understand the

kinetics of selected excitation wavelengths.

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CHAPTER 1 INTRODUCTION

“Character is as important in science as it is in any other field” David Hahn

Figure 1-1. Merocyanine-540 chemical structure. When in solution the 𝑁𝑎+dissociates leaving the molecule with both polar and non-polar character.

Merocyanine-540 (MC540), shown in Figure 1-1, is a molecular dye which has

perplexed scientist since discovering the dye selectively binds to leukemia cells in the

late 1970’s.1 Figure 1-2 shows that MC540 bound to leukemia cells is emissive in the

dark field, while healthy cells are dark. Soon after discovering selective binding to

leukemic cells, it was discovered that cells stained with MC540 and irradiated with

visible light would die; though leukemia cells die at orders of magnitude higher (~0.01%

survival) compared to healthy cells (>80% survival).2 This discovery led to a boom of

basic science research to try to understand the excited state dynamics of MC540 to be

able to understand the mechanism of the highly selective cytotoxicity. It was established

that MC540 forms a triplet state, and an unstable isomer after absorbing visible light.3

Plenty of debate in the literature exists to the mechanism involved in killing leukemia

cells, some arguing that the triplet formation kills leukemia through formation of singlet

oxygen, and others claiming it’s the isomerization process which kills leukemia by

disturbing the cell membrane. But no experiment proves conclusively which process

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kills leukemia, because it is hard to generate the triplet and isomer independently with

the irradiation sources used for in-vitro experiments.

In 1986, work by Clakson et al. conclusively showed that MC540 is not a viable

treatment method for leukemia—MC540 does significant harm to healthy cells.4 The

percent recovery (compares the growth of a cell line exposed to drug, and one not

exposed to drug) of healthy cells exposed to MC540 is ~20% recovery at a dose which

would kill leukemia cells with more selectivity than healthy cells. For comparison, a high

dose of a chemotherapy drug used to treat leukemia, vincristine, has ~80% recovery for

healthy cells and ~25% recovery for leukemic cells.5 MC540 does more harm to healthy

cells than a high dose of chemotherapy does to cancer cells—interest in MC540 on the

medical application side quickly diminished after discovering MC540 would not cure

leukemia. However, MC540 remained an interesting system for basic science, a

predictive model for the excited state dynamics of MC540 remains elusive despite

intense study on the molecule. Each time a new experimental method is applied to

MC540 something new is discovered that violates the previously held predictive model,

meaning our models are wrong—a model that can’t predict experimental results is

wrong.

Complicating things further than the complexity of the molecules excited state

dynamics is the loss of primary referencing. Many things about MC540 are assumed in

the literature because they are referenced so frequently making it difficult to distinguish

between what is known (direct experimental evidence), what is suspected (calculations

and model systems), and what is speculative.

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Figure 1-2. Selective staining of leukemia cells by MC540 results in emission in the dark field, with no emission from healthy cells. A) Leukemic mouse cells seen by microscopy and in the dark-field, B) healthy human cells in the top panel, showing no emission and leukemic cells in the bottom panel showing emission. Part A, reprinted from, Cell, Vol. 13, J. Valinsky, T. Easton, E. Reich, Merocyanine 540 as

a Fluorescent Probe of Membranes: Selective Staining of Leukemic and Immature Hemopoietin Cells, 487-499, Copyright (1978), with permission from Elsevier. Part B, reprinted from Cancer Research, Copyright (1986), Vol. 46, 4892-4895, J. Atzpodien, S. Gulati, B. Clarkson, Comparison of the Cytotoxic Effects of Merocyanine-540 on Leukemic Cells and Normal Human Marrow, with permission from AACR.

Dark-Field Microscopy (emission)

Microscopy (absorption)

Mouse Cells (leukemic)

Human Cells (healthy)

Human Cells (leukemic)

A

B

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MC540 remains untested to the relativly new technique of two-dimensional

optical spectroscopy, until now. We shed light on the excited state dynamics of MC540

using a newly built instrument able to apply the new experimental technique in a difficult

to access region of the visible spectrum. As history of MC540 predicted, the new

findings cannot be explained by the current models for the excited state dynamics of

MC540, meaning we need a new predictive model. More work besides my own will be

needed to understand the excited state dynamics of MC540, but this work expands our

understanding of a complex system.

Background

Some terminology and concepts are needed for the reader to be able to follow

the experimental methods used to study MC540 and the results. Transient absorption

(TA) is a basic experimental method now in the mainstream, so it will not be introduced

in detail, however, an excellent review article6 is available if more than a refresher is

needed. An understanding of quantum mechanics and its use with first-order light-

matter interaction perturbation theory is also assumed—when a certain result is needed,

it will be reviewed, but not derived.

What is Coherence?

When I introduce my work, “what is coherence?” is often the first question asked.

Coherence is a ‘catch-all’ term in science, so it is difficult to pin down and explain,

because it represents many concepts. Coherence is maintaining the ability to predict the

state of an oscillating system at some future time. For example, Figure 1-3 shows the

oscillation of simple cosine wave that gets interrupted and restarts after an interruption.

All waves are coherent but the state of the oscillation as shown only has coherence

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between interruptions, because if the interruptions are random there is no way to predict

the future state of the oscillation once it has been interrupted. If the interruptions follow

some statistical distribution, such as Poisson distribution for collisions, then the mean

time between collisions is the “coherence time” of the system. There are many others

forms of coherence and all are called some form of “coherence”. Coherence can be lost

by interruptions(collisions), damping (decay), destructive interference (mixing many

waves such that it becomes impossible to predict the future evolution) and any other

process that prevents future prediction of the system.

Figure 1-3. Cosine oscillation over time that restarts after an interruption (dashed line).

An example of incoherent and coherent fields in spectroscopy is emission of

photons from an excited state. In spontaneous emission, a single emitted photon is

coherent but photons are emitted at random times and with random phase (phase

explained next section), making it impossible to predict the state of oscillation of each

photon. When a spontaneous emission signal is measured the mixture of the many

emitted photons with random time evolution destructively interfere and the signal has no

clear “wave-nature”. Stimulated emission on the other hand is coherent because the

emission is not spontaneous (random), and follows a clear dependence on the phase of

the perturbing field, the emitted photons will follow the time dependence of the field

stimulating the emission. Lasers are based on stimulated emission and are therefore

coherent. Lamps (fluorescent bulbs and incandescent bulbs) work on spontaneous

emission and are not coherent.

… …

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The working definition used in optical spectroscopy to determine whether a signal

from a system is coherent or incoherent is phase dependence of the signal on the

perturbing field (laser). Phase is explained next.

Phase

The phase of a wave is the instantaneous position of a point (specified time) in

the time evolution of a wave. Figure 1-4 shows a cosine evolving in time, the blue point

is at phase zero, the red point is at phase 3𝜋

2, the green point is at phase 2𝜋, and the

purple point is at phase 6𝜋; each defined by what the value of cosine would yield the

current position of the wave. From Fourier theory, a cosine oscillation has no phase

(imaginary) component, while a sine, which is just a cosine with phase 𝜋/2, has no real

component, and entirely in the phase (imaginary) component. The “time-zero” of a wave

is arbitrary in experiments thus the “phase” of the wave is assigned as the deviation

from a simple cosine oscillation that starts at zero. Figure 1-5 shows a damped

(decaying) cosine oscillation. The phase of the decaying cosine signal is 𝜋/2, because

at “time-zero” the oscillation is a cosine with phase 𝜋/2. In NMR, the start of the

measurement and the start of the signal which is being measured often don’t coincide,

so the phase of signal is an “error” because the start time of the signal is unknown. In

two-dimensional optical spectroscopy (introduced in Chapter 2), the start time of the

measurement is well-defined, and starts at the same time as the signal which is

measured, so when the phase of the signal is not zero it is not a phase error, but the

actual phase of the signal being measured. It will be shown in Chapter 3, that the phase

of the signal can be controlled with the phase of the laser pulse generating the signal,

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thus two-dimensional optical spectroscopy is a coherent spectroscopy because the

signal is phase dependent.

Figure 1-4. Cosine oscillation over time with points at different phase.

Figure 1-5. Damped (decaying) cosine oscillation with a phase of 𝜋/2.

Ultrafast optical pulses

The Fourier transform of a Gaussian is a Gaussian, so a Gaussian pulse in the

time domain requires a Gaussian distribution of frequencies. Light waves are composed

of photons and photons only have a single frequency, so a pulse in the time-domain

cannot be composed of a single frequency photon. A pulse of coherent light (laser

pulse) is achieved by the constructive interference between many different “colors”

(frequencies in the optical range of the electromagnetic spectrum are visible to human

eyes and seen as distinct colors). To ensure constructive interference the phase of

individual frequency components must be fixed (phase-locked), because random phase

or phase drift result in destructive interference. Figure 1-6 shows the result of

superposition of many different frequencies (top panels) resulting in a pulse of light

…

…

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(bottom panel), represented by the electric field E(t). Superposition of waves with phase

zero generate a phase zero pulse (red colors), and 𝜋/2 phase waves superimpose for a

pulse with phase 𝜋/2 (blue colors).

Figure 1-6. Phase dependence on wave mixing and illustration of phase of a pulse. The red pulse has the mixing waves locked at zero phase, and the blue wave has the mixing waves locked at 𝜋/2 phase. This is only a caricature because many more frequencies than the ones shown would need to mix to make the pulse displayed.

The duration, Δ𝑡 (full width at half maximum), of a Gaussian laser pulse is limited

by the equation 1-1,

Δ𝑡 ⋅ Δ𝜈 ≥ 0.441 (1-1)

where Δ𝜈 is the bandwidth of frequencies (full width at half maximum), and the constant

0.441 is the result for Gaussian pulses when the Δ represents full width at half

maximum and accounting for the Heisenberg uncertainty principle,

Δ𝑡 ⋅ Δ𝐸 ≥ ℏ (1-2)

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where Δ𝐸 is the uncertainty in energy (not the electric field). A transform-limited

Gaussian pulse is defined as a pulse which satisfies Δ𝑡 ⋅ Δ𝜈 = 0.441, implying that it is

not possible to make the pulse shorter in time without more spectral bandwidth.

When dealing with laser pulses, it is inconvenient to keep track of all the

individual frequencies which compose the pulses electric field, instead an effective

representation is made, given by equations 1-3,

�� (𝑡) = 𝐴 (𝑡) ⋅ cos(𝜔𝑡 + 𝜙(𝑡)) (1-3)

where the electric field, �� (𝑡), of an electromagnetic wave is represented with a carrier

frequency oscillation, 𝜔, inside a pulse envelope, 𝐴 (𝑡), and phase of 𝜙(𝑡) which can

have time dependence. An approximation can simplify the math whenever an electric

field or its response will be measured. A cosine can be rewritten in the form given by

equation 1-4,

cos(𝜔𝑡 + 𝜙) = ℜ[𝑒𝑖(𝜔𝑡+𝜙)] (1-4)

by instead representing the field oscillations without the requirement of only considering

the “real” component, given by equation 1-5,

cos(𝜔𝑡 + 𝜙) ≅ 𝑒𝑖(𝜔𝑡+𝜙) (1-5)

The approximation given by equation 1-5 greatly simplifies math involving an

electric field treated semi-classically as a transverse wave. The field can thus be written

as equation 1-6,

�� (𝑡) = 𝐴 ′(𝑡)𝑒𝑖(𝜔𝑡+𝜙) (1-6)

where 𝐴 ′ is a constant multiple of 𝐴 in equation 1-3 that accounts for the difference in an

amplitude measured by a detector, when ignoring detector response (discussed later).

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This approximation is valid in most circumstances involving optical frequency

pulses because the wavelength of an optical pulse is much longer than a typical

absorbing molecule, ~100’s of nm compared to 0.1-1 nm (meaning the field amplitude

can be treated as constant at any single time of the interaction ignoring the oscillations

of the field), and detectors have a response time much longer than the period of optical

pulses, and can thus not resolve the oscillations of the field. By representing the

oscillations of a field as equation 1-6, the field no longer oscillates in intensity but moves

in and out of the real plane and the phase plane (implying intensity does not oscillate),

given by the equation 1-7 and equation 1-8,

ei(ωt+ϕ) = cos(𝜔𝑡 + 𝜙) + 𝑖 ⋅ sin(𝜔𝑡 + 𝜙) (1-7)

|ei(ωt+ϕ)| = 1 (1-8)

Intensity is given by the magnitude of the field convoluted with the response of the

detector squared, given in equation 1-9,

𝐼(𝑡) = |�� (𝑡) ∗ 𝑅(𝑡)|2 (1-9)

where 𝐼(𝑡) is the measured intensity of the field and 𝑅 is the response of the detector.

Thus, the intensity will not oscillate and have no phase dependence if the field is

represented using the approximation giving in equation 1-6 and the detector response is

ignored; or if the response time of the detector is too slow to resolve the real form of the

electric field giving by equation 1-3 (fast optical detectors have ~1 nanoseconds

response time and optical frequencies have a period of ~2 femtoseconds meaning an

optical detector cannot detect the oscillations of the field).

25

Coherent Mixing On A Detector

The intensity of two pulses, �� 1 and �� 2, mixing on an intensity detector is phase

dependent even if the detector cannot resolve the phase or oscillations of each field

independently. Ignoring the response time of the detector by using the assumption in

equation 1-6, the phase dependence of mixing fields on a detector is derived in

equations 1-10 through 1-16:

𝐼(𝑡) = |�� 1(𝑡) + �� 2(𝑡)|2 (1-10)

𝐼 = (�� 1 + �� 2) ⋅ (�� 1 + �� 2)∗ (1-11)

𝐼 = �� 1 ⋅ �� 1∗ + �� 1 ⋅ �� 2

∗ + �� 2 ⋅ �� 1∗ + �� 2�� 2

∗ (1-12)

𝐼 = 𝐴 12 + �� 1 ⋅ �� 2

∗ + �� 1∗ ⋅ �� 2 + 𝐴 2

2 (1-13)

To clean things up and end at an important result, the two fields will be assumed

to be in the same direction, losing the need for vector notation.

𝐼(𝑡) = 𝐴12 + 𝐴1𝑒

𝑖(𝜔1𝑡+𝜙1) ⋅ 𝐴2𝑒−𝑖(𝜔2𝑡+𝜙2) + 𝐴1𝑒

−𝑖(𝜔1𝑡+𝜙1) ⋅ 𝐴2𝑒𝑖(𝜔2𝑡+𝜙2) + 𝐴2

2 (1-14)

𝐼(𝑡) = 𝐴12 + 𝐴2

2 + 2 𝐴1 𝐴2 cos((𝜔1 − 𝜔2)𝑡 + 𝜙1 − 𝜙2) (1-15)

𝐼(𝑡) = 𝐴1(𝑡)2 + 𝐴2(𝑡)

2 + 2 𝐴1(𝑡) 𝐴2(𝑡) cos(𝛥𝜔12𝑡 + 𝛥𝜙12) (1-16)

Equation 1-16 explains how two pulses can interfere on a detector depending on their

phase and frequency difference. The interference term is important because it allows a

field with an 𝐴2 too small to be measured directly, to be measured indirectly by mixing

with a field that can be measured and looking at the cross term. When the two pulses

are the same, the cross term is called a homodyne. When the two pulses are different,

the cross term is called a heterodyne. A Michelson interferometer is an example of

using the homodyne to measure an ultrafast pulse; an optical detector is too slow to

resolve each pulses time profile, but by scanning one pulse in time over the other, the

cross term shows a time dependence proportional to the field temporal profile. Using the

26

approximation given in equation 1-6 to derive equation 1-16, the full signal measured by

a Michelson interferometer is not reproduced. The fringe oscillations in an interferogram

are a result of a cos((𝜔1 + 𝜔2)𝑡 + 𝜙1 + 𝜙2) term that is lost by assuming the field is not

oscillating, because the 𝑒−𝑖(𝜔𝑡+𝜙) term of a cosine is ignored. Working out equation 1-9

using the full form of the cosine given by the Euler formula,

cos(x) =1

2[𝑒𝑖𝑥 + 𝑒−𝑖𝑥]

(1-17)

and including the detector response will fully reproduce the signal generated by the

coherent mixing of waves on a detector, but the math gets complicated because the

convolution with the response of the detector cannot be ignored. The full form of the

cosine is rarely used when explaining theory and instead it is mentioned that there is an

extra term lost by approximation.

Heterodyne detection is important, because a 2D-S signal is the result of a third-

order weak perturbation, which is too weak to be measured directly by a detector. But

by mixing the signal with another pulse on the detector, the cross term can have enough

intensity to be measured.

In quantum mechanics, the wave function is a complex wave, that oscillates in

and out of the real and imaginary plane, the amplitude is both real and complex, but an

electric field component of an electromagnetic wave is purely real. Representation of an

electric field as a complex wave simplifies the math in light matter interactions and when

the magnitude of the wave is measured, but having a non-zero complex component

does not represents the real wave.

27

Photoisomerization

Isomerization is a large field in chemistry and biology, being an important part of

many mechanisms. We will limit our discussion to photoisomerization process, where a

molecule can be transformed to another configuration through the absorption of light.

The term ‘trans’ and ‘cis’ are often used to describe two configurations of a molecule

with isomerization along a carbon double bond. Trans corresponds to when the two

adjacent bonds are on opposite sides, and cis corresponds to when the two adjacent

bonds are on the same side. When a carbon double bond is not involved or if the

convention of adjacent bonds becomes ambiguous, the terms used to describe two

isomers are, Z and E. Given by the first letters for the German words together

(zusammen) and opposite (entgegen). Cahn–Ingold–Prelog priority rules are used to

determine which moieties have priority, if the two highest priority parts are on the same

side, the molecule is a Z-isomer.

Isomerization along a carbon double bond is very relevant in chemistry and has

been extensively studied. The text book7 explanation of photoisomerization along a

carbon double bond are shown in Figure 1-7, where a double-well exists in the ground

state (Ψ), and an excited state (Ψ∗) couples to both wells. The photoisomerization of

stilbene is shown in Figure 1-8, directly under Figure 1-7B, which shows the potential

surfaces to help explain the behavior observed in the fluorescent quantum yield. Trans-

stilbene must overcome a steric hindrance, shown as an activation energy, 𝐸𝑎 to form

the cis-isomer, resulting in a potential well that can trap some of the population and

result in emission from the excited state. The height of the barrier which needs to be

overcome determines the rates and yields of isomerization. Cis-stilbene has a torque

applied by steric interactions resulting in no potential well in initial excited state, thus no

28

emission is observed because the rate of isomerization is significantly faster than

emission.

When two electronic potential energy surfaces get close in energy such as that

shown in figure 1-7 where the ground state electronic surface reaches the excited state

electronic surface, there is a breakdown of the Born-Oppenheimer approximation.

Born-Oppenheimer approximation (BOA) allows the electronic (electron) and

vibrational (nuclei) component of a wave function to be treated independently because

nuclear motion is so slow compared to electronic motions, thus they are not coupled

significantly. However, when two different electronic wave function get close in energy,

the vibrations of one electronic surface can couple to another electronic surface

vibrations—breakdown of the Born-Oppenheimer approximation. Breakdown of the

BOA for surface crossings and conical intersections are the text book example for

intersystem crossing (ISC) to a triplet state from a singlet state, and internal conversion

(IC).

Triplets and electro-vibrational coupling

Intersystem crossing (ISC) and internal conversion (IC) are terms used when two

electronic states are coupled through vibrational modes—breakdown of the Born-

Oppenheimer approximation (BOA). When the transition is forbidden (i.e. spin-

forbidden), the coupling is termed ISC. Allowed transition are termed IC.

Singlet, doublet, triplet… states are named because of the signal generated by

NMR/EPR. A singlet electronic state, will make a single signal peak, and a doublet state

will form two signal peaks, and so on. The number of peaks is related to the spin of the

system, a system with all the spins paired will only give one transition frequency after

29

splitting from a strong magnetic field. A triplet state has two electrons with unpaired

spin, the splitting after a strong magnetic field will have 3 transition signals.

Figure 1-7. Carbon bond isomerization represented by both a simple free rotor potential and a more complicated model for a restricted rotor. A) Free rotation potential, B) restricted rotation potential showing that the initial excited state must overcome a barrier to reach the twisted geometry. Figure adapted from Turro,

N. J.; Scaiano, J. C.; Ramamurthy, V. Principles of Molecular Photochemistry: An Introduction University Science Books: California, 2008; pp 289 & 341. Reproduced with permission from University Science Books, all rights reserved.

Figure 1-8. Isomerization of stilbene induced by photo absorption with corresponding fluorescence quantum yield.

The spin of a system is a conserved quantity when the BOA holds; when it

breaks down, forbidden electronic transitions which violate conservation of spin can

occur. A vibration can couple two electronic state states, that don’t have overlap in a

stationary frame (electronic orbitals not accounting for vibrations), called spin-orbital

mixing. A simple example for spin orbital mixing from a vibration is shown in Figure 1-9.

A B

ℏ𝜔

trans cis

ℏ𝜔

30

Figure 1-9. Spin-Orbital mixing leading to forbidden intersystem crossing. Figure adapted

from Turro, N. J.; Scaiano, J. C.; Ramamurthy, V. Principles of Molecular Photochemistry: An Introduction University Science Books: California, 2008; pp 287. Reproduced with permission from University Science Books, all rights reserved.

Figure 1-10. Franck-Condon overlap between two vibrational wave functions, can couple electronic states as IC, or optical transitions. A) F-C overlap from surface crossing resulting in IC between 𝑆2 ↔ 𝑆1, B) F-C effect on Absorption spectrum. Figures adapted Turro, N. J.; Scaiano, J. C.; Ramamurthy, V. Principles of Molecular

Photochemistry: An Introduction University Science Books: California, 2008; pp 129 & 292. Reproduced with permission from University Science Books, all rights reserved.

When vibrations can couple two electronic transition in the stationary frame, IC

occurs because of wave function overlap. The overlap between two stationary

vibrational wave functions is called Franck-Condon overlap (F-C). Figure 1-10A shows

how F-C overlap can couple vibrational modes from surface crossings and effect optical

transition between two electronic surfaces. If the energy separation between two

31

surfaces is accessible through thermal perturbations, IC will occur if the F-C factor is

large enough for the transition to be allowed. At room temperature kT ~ 200 𝑐𝑚−1, is on

the same order of low energy bending and twisting modes. If the energy gap is larger

than that accessible by thermal fluctuations, a perturbing field is required to couple two

electronic surfaces, as either a resonant absorption or emission photon. The effect of F-

C on absorption spectrum is shown in Figure 1-10B.

Ultrafast photoisomer formation

Surface crossings and conical intersections can lead to ultrafast isomerization

processes, such as that observed for retinal rhodopsin.8 Using transient absorption

(TA), the ultrafast formation of retinal rhodopsin was observed to occur within 200 fs by

tracking the stimulated emission and photoinduced absorption as a function of time.

Figure 1-11 depicts how the formation of the isomer was tracked over time by TA.

Starting at the initial excited state (star 1), reaching a conical intersection (star 2) and

then changing isomer state (star 3).

Figure 1-11. Wave-packet dynamics involved in ultrafast formation of retinal rhodopsin isomerization involving a conical intersection. Reprinted by permission from Macmillan

Publishers Ltd. [Nature] Polli, D.; Altoè, P.; Weingart, O.; Spillane, K. M.; Manzoni, C.; Brida, D.; Tomasello, G.; Orlandi, G.; Kukura, P.; Mathies, R. A.; Garavelli, M.; Cerullo, G. Conical intersection dynamics of the primary photoisomerization event in vision Nature 2010, 467, 440-443, copyright (2010).

32

A short time after the work on retinal rhodopsin, theoretical predictions that the

conical intersection separation could be tuned with solvent polarity were experimentally

verified on a simple merocyanine molecule.9 Tuning a conical intersection to have a

smaller energy gap results in less thermal fluctuations needed to initiate IC or ISC,

making the transition rate higher.

Ultrafast Optical Pulses

Ultrafast optical spectroscopy relies on being able to produce ultrafast optical

pulses with the desired properties. Electronics to characterize the pulses directly don’t

exist, so other methods to indirectly characterize the pulse are used, such as coherent

wave mixing on a detector. Once a pulse is characterized, it can be controlled: changing

its time, changing its frequency, and changing its phase. Being able to control ultrafast

pulse is critical, because very few ultrafast lasers exists to preform experiments outside

a narrow range of wavelengths available by Ti:sapphire and Fiber lasers.

Pulse characterization

The standard pulse characterization method used in ultrafast optical

spectroscopy was pioneered by Trebino10, called Frequency-Resolved Optics Gating

(FROG). FROG is a spectrally-resolved autocorrelation; an autocorrelator would only

give the intensity of a pulse as a function of time, while FROG provides intensity and the

corresponding frequency. A diagram of the simplest form of FROG can be found in

Figure 1-12.

33

Figure 1-12. Frequency-Resolved Optical Gating (FROG) diagram. Figure adapted from

Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, Chapter 4, 2000, pp. 65, Rick Trebino, copyright (2000). With permission of Springer Nature.

When dealing with broadband optical pulses, it is important to know where each

frequency is in time, not just the shape of the intensity autocorrelation. The critical

importance of this will be demonstrated in Chapter 3 when dealing with a complex

optical pulse. Sometimes, it is impossible or impractical to generate a non-linear signal

for FROG using autocorrelation, so instead an unknown pulse is mixed with a known

pulse to characterize the unknown pulse in a crosscorrelation FROG (X-FROG). X-

FROG can give essential information about the chirp of a pulse, while an autocorrelation

FROG will only show that there is chirp without being able to determine the exact

direction of the chirp.

Pulse temporal chirp is coined from the sound a bird makes when it chirps, an

audio frequency sweep from high to low frequencies or low to high. Linear chirp in

optical pulses is a result of individual frequencies not travelling together with the same

phase. Pulses shown in Figure 1-6, all have the same phase for each frequency

component, as is shown with the dashed black line. A chirped pulses frequency

34

components would look like Figure 1-13A and result in a temporal pulse profile with the

lowered frequencies arriving first, as shown in Figure 1-13B.

Figure 1-13. Linear chirp of frequency components result in a pulse that appears to sweep frequencies. A) frequencies with a negative linear dependence in phase as a function of frequency. Linear chirp is linear in phase, not linear in time as shown with the dashed-red guide line. B) Resulting chirp of an ultrafast pulse with frequency components with negative chirp. This figure is only an illustration, the amount of frequencies needed to make the pulse shown in B is significantly higher than those shown in A.

Chromatic dispersion: All materials, including air, have a wavelength

dependent refractive index that changes the phase of a frequency after traveling

through the medium. An example is depicted in Figure 1-14. The index of refraction,

𝑛(𝜆), of a material is an indication of the phase velocity of light in the medium compared

with that in a vacuum, given by equation 1-18.

n(𝜆) =𝑐

𝑣𝑚(𝜆) (1-18)

The speed of light, c, is a conserved quantity, so when light travels in a medium

at a slower velocity, it travels a longer optical path length (OPL) to conserve the speed

A

B

35

of light, given by equations 1-19. OPL makes chromatic dispersion easier to

understand, as depicted in Figure 1-15 and Figure 1-16.

OPL = n(λ) ∗ 𝐿𝑚 (1-19)

𝐿𝑚 represents the distance traveled inside a dispersive medium. OPL can be

understood as the effective distance traveled, allowing time of arrival to be calculated

using the speed of light. Figure 1-14 depicts how two different wavelengths would travel

different effective paths inside a medium. Each arriving at the end at separate times, if

they started together. The blue wave traveled 50% longer time inside the medium.

Figure 1-15 depicts chromatic dispersion and how Snell’s Law works. Since different

wavelength travel at different speeds in a material, the blue wavelength spends more

effective distance in the medium, so the two colors will leave the medium spatially

separated. Transparent lenses rely on differences in OPL to focus beams of the same

color, and will not focus all colors at the same focal point, because each color

experiences a different OPL. Optical lenses have the focus given in terms of 633 nm, it

is only the focal point for 633 nm, redder wavelengths will focus farther away than 633

nm, and bluer wavelengths will focus closer than 633 nm. When the focus position of

many colors is critical, curved mirrors are required to avoid the problem of chromatic

dispersion.

Figure 1-15 shows that two different wavelengths entering a medium propagating

in the same direction will separate spatially inside of a medium. However, by tuning an

external angle between the two wavelengths as the beams enter the medium, the

beams can be made to co-propagate inside the medium, as seen in Figure 1-16. The

external angle dependence and ability for two wavelengths to co-propagate in space

36

inside a medium is important for non-collinear optical parametric generation, which will

be introduced in Chapter 2.

Figure 1-14. Optical path length difference for two wavelengths in a dispersive medium. Wavelength and OPL are color coded.

Figure 1-15. Chromatic dispersion of two wavelengths because of travel in a dispersive medium. Blue and Red waves and material match those in Figure 1-14. Black lines are all parallel and show that the direction of propagation is conserved.

Figure 1-16. Co-propagation of two different wavelengths inside a medium can be achieved by adding an external angle to the propagation of the beams.

37

Controlling ultrafast pulses

Many wave mixing methods exist to generate desired wavelengths from one

fundamental laser pulse. The most common methods are optical parametric generation

(OPG), and optical parametric amplification (OPA). The underlying theory is complex

because it relies on non-linear response of mediums, so it will not be introduced in detail

(any optical ultrafast spectroscopy book covers OPA and OPG in detail because it is the

first step a laser pulse experiences in most experiments). The basic concepts of OPG

and OPA are illustrated in Figure 1-17, as well as the naming convention for pump,

idler, signal/seed. The range of wavelengths that can be generated by wave mixing is

governed by the conservation of energy and momentum, given by equation 1-20, where

|�� | =2𝜋

𝜆. Mixing can be simplified to only show the wavelength dependence, ignoring the

direction of propagation as equation 1-21.

k pump = �� 𝑠𝑖𝑔𝑛𝑎𝑙 + �� 𝑖𝑑𝑙𝑒𝑟 (1-20)

1

λpump=

1

𝜆𝑠𝑖𝑔𝑛𝑎𝑙/𝑠𝑒𝑒𝑑+

1

𝜆𝑖𝑑𝑙𝑒𝑟

(1-21)

Equation 1-20 is manipulatable, for example, �� 𝑝𝑢𝑚𝑝 − �� 𝑠𝑖𝑔𝑛𝑎𝑙 = �� 𝑖𝑑𝑙𝑒𝑟 is called

down conversion because two pulses mix to make a lower frequency pulse. If the idler

and signal are the same, the processed is called second harmonic generation. Equation

1-20 written as �� 𝑠𝑖𝑔𝑛𝑎𝑙 + �� 𝑖𝑑𝑙𝑒𝑟 = �� 𝑝𝑢𝑚𝑝 is called up conversion because two pulses mix

to make a higher frequency pulse. Pulses generated from an OPA/OPG processes can

be used for a different OPA/OPG processes, for example an 800 nm wave can be

doubled to 400 nm, then 800 nm and the generated 400 nm can be mixed in another

38

crystal to form 266 nm. OPA/OPG is a result of non-linear response of a medium, thus

will not occur in vacuum.

Figure 1-17. Simplified illustration of coherent mixing for OPG and OPA. OPG generates new wavelengths from one. OPA is amplification of one pulse at the expense of another, resulting in a third pulse needed to conserve momentum. Pump, signal/seed, and idler are named according the wavelength of the pulses.

For OPG/OPA processes to occur, the mixing waves must overlap in space and

time to coherently mix. The chromatic dispersion of materials make overlap in space

and time quite challenging to overcome because every material has a wavelength

dependent index of refraction, which means two pulses of different wavelengths will

separate in time as they travel in a medium.

Non-linear Material

Non-linear Material

pump

signal

idler

pump

seed

idler

signal

OPG

OPA

𝜆𝑝𝑢𝑚𝑝 < 𝜆𝑠𝑖𝑔𝑛𝑎𝑙/𝑠𝑒𝑒𝑑 < 𝜆𝑖𝑑𝑙𝑒𝑟

𝜔𝑝𝑢𝑚𝑝 > 𝜔𝑠𝑖𝑔𝑛𝑎𝑙/𝑠𝑒𝑒𝑑 > 𝜔𝑖𝑑𝑙𝑒𝑟

39

Birefringent crystals have two index of refractions, an ordinary and

extraordinary, each with different values as a function of wavelength; the crystal

structure determines if a crystal will be birefringent. If a condition exists where both

wavelengths can experience the same effective index of refraction, one wavelength can

experience the ordinary index of refraction, and the other wavelength extraordinary

index of refraction, both waves can co-propagate in the material. When two

wavelengths experience the same effective speed in a material it is called the phase

matching condition. Materials which have negligible difference in index of refraction as a

function of wavelength, like air for optical pulses, are always phase matched. Indeed

OPA/OPG processes will occur in air at high enough intensities.11 OPA/OPG efficiency

is a function of the polarizability of the material, so the polarizability of a material is just

as important as the ability to phase match. Air can phase match easily, but has very low

polarizability making it a poor non-linear material. The most common nonlinear crystal

for optical pulses is 𝛽 −barium-borate (BBO) because it has a decent phase matching

range in the optical range and has a high polarizability.12

40

CHAPTER 2 TWO-DIMENSIONAL SPECTROSCOPY

"Let's change the world, one femtosecond pulse at a time." Russ Bowers

The objective of this chapter is to introduce the reader to the key concept of Two-

Dimensional Spectroscopy (2D-S); included here is an introduction of the theory, how to

perform an experiment, analyze the data, and what can be learned from pump-probe

geometry 2D-S. This chapter will not go into detail on the theory or formalism and will

instead focus on diagrammatic perturbation theory (DPT) which is simpler to

understand. From DPT, the experimental method will be introduced, followed by data to

explain how the equations from the theory relate to the signals observed. For a detailed

understanding of the underlying quantum mechanics and formalism, there is an

introductory book by Hamm and Zanni13, and a literature review by Cho14.

History of Two-Dimensional Spectroscopy

Two-Dimensional Spectroscopy (2D-S) was first introduced in pulsed NMR

experiments.15 Warren was the first to apply the concepts of 2D-S to optical pulses

using femtosecond spectroscopy16, but the method was limited because shaping optical

pulses is very difficult compared to shaping RF pulses. The fastest electronics work in

the 100’s of GHz range and can thus modulate pulses for EPR (~95 GHz and lower)

and NMR (~1 GHz and lower). An optical pulse has a frequency in the THz range which

is too high for modulation through electronic shapers. The high frequency of optical

pulses also leads to phase instability because a difference of a ~100 nm optical path

(thermal fluctuations of materials or air density changes) is on the order of the optical

wavelength. Originally, coherent optical pulse pairs were made through diffractive

optics17, but the method was plagued by phase distortions because each pulse would

41

travel separate locations in space. The problems of phase distortions were solved by

taking advantage of optical pulse shapers to turn one coherent pulse into two;18 by

having the pulses pair travel the exact same path, fluctuations in optical path would be

eliminated because both pulses would experience the same net phase change and 2D-

S signal is only dependent on the difference in phase of the two pulses. A short time

after, it was shown that optical 2D-S could extract more information by using broadband

detection pulses, so that experiments were not limited to detecting the range that was

excited.19 Finally, 2D-S was put into the mainstream by showing how to turn a TA

experimental setup into 2D-S using a pulse shaper.20 The current direction of 2D-S is

ultra-broadband excitation and detection, in the attempt to collect the most amount of

information possible.

Diagrammatic Perturbation Theory

Diagrammatic Perturbation Theory (DPT) allows multi-photon spectroscopy

theory to be more easily understood by using Feynman diagrams built from time-

dependent density matrix perturbation theory to keep track of each photon interaction

and the overall response of the system. DPT assumes the perturbing fields are weak

allowing to only consider the first order perturbation, thus a multi-photon interaction

response of a system can be built using linear response theory for each perturbing field.

To build the theory, some basic formalism needs to be introduced.

|𝛹𝑖(𝑡)⟩ = ∑𝑐𝑘(𝑡)|𝑘⟩

𝑘

(2-1)

𝜌(𝑡) ≡ |𝛹(𝑡)⟩⟨𝛹(𝑡)| (2-2)

𝜌𝑛𝑚(𝑡) ≡ ⟨𝑛|𝛹(𝑡)⟩⟨𝛹(𝑡)| 𝑚⟩ = 𝑐𝑛(𝑡) ⋅ 𝑐𝑚∗ (𝑡) (2-3)

∴ 𝜌𝑙𝑙(𝑡) = |𝑐𝑙(𝑡) |2= P𝑙(𝑡)

(2-4)

42

where 𝜌(𝑡) is the projection operator into density matrix notation and |Ψi(𝑡)⟩ is the time

dependent wave function in an eigen basis for a single “ith” molecule of an ensemble.

𝜌𝑛𝑚 is the corresponding matrix element, (n,m). The matrix elements are products of the

time dependent amplitudes and their complex conjugates, 𝑐𝑛(𝑡)𝑐𝑚∗ (𝑡), of the eigen

states. Thus, in the eigen basis, the diagonal elements of 𝜌, 𝜌𝑙𝑙 provides the probability

of measuring the corresponding state 𝑙 as a function of time, P𝑙(𝑡). Representing the

state of the system with 𝜌 is convenient if the initial condition of the system, |Ψ(𝑡)⟩, is

known, because 𝜌 can be evolved in time using time-dependent perturbation theory as

matrix elements. Using perturbation theory to treat the light-matter interaction of a two-

level system is a simple way to introduce DPT because it captures the essentials

needed to understand 2D-S. To start, we need to know the initial state of the system; for

electronic transitions in the visible regime the lowest electronic state can be assumed.

This assumption can be understood by considering the Boltzmann distribution at room

temperature for a two-level system separated by an energy gap of ~550 nm (green

light); the excited state is negligibly populated. In the following, |𝐴⟩ will represents the

ground state, and |𝐵⟩ the excited state for the two-level system.

2D-S is a four-wave mixing process, in which each electric field, 𝐸n , is resonant

with the A↔B transition and therefore couples states A & B. When the electric field 𝐸𝑛

interacts with the system, the system will have population transition to the other state.

Each of the 4 waves occur at separate times, and it is convenient to look at the

difference in time between the pulses, instead of absolute time. The naming convention

for the time differences is shown in Figure 2-1

43

Figure 2-1. Time assignment of the 4-wave interaction given as a difference in time between pulses.

In DPT, electric field interactions are represented with arrows. An arrow inward,

represents an absorption event, and an arrow outward represents a stimulated emission

event. Arrows on the left side are ket side interactions, and arrows on the right are bra

side interactions. Figure 2-2 shows an absorption event on the ket side.

Figure 2-2. Single ket side electric field interaction represented by DPT. An arrow in represents absorption, and the arrow on the left side represents a ket side interaction. Dashed lines represent breaks in time-evolution of the system because of a perturbing electric field (one of the four waves in a 4-wave mixing process).

The dashed line in Figure 2-2 represents the interaction of the system with the

first field, 𝐸1. Because the difference in time between pulses is used, time starts at the

first interaction. Time evolves upward in a DPT figure, so for the single interaction

shown in Figure 2-2, the system evolves in time in the state |𝐵⟩⟨𝐴| with the time

evolution given by equation 2-5, until the next field arrives.

𝑅(3) ∝ eiωBA𝜏 ⋅ e−Γ𝜏 (2-5)

where 𝑅(3) is the third-order system response contribution from the first field. 𝜔𝐴𝐵 is the

frequency of the transition between state A and B, and Γ is the dephasing/decoherence

rate of |𝐵⟩⟨𝐴|. These mixed states, correspond to off diagonal elements of the density

0 Time

44

matrix representing a superposition of eigen states |𝐴⟩ and |𝐵⟩, and are called

coherences because there is a phase dependence in their time evolution, evolving with

𝜏. Coherence in the system will evolve until the next interaction with an electric field.

Figure 2-3. Interactions with two electric fields represented by DPT.

A two-wave interaction would be depicted by Figure 2-3. The second electric field

shown puts the system into state |𝐵⟩⟨𝐵|. This eigen state is referred to as a population

state, because if it was measured, it would directly give the probability of being in state

B and it corresponds to on-diagonal elements of the density matrix. The population

states evolve in time as a decay with time 𝑇, given by equation 2-6.

where 𝜏𝐵 is the life-time of state |𝐵⟩⟨𝐵|, a term accounting for both spontaneous

emission and non-radiative relaxation processes. The third interaction in a two-level

system shown so far can only be stimulated emission, because there isn’t a higher level

to absorb into and would be represented as Figure 2-4.

Figure 2-4. Three-wave interaction represented by DPT.

The third wave is stimulated emission and the system goes into another coherent

state, |𝐴⟩⟨𝐵|, which evolves with the equation 2-7.

𝑅(3) ∝ 𝑒−𝑇𝜏𝐵

(2-6)

45

𝑅(3) ∝ 𝑒−𝑖𝜔𝐵𝐴𝑡 ⋅ 𝑒−Γt (2-7)

where, 𝑡 is the time that passes between the third pulse and when the final signal is

measured. Γ for |𝐴⟩⟨𝐵| is the same as for equation 2-5 because the superposition

losses coherence at the same rate. The fourth and final wave, is the response that is

detected in 2D-S. The system must end in a population state because the response is

an observable signal. So, the system must end in |𝐴⟩⟨𝐴| or |𝐵⟩⟨𝐵|. The combination of

the 3 waves and the final wave are represented in Figure 2-5.

The system response, 𝑅(3) shown in figure 2-5, is a third-order response of three

perturbations generating the response. The final response can thus be written as a

product of factors of equation 2-5, 2-6, and 2-7, of 𝑅(3) as equation 2-8:

Figure 2-5. Three-wave interaction with third order response represented by DPT.

𝑅(3) ∝ 𝑒𝑖𝜔𝐵𝐴𝜏 ⋅ 𝑒−Γ𝜏 ⋅ 𝑒−𝑇𝜏𝐵 ⋅ 𝑒−𝑖𝜔𝐵𝐴𝑡 ⋅ 𝑒−Γ𝑡

(2-8)

Figure 2-6. Four non-degenerate four-wave mixing paths for a two-level system represented by DPT.

For a two-level system, there are four non-equivalent ways leading to four-wave

mixing response, represented in Figure 2-6. All responses will be simultaneously

A B C D

46

generated and the observable signal from the system would be given by a combination

of all the cases, given by equation 2-9.

𝑆(3) ∝ ∑[𝑅𝑖(3)

− 𝑅𝑖∗(3)

]

𝑖

(2-9)

The third order signal, 𝑆(3) is made up of each of the non-degenerate system

responses and their complex conjugate. Third order responses that are emitted on the

ket side, one example shown in Figure 2-7, are the complex conjugates of one of the

bra side responses shown in Figure 2-6A, and are thus accounted for in equation 2-8.

Showing DPT figures with the response on the ket or bra side is a matter of preference.

The subtraction of the response and complex conjugate is the result of using the density

matrix representation of time evolution, because the observable is the trace of the 𝜌(𝑡);

the math involved to go from qualitative DPT figures to the final form of the observable

signal in a quantitative form is beyond the scope of this work, but is explained clearly in

an open access lecture by Tokmakoff.21

Figure 2-7. A ket side response is the complex conjugates of the bra side response.

This diagram is 𝑹𝟏∗ (3)

from Figure 2-6A.

Something ignored up to here is the dependence of the direction of propagation

of the four fields. From conservation of momentum we can get the direction of the

emitted signal from equation 2-10.

�� 𝑠𝑖𝑔 = 𝑘1 + 𝑘2

+ 𝑘3 (2-10)

47

were, �� 𝑖 is the wave vector with magnitude |�� | =𝜔

𝑐, 𝜔 being the angular frequency of the

field, and c the speed of light. Because of the rotating wave approximation used in

perturbation theory, the true field direction is lost; a pulse incident from the left is

indistinguishable from a pulse incident from the right. Instead, a pulse that interacts with

the ket side has a positive k direction, and a pulse that interacts with the bra side has a

negative k direction. This can be understood by the field direction, given by 𝑒𝑖�� ⋅𝑥 , a bra

side interaction is the complex conjugate of the field, so 𝑒−𝑖�� ⋅𝑥 represents a field from

the opposite direction even though the actual field direction is the same for both a ket

and bra interaction. A stimulated emission event is the complex conjugate of an

absorption, so an arrow out on the ket side is negative, and an arrow out on the bra side

is positive. Tokmakoff explains the math behind the field vector direction in an open

access lecture on page 17.21

Pump-Probe Geometry Two-Dimensional Spectroscopy

2D-S in the pump-probe geometry is a special case of four-wave mixing,

depicted in Figure 2-8. In this geometry, the third pulse is used as a heterodyne to

observe the third order signal on a detector. Only the third order response which

propagate in the same direction as the third beam are measured. The direction of the

third order signal is determined by equation 2-10, so to make the signal share the

direction of the third pulse, ±�� 1 must equal ∓�� 2. Once again, this does not mean, that

the pulse needs to propagate in opposite directions, only that one pulse interacts with

the ket side and the other with the bra side, or vice versa. The observable signal is a

sum of the system response and its complex conjugate, thus the response shown in

48

magenta in Figure 2-8, will also be measured because it is the complex conjugate of the

red response.

Figure 2-8. Illustration of four-wave mixing in the pump-probe geometry and the corresponding third order response signal directions, color coded with the wave vector interactions. Only the qualitative directions are shown.

In DPT, the pump-probe geometry response can be realized if the first two

interactions have opposite directions. For a two-level system, all the cases meet this

condition because two arrows in the same direction and on same bra/ket side are not

possible. But, that is not the case for more complicated systems. The simplest example

where two fields with the same direction is allowed is a three-level system, with states,

A, B, and C. An example is depicted in Figure 2-9.

Figure 2-9. Three level system with two consecutive bra interactions in the same direction represented by DPT.

In the example given in Figure 2-9, the first two interactions have the same

direction, so the third order signal will not be in the direction of the third pulse; the third

order signal will be emitted in the direction of the orange arrow shown in Figure 2-8,

49

which corresponds to 𝑘𝑠𝑖𝑔 = −𝑘1 − 𝑘2 + 𝑘3 [a bra side absorption (negative), a bra side

absorption (negative), and a bra side emission (positive)]. The direction of a field is not

the only consideration because �� 𝑖 is a vector and has magnitude; even if the first two

interactions have opposite direction, they will only cancel if they also have the same

magnitude. Interactions like the one depicted in Figure 2-10, would not be measured in

the pump-probe geometry because a field that couples 𝐴 ↔ 𝐵 has a different magnitude

than a field which couples 𝐴 ↔ 𝐶, because |�� | ∝ 𝜔 and 𝜔𝐴𝐵 ≠ 𝜔𝐴𝐶.

Figure 2-10. Four-wave mixing with the first two fields not having the same magnitude

Only signals that co-propagate in the direction as the third pulse are measured in

the pump-probe geometry 2D-S; thus, only signals that go to a population state after the

first two fields are detected. Therefore, 2D-S in the pump-probe geometry yields only

“absorptive signals”. Although pump-probe geometry 2D-S reduces the amount of

information which can be collected in a four-wave mixing experiment, it greatly simplifies

the experiment for two reasons: (1) the pump pulses co-propagate reducing the phase

error associated with thermal phase distortions from different beam paths for optical

frequency pulses, and (2) the weak third order signal co-propagates with the probe

pulse, allowing the probe pulse to heterodyne the signal on the detector and can thus

be measured (see chapter 1 > What is Coherence > Coherent Mixing, to see what is

meant by heterodyne detection). Because the third pulse is used as the heterodyne

reference, the measured 2D-S signal is detected at the same time as the third pulse;

50

when the third pulse is not present on the detector, the third order signal is too weak to

measure. Equation 2-8 simplifies to equations 2-11 because 𝑡 = 0; no time is allowed

for the final state to evolve in the pump probe geometry.

𝑅(3) ∝ 𝑒𝑖𝜔𝐵𝐴𝜏 ⋅ 𝑒−Γ𝜏 ⋅ 𝑒−𝑇𝜏𝐵

(2-11)

The 2D-S response in the pump-probe geometry has two independent variables,

𝜏 and 𝑇. The first pulse always put the system into a coherence, so 𝜏 is termed

“coherence time” (“evolution time” in 2D-NMR, but called coherence in pump-probe 2D-

S because it is the time the system evolves in a coherence). In the pump-probe

geometry, the system is always put into a population state by the second pulse, so 𝑇, is

termed “population time” (“storage/mixing time” in 2D-NMR, but called population in

pump-probe geometry 2D-S because 𝑇 represents the time the system spends in a

population state). When 𝑇 is held constant, and 𝜏 is scanned, the result is a signal that

oscillates at the frequency 𝜔 of the transition and decays with Γ as the system losses

coherence. Keeping 𝜏 constant and scanning 𝑇 results in a decaying signal whose

amplitude and sign is determined by 𝜏.

Up to now, the presentation of the simplified theory has not highlighted the utility

of 2D-S. The signals that could be extracted from the presented level of theory could

otherwise be measured by simpler methods: Γ, the decoherence of a state AB can

come from photon-echo experiment looking at how the echo decays as a function of

wait time; 𝜔𝐵𝐴, can be measured by absorption and emission spectra; and the life-time

of the excited state, 𝜏𝐵, can be acquired from a transient absorption experiment. The

potential of 2D-S doesn’t become apparent until the rules of the simplified model are

relaxed, and the system can change states during the evolution time between pulses—a

51

more accurate model of what occurs during an experiment. For example, consider the

interaction for three-level system depicted in Figure 2-11.

Figure 2-11. Example of four-wave mixing where the system changes states between two field interactions depicted by DPT.

The first two pulses put the system in the population state |𝐶⟩⟨𝐶|, where it can

evolve during the delay time 𝑇 and even change to state |𝐵⟩⟨𝐵| before the third pulse

arrives. This evolution of the system would result in a 2D-S signal that oscillates with the

frequency, 𝜔𝐴𝐶, detected in state |𝐵⟩⟨𝐵| by the third pulse. By changing the delay time,

𝑇, the transfer from state |𝐶⟩⟨𝐶| to |𝐵⟩⟨𝐵| can be followed in time and the rate

measured. This is the significant advantage of 2D-S over other methods; it allows the

observation of states that are coupled together because a signal will oscillate at the

frequency of the coherence that it originates from.

The potential to measure the coupling between states allows many processes to

be measured. For example, 2D-S can measure inhomogeneous broadening of a line

shape because the signal oscillates at the natural frequency, even though it would be

measured in all the possible micro environments probed at different delay times, 𝑇.

2D-S can also measure coherent and incoherent coupling of states. A coherent

superposition of states results in the 2D-S signal where the population of two states

oscillate between the two states as 𝑇 is scanned. An incoherent coupling of states is

52

measured as the decay of one population, and growth of another as the population of

one state is transferred to the other state without an oscillating behavior.

Having introduced the theory, the focus will shift on matching theory with

experimental implementation.

Experimental Introduction

Figure 2-12. Simplified diagram of a pump-probe geometry experimental setup.

All the components needed for a pump-probe geometry 2D-S experiment are

diagramed in Figure 2-12. A pulsed ultrafast laser is used to produce a fundamental

coherent pulse, from which all other pulses will originate. It is important to use the same

laser to generate all the pulses used for an experiment, because 2D-S is only sensitive

to phase differences; if all the pulses experience the same phase change because of

laser phase drift, it will not affect the data. The fundamental laser we use is a

commercial chirped-pulse amplified laser, SpitFire (Spectra-Physics) operating at a

repetition rate of 1 kHz with 800 nm central wavelength. The fundamental gets split into

< 1 𝑝𝐽

~2 𝜇𝐽

Δ𝑡 ~ 400 fs

Δ𝜆 ~ 100 nm

~ 100 𝜇𝐽 Δ𝑡 ~ 50 fs Δ𝜆 ~ 25 nm

~100 𝑛𝐽 Δ𝑡 ~ 28 fs Δ𝜆 ~ 100 nm

𝝉 : 0 - 1.4 ps 𝝉

53

two parts, with most laser energy/pulse going to generate the first two pulses in 2D-S.

We call these pulses “pumps” because of the pump-probe geometry. Generally, the

system of interest is at a different wavelength than the fundamental laser, so some

wave mixing method is used to change the wavelength of the fundamental to a different

range. A fraction of the split fundamental not used to generate the pump pulses is used

to generate the third pulse, which we refer to as the “probe”. After generating the

desired pump pulse wavelengths, the pump pulse is taken to a pulse shaper, which can

modulate the pump pulse to generating a pulse pairs with a controllable time spacing 𝜏.

The pumps and probe are overlapped(superimposed) on a sample in space and time, to

generate the 2D-S signal. The probe, which co-propagates with the 2D-S signal is then

frequency resolved and measured using a spectrograph and CCD camera. The signal is

digitized and sent to a computer for signal analysis.

The breakdown of the individual components will be explored further, part by

part. The following is required for a 2D-S experiment in the pump-probe geometry:

Two pump pulses with-

• Spectral bandwidth covering the absorption range of interest

• Enough pulse energy to excite a detectible signal (system dependent: pJ-mJ)

• Pulse width shorter than the dynamics to be studied

• Stable and controllable phase

• controllable delay 𝜏 One probe pulse with-

• Spectral bandwidth covering as much range as possible

• Pulse width shorter than the dynamics to be studied

• Detectible intensity for the heterodyne cross term signal

• Fixed and controllable delay 𝑇 between pump and probe

Broadband detector with-

• Ability to spectrally resolve signal

• High sensitivity to distinguish weak oscillations from noise

54

Two Pump Pulses

2D-S requires three pulses to generate the third-order signal. The first two pulses

are called pump pulses because they initiate the coherence and then put the system

into a population state. The fluence of a field is linearly dependent to the probability of a

transition, in the weak-field limit. Thus 2D-S signal is dependent to pump fluence; you

want the most fluence while maintaining linear absorption.

The spectral bandwidth of the pump pulses is important because only transitions

with frequencies within the pump bandwidth will yield 2D-S signal. To measure the

coupling between two states, the pump bandwidth must contain both transition

frequencies; the major difference between 2D-NMR and optical 2D-S. For example, all

of 2D-NMR can be collected with less frequency bandwidth (bandwidth 0 to ~1 GHz),

than observing a red (650 nm, 461 THz) and orange (590 nm, 508 THz) transition,

which would require 47,000 GHz of bandwidth. Given the technical constraints of

generating pulses with enough bandwidth and fluence, systems studied by optical 2D-S

are limited to where in the UV-VIS spectrum pulses can be generated.

In the last 20 years, a new versatile method has been developed that allows the

generation of very broadband optical pulses, with enough energy and phase stability

between the different frequencies components. The method is based on optical

parametric amplification (OPA) of non-collinear propagating pulses. Coined NOPA,

because of the noncolinear propagation between the pump and seed, compared to

traditional OPAs.

Noncollinear optical parametric amplifier

A NOPA is based on a tunable inflection point in the phase matching condition

for a Type I non-linear crystal which is multi angle dependent22, depicted in Figure 2-13.

55

Figure 2-13. Depiction of angles involved in NOPA phase matching. A) Diagram of important angles, B) change in phase matching conditions as a function of pump and signal angles. Figures reprinted from Optics Communications, Vol. 203, P. Tzankov,

I. Buchvarov, T. Fiebig, Broadband Optical Parametric Amplification in the Near UV-VIS, pp. 107-113, copyright (2002), with permission from Elsevier.

By controlling the cut of the crystal, and the angles of the incoming beams, the

phase matching region of crystal can be made much broader than if the signal and

pump traveled colinearly. The effect of the angle of the crystal on the bandwidth

generated is illustrated in Figure 2-14.

Figure 2-14. NOPA spectrum dependence as a function of phase matching angle in BBO. Figures reprinted from Optics Communications, Vol. 203, P. Tzankov, I. Buchvarov, T. Fiebig,

Broadband Optical Parametric Amplification in the Near UV-VIS, pp. 107-113, copyright (2002), with permission from Elsevier.

NOPA/OPA theory is based on non-linear 3-wave mixing interaction, where a

pump pulse interacts with a seed pulse, transferring energy to generate a signal pulse,

and an idler pulse. The theory is more complicated than 2D-S theory because it is a

56

non-linear 3-wave mixing process, so I will not go into detail. Theory, math, and

parameters to make a NOPA are covered very clearly in work by Fiebig.22 The gist of

NOPA/OPA theory: waves will only coherently interact (needed for non-linear

interactions), if they remain phase locked relative to each other. All materials have a

wavelength/frequency dependent dispersion, so two distinct colors will travel at different

speeds inside a medium because they each experience a different dispersion, causing

a phase drift. Phase drift results in decoherence, preventing coherent mixing.

Birefringent crystals have two independent dispersion axes, called ordinary and

extraordinary. Two beams of distinct color can co-propagate in a non-linear crystal if a

condition exist where one beam experiences the dispersion of the ordinary axis and the

other the dispersion of the extraordinary axis, and the dispersions are equal. This

condition is called, “phase-matching” because both beams experience the same

effective dispersion, and thus will not de-phase, allowing coherent non-linear mixing.

The angle of the crystal needed to achieve phase matching is called the phase

matching angle. The spectral bandwidth range (color range) that can phase match in a

non-linear crystal, determines the range which can be amplified by coherent mixing.

Adding an angle between the two mixing beams allows for more bandwidth phase

matching at the inflection points of some phase matching angles, shown in Figure 2-14.

The NOPA we built was based on the design by the Miller group which takes

advantage of anamorphic focusing to enhance the bandwidth generation.23 Through

anamorphic focusing of the 400 nm pump beam on the NOPA BBO, there can be two

different perpendicular focus lengths for the pump beam. The axis which corresponds to

the extraordinary dispersion axis of the crystal can have a tight focus because this is the

57

direction which determines phase matching. The axis of the pump not involved with

phase matching can have a longer focus, allowing for more pump energy in the

bandwidth generation axis with a reduced risk of damaging the BBO. Figure 2-15

compares the increased bandwidth obtained through anamorphic focusing with a

spherical focusing NOPA of similar pump energy.

Figure 2-15. Comparison of NOPA spectrum generated with anamorphic focusing and spherical focusing. Figure reproduced from Johnson, P. J.; Prokhorenko, V. I.; Miller, R. J.

Enhanced bandwidth noncollinear optical parametric amplification with a narrowband anamorphic pump Opt. Lett. 2011, 36, 2170-2172.

A schematic of the NOPA we build is found in Figure 2-27. We made

modifications compared to the Miller group design23: we used a dichroic mirror as a

harmonic separator (splitting 800nm/400nm) to use the leftover fundamental 800 nm

from second harmonic generation to create white light for the seed of the NOPA. We

also moved the delay line from the seed beam to the pump beam because of space

constraints. The cut for the NOPA BBO and the external angle are different from the

original design because our fundamental laser is at a different wavelength than the

Miller group; our NOPA BBO crystal is cut at 31.55 degrees, with no coating. The high

fluence of the 400 nm pump would burn any AR or protective coating. The external

58

angle between the pump and white light seed is 2.8 degrees, with the seed beam

normal to the crystal face. The equations needed to determine the cut of the crystal and

external angle are shown by Fiebig22. A list of important optics in the NOPA we built

can be found in Table 2-1. The spectrum of our NOPA is shown in Figure 2-16.

Figure 2-16. Optimized spectrum of the NOPA with an output energy of 2.0 𝜇J/pulse.

Pulse shaping

A commercial pulse shaper, SLM-640 (CRI, Cambridge MA), was used to

achieve the last requirements needed for the two pump pulses: Short duration, fixed

and controllable phase, and controllable delay between pump pulses.

The dual mask SLM-640 is a light modulator that can alter the phase and

amplitude of a horizontally polarized incident laser pulse using birefringent liquid

crystals. The SLM works by independently controlling 640 pixels per LCD mask through

an applied voltage. When a voltage is applied to each independent pixel, crystal in each

pixel align with the field increasing their extraordinary index of refraction. The SLM takes

advantage of the change in extraordinary index of refraction to change the amplitude

and/or phase of the laser pulse, behaving as a wave retarder. A simplified illustration of

how an SLM works is shown in Figure 2-17.

0

Wavelength (nm)

Inte

nsity

(ar

b.)

450 500 550 600 650 700

59

Figure 2-17. Illustration of how individually controlling SLM pixels for a pulse in the Fourier plane can alter the phase and amplitude. This figure does not capture the true mechanism of the SLM, because both makes change the phase and amplitude simultaneously. Part A is adapted from Nuernberger, P.; Vogt, G.; Brixner, T.;

Gerber, G. Femtosecond quantum control of molecular dynamics in the condensed phase Phys. Chem. Chem. Phys. 2007, 9, 2470-2497. Part B was produced by Valeria D. Kleiman and reproduced with permission.

Pulse shapers modulate the pulse in the Fourier plane, where each induvial

frequency is separated in space. A 4-f compressor is needed to take the pump pulse

into the Fourier plane, and then recombine the pulse after it has been modulated. A

simplified illustration of a 4-F compressor is shown in Figure 2-17A. The 4-f compressor

design we used came from a former group member who went through the work of

determining the best 4-f configuration to reduce distortions on the beam.10 The 4-f

designed was for 800 nm pulses, making it impractical to make simple changes to adapt

for visible light. We kept the location of the major optical components, but instead of

using polarization to extract the incoming and outgoing beam (A faraday rotator which

would work for the entire NOPA bandwidth was not available), we used a small angle in

the beam path to spatially separated the beams. The spatial separation allows for a

pick-off mirror to be used. The design of the tilted 4-f compressor is shown in Figure 2-

18. The design we used is called a tilted folded 4-f compressor and is described in more

detail in Chapter 3.

A B

60

Figure 2-18. Tilted folded 4-f compressor diagram.

One Probe Pulse

For 2D-S in the pump probe geometry, the probe pulse works as both the third

pulse and a heterodyne local oscillator for the third-order signal. The range of

wavelengths that can be probed is limited to the bandwidth of the third pulse (excluding

detector and optics limitations), thus the use of broadband continuum (white light). In

addition, the temporal resolution of the experiment is affected by the pulse width.

Generating a broadband continuum is achieved by tightly focusing an ultrafast laser

pulse on clear medium such as sapphire or bulk glass, resulting in self phase

modulation from the high intensity yielding a broadband laser pulse which is also short

in time.24 The spectrum of the supercontinuum is dependent on the fluence of the tightly

focusing pulse, a typical spectrum generated in sapphire with an 800 nm pulse is shown

in figure 2-19.

The probe pulse needs to be low intensity for two reasons: (1) a sensitive

detector is needed to distinguish noise oscillations from 2D-S signal, and sensitive

detectors saturate easily; (2) the intensity of the probe needs to be low enough to not

61

overshadow the intensity of the heterodyne term. A white light continuum generated in

sapphire has energy in the pico-Joules, already close to the saturating limit of CCD

cameras.

Figure 2-19. Typical white light spectrum generated in sapphire with different fluence. The intensity is not normalized.

Accurate and precise delays of the third pulse are also needed to maintain

control of the population time 𝑇. Phase stability is not critical for the third pulse

(population states are invariant to phase) so a commercial optical delay line can be

used. We use a ThorLabs DDS220 (New Jersey) which has a 220 mm range with

reproducibility down to ±0.5 fs, in a single pass retroreflector configuration.

Broadband Detector

2D-S signal is weak because it is a third-order signal originating from three weak

perturbations. Going back to equation 1-11, to measure the cross term (heterodyne) to

extract the 2D-S signal, the amplitude squared of the probe pulse cannot be significantly

greater than the amplitude of the probe pulse multiplied with the amplitude of the 2D-S

signals. The limit to which 𝐴𝑝𝑟𝑜𝑏𝑒2 can be distinguished from 𝐴𝑝𝑟𝑜𝑏𝑒 ⋅ 𝐴2𝐷−𝑆 is detector

dependent. CCDs are ideal to look for the oscillations of 𝐴𝑝𝑟𝑜𝑏𝑒 ⋅ 𝐴2𝐷−𝑆 as 𝜏 is scanned

because they are multi-element detectors with high sensitivity and low noise. Coupling a

62

CCD to a spectrograph allows the individual pixels of the CCD to spectrally resolve the

2D-S signal. In our experiments, we combine a 260i spectrograph (Oriel, Oregon) and a

MicroMax CCD camera (Roper Scientific, New Jersey) to collect the 2D-S signal. The

configuration of the spectrograph with the size of the CCD chip, allows us to collect a

range of wavelengths from 430 nm to 655 nm when a 150 𝑔𝑟

𝑚𝑚 grating is used. This

range is tunable because the grating is rotatable, changing the central wavelength. The

spectrograph has 3 different gratings (1200 𝑔𝑟

𝑚𝑚, 600

𝑔𝑟

𝑚𝑚, and 150

𝑔𝑟

𝑚𝑚) giving us the

ability to change the dispersion on the CCD to look at smaller range of wavelengths with

better spectral resolution.

Making Raw Data Meaningful

Now that the theory and method has been introduced, the focus shifts to turning

measured data into something meaningful and “easy” to interpret. Like 2D-NMR, the

raw time-domain data contains lots of information, but in a format not easy to interpret.

Through signal processing (Fourier Transformation), the time-domain data are

converted to a frequency-domain spectrum. Figure 2-20 shows a caricature often used

to explain how to read a 2D-S plot. A three-level system is used with two transitions

from the ground state at frequency, 𝜔𝐴𝐶 and 𝜔𝐴𝐵. Other transitions will be ignored for

the simplified explanation (i.e. no stimulated emission). 2D-S data is a 3D matrix

because there are 3 parameters, 𝜔𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 (FFT of 𝜏), 𝜔𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛, and 𝑇. There is no

way to represent a 3D matrix as a figure on a two-dimensional sheet of paper, so only

slices at constant T are plotted, either alone or as series adjacent to each other to

represent 𝑇 time evolution. In dynamic two-dimensional media (i.e. movie) the 𝑇 slices

can be shown as snapshots in a film. Figure 2-20 shows a single T slice of “data” for a

63

3-level system. The dashed line is called the diagonal because it represents signals

excited and detected at the same frequency (𝜔𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 = 𝜔𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛). If population from

state C decays into state B, a signal will be detected at 𝜔𝑑𝑒𝑐𝑡𝑖𝑜𝑛 = 𝜔𝐴𝐵 when

𝜔𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 = 𝜔𝐴𝐶, referred to as an off-diagonal peak because signal is detected at a

different frequency than the excitation (implying coupling between the two states in this

example).

Figure 2-20. Simplified caricature of 2D-S data to explain on-diagonal and off-diagonal signals.

Optical 2D-S Pump-Probe Spectroscopy is a Differential Spectroscopy

Unlike 2D-NMR, a 𝜋-pulse to prepare a pure population state (other than the

ground state) is not possible in optical spectroscopy. Instead optical two-dimensional

spectroscopy operates in the weak field limit were only a fraction of the population is

transferred to an excited state (the linear range of Rabi-oscillation). Thus, optical 2D-S

is a differential spectroscopy, comparing the change in unperturbed ground state

absorption, with an absorption with a fraction of population in the excited state. The

64

caricature shown in Figure 2-20 does not represent what an optical 2D-S signal will

measure because a differential optical spectrum is cluttered with many overlapping

signals at the same detection frequency. Extracting useful information from an optical

2D-S experiment is quite challenging and still an unsolved problem in the relativly new

field of optical frequency 2D-S. In Chapter 4, I will show how I extracted information

from a 2D-S experiment by coupling what was learned from TA experiments (a slice of

2D-S data in the pump-probe geometry corresponds to an equivalent TA experiment at

the corresponding excitation wavelength, covered next).

A Slice of Pump-Probe 2D-S Data Corresponds to a TA experiment

As an example, 2D-S data I collected for the laser dye DASPI will be presented

to explain 2D-S signals, comparing to published transient absorption (TA) data of

DASPI25 for validation. I am the first person (besides the Miller group) to successfully

build and use the blue-green NOPA for any experiment. Giving a hint to the complexity

of the instrument; many other ultrafast groups tried to use the blue-green NOPA for

experiments because of the many interesting and unstudied systems accessible only by

the NOPA designed by the Miller group. The Miller group only published one article26

(conference paper) using the anamorphic NOPA for 2D-S experiments preformed in the

box-car geometry using diffractive optics. I am the first to collect pump-probe geometry

2D-S data using the blue-green NOPA (hence the need for an extensive Chapter 3

covering all the problems we needed to overcome). There is no choice but to use a well-

studied molecule (DASPI) to benchmark our instrument because no published pump-

probe 2D-S exists to reproduce in the wavelength range our instruments operates in.

DASPI 2D-S data was collected in methanol, at room temperature, in a 2 mm optical

path cuvette with an optical density of 0.3 OD at 480 nm. The sample was stirred with a

65

PTFE coated magnetic stir bar to avoid heating effects from the laser. The pump pulse

energy was ~15 nJ/pulse with a spot size of ~170 𝜇m. The probe pulse was a

broadband continuum, generated in sapphire, with a spot size of ~80 𝜇m at the sample

position.

Figure 2-21. Raw 2D-S data for DASPI scanning 𝜏 at constant 𝑇 = 30 𝑓𝑠. A) Data for all detection wavelengths seen by CCD, B) a single detection wavelength, the colored dots relate to Figure 2-22

Figure 2-21A is a plot of the signal measured by the CCD at a fixed 𝑇, while

scanning 𝜏 for DAPSI. This signal is given by the change in intensity of the probe

(Δ𝐶𝑜𝑢𝑛𝑡𝑠) as a function of detection wavelength and delay 𝜏 between the two pumps.

A

B

66

Figure 2-21B shows a single detection wavelength (one horizontal slice of Figure 2-

21A). The 2D-S signal is governed by equations 2-11, when 𝑇 is held constant, the

signal will oscillate with a decay. Figure 2-22 shows the 2D-S signal when 𝜏 is held

constant, and 𝑇 is scanned. The signal will appear as a TA trace with signal sign and

amplitude governed by 𝜏.

Figure 2-22. Raw 2D-S data for DASPI scanning 𝑇 and constant 𝜏. Line colors correspond to equivalent color coded 𝜏 in Figure 2-21B

Data presented in Figures 2-21 and 2-22 in the time-domain are not easy to

interpret and extract information. A Fourier transform along the 𝜏 dimension is

preformed to convert to 𝜔𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛. UV-Vis spectroscopy is typically reported in

wavelength, so 2D-S plots have 𝜆𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 instead. Figure 2-23A shows processed data

for the raw data shown in Figure 2-21, represented in Δ𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛. Figure 2-23B

shows data for a different 𝑇 time at 750 fs, after the dye DASPI has red shifted

(explained when TA data is introduced). The units for plotting 2D-S data are not yet

established in the community, some use Δ𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛, and others use Δ𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛.

We choose Δ𝐴, because it shows data in a log scale, thus making weaker signals more

noticeable. Figure 2-24 shows DASPI data in Δ𝐴. Keeping track of the absolute intensity

67

of a signal is difficult after an FFT, so 2D plots are often in relative units, either

normalized, or just keeping the intensity output of the FFT.

Figure 2-23. Processed 2D-S data for DASPI at two different 𝑇 values shown in Δ𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛. A) 𝑇 at 100 fs, B) 𝑇 at 750 fs

Figure 2-24. Processed 2D-S data for DASPI at two different 𝑇 values shown in Δ𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛. A) 𝑇 at 100 fs, B) 𝑇 at 750 fs.

The processed 2D-S plots shown in Figure 2-23 and 2-24 are still too

complicated for anyone other than an expert in optical 2D-S to extract information.

A B

A B

68

Figure 2-25. Published TA DASPI data. Figure explained in text. Reprinted from Bingemann, D.;

Ernsting, N. P. Femtosecond solvation dynamics determining the band shape of stimulated emission from a polar styryl dye J. Chem. Phys. 1995, 102, 2691, with the permission of AIP Publishing.

To help explain what the data represents, published TA results for DASPI in

methanol excited at 470 nm will be introduced. Figure 2-25 shows the information

needed from a steady-state measurement and TA experiments needed to help interpret

2D-S data. Figure 2-25A shows the absorption and emission spectrum of DASPI in

methanol. Figure 2-25B shows the composition of the TA signal where ESA is excited

A

B

C

69

state absorption (a positive signal), ABS is ground state bleach (a negative signal

associated with missing ground state absorption), and GAIN is stimulated emission (a

negative signal that shifts in time as the excited state cools from a hot vibrational state,

until finally settling at the ground vibrational state of the excited electronic state). Figure

2-25C shows snap shots of the TA spectrum collected at different probe delays.

Figure 2-26 plots 2D-S data next to TA data, with slices of the 2D-S plot which

correspond to a TA experiment; pump-probe 2D-S experiment is an excitation

wavelength resolved TA experiment.

70

Figure 2-26. A slice of pump-probe 2D-S data for a given excitation wavelength correspond to an equivalent TA experiment at the same excitation wavelength. A) 2D-S data collected for DASPI at 𝑇 = 750 𝑓𝑠 with the white dashed line representing the diagonal, B) Slice of 2D-S plot at 477 nm excitation, C) published TA data for DASPI collected at 470 nm excitation with ~60 fs pulses, lines are color coded with part B. Part C of this figure was adapted from

Bingemann, D.; Ernsting, N. P. Femtosecond solvation dynamics determining the band shape of stimulated emission from a polar styryl dye J. Chem. Phys. 1995, 102, 2691, with the permission of AIP

Publishing.

𝑻 = 𝟕𝟓𝟎 𝒇𝒔

𝑇 (𝑓𝑠) 200 300 750

A

B

C

71

Table 2-1. List of optics used in the NOPA with numbers associated with Figure 2-23.

Optic Number

Optic Type Description Company

1 SHG-BBO 1 mm BBO cut for 800 nm SHG. AR coated (800 nm Front / 400 nm Back)

New light photonics

2 Dichroic Mirror Transmits 400 nm and reflects 800 nm. 99.9% R of 800 nm and 98% T of 400 nm.

CVI

3 Retroreflector Hollow-corner cube reflector. Protected aluminum

Melles-Griot

4 Cylindrical Lens 25.4 mm square cylindrical singlet lens focusing vertically. +750 mm focus at 633 nm

CVI

5 Cylindrical lens 25.4 mm square cylindrical singlet lens focusing horizontally. +250 mm focus at 633 nm

CVI

6 NOPA BBO 1 mm BBO cut at 31.55º. No coating United Crystals

7 Variable ND Filter Reflective variable ND filter 0.01-4.00 OD ThorLabs

8 Spherical Lens 25.4 mm round singlet lens, AR coated for 800 nm. +50 mm focus at 633 nm.

CVI

9 Sapphire Window High quality 2 mm thick, 1 inch window with no coating.

CVI

10 Off-axis Parabolic Mirror

50.8 mm optic with 25.4 mm effective focal length. Protected aluminum.

Newport

11 Spherical Mirror 25.4 mm round concave mirror with protected silver coating. +500 mm focus.

CVI

12 Spherical Mirror 50.8 mm round concave mirror with protected silver coating. +250 mm focus.

CVI

72

Figure 2-27. NOPA schematic. A list of optics corresponding to the numbers next to optics is provided in Table 2-1. Black

lines represent mirrors. The linear polarization states of the beams are: 800 nm is vertical, 400 nm is horizontal, white light seed is unpolarized, NOPA generation is vertical, and the final polarization leaving the NOPA horizontal. The turning mirror, circled in yellow, of the 400 nm path, determines the angle between the pump and probe, and is used for pump-probe overlap at the NOPA BBO.

12

3

4

5

6

8

9

7

10

11

12

Turning periscope

𝛼𝑒𝑥𝑡 = 2.8°

73

CHAPTER 3 IMPLEMENTATION AND TROUBLESHOOTING

“Lasers bring more misery than happiness; but, more lasers more fun.” Nico Omenetto

Having introduced 2D-S basics in Chapter 2, focus will now shift to much more

technical information required to build, preform, and analyze a pump-probe 2D-S

experiment and avoid the many pitfalls we faced because 2D-S is not yet a turn-key

method. This chapter will assume an advanced understanding of spectroscopic

methods and theory that have not been introduced. Several books10,13,27-29 are

recommended to help the reader follow this chapter.

Figure 3-1. Simplified diagram of a pump-probe geometry experimental setup.

Each instrument and their problems will be introduced in the order that the laser

beam propagates, starting where the fundamental laser beam is split for the NOPA

generation and ending at the CCD. Then focus will shift to data collection and analysis,

< 1 𝑝𝐽

~2 𝜇𝐽

Δ𝑡 ~ 400 fs

Δ𝜆 ~ 100 nm

~ 100 𝜇𝐽 Δ𝑡 ~ 50 fs Δ𝜆 ~ 25 nm

~100 𝑛𝐽 Δ𝑡 ~ 28 fs Δ𝜆 ~ 100 nm

𝝉 : 0 - 1.4 ps 𝝉

74

including the important things we learned that should be passed on. The layout of the

instrument is shown in Figure 3-1.

NOPA Generation

Figure 3-2. Some typical NOPA spectrum achievable day-to-day with energies between 1.5 to 1.8 𝜇J/pulse.

The NOPA we built was designed around anamorphic focusing to enhance

bandwidth generation23, introduced in Chapter 2. A schematic of our NOPA can be

found in Figure 2-27. The intensity spectrum generated by a NOPA is very sensitive to

the external angle of the pump/seed beams and spatial-temporal overlap, making it

difficult to reproduce the optimized spectrum and energy per pulse shown in figure 2-15.

The seed used for the NOPA will be discussed later. Many hours of labor are needed to

optimize the NOPA generation to be “optimal”, 2 𝜇J/pulse with full bandwidth. Day-to-

day laser fluctuations require the NOPA to be constantly realigned. Instead of focusing

our time and energy on getting the optimal NOPA generation, we optimize until a

“workable” NOPA spectrum for an experiment is generated (we are not energy limited in

our 2D-S experiments so getting the most power is not important). The intensity spectra

75

shown in Figure 3-2 are typical NOPA spectrums that can be achieved daily with only

30-60 min of optimization by an experienced user. Workable spectrums for an

experiment needs to cover the full range of wavelengths that are modulated by the

pulse shaper (475 nm to 565 nm, explained later).

NOPA generation of at least 1.45 𝜇J/pulse is recommended to ensure that the

spectrum will remain stable throughout an experiment (~20-30 hours). The stability of a

NOPA is energy dependent, too little power and it is unstable, too much power and it is

also unstable (1.5 to 2.0 𝜇J/pulse is the “sweet-spot” of our system). The NOPA cannot

be pumped with more energy than the designed 12 𝜇J/pulse of 400 nm at the crystal

position, because the design is near the damage threshold for an uncoated 𝛽 −barrium

borate (BBO) crystal.

A known issue of anamorphic focused NOPA design is the resultant spatial chirp

(wavelengths spread in space) from anamorphic focusing seen in Figure 3-3A.

Figure 3-3B shows that tightly focusing the pump in the phase matching direction

results in a sweep of angles of the pump inside the BBO crystal given by 𝛿𝛼𝑖𝑛. The

different angles inside the crystal, edges shown in red and green lines, will experience

different phase matching angles, a sweep from red to green angle in Figure 3-3B.

Figure 3-3C shows the phase matching conditions dependence on the phase matching

angle, NOPA spectrum generation at the edges will not be equal. The smaller angle

(green) generates more of the inner wavelengths and the large angle (red) the outer

wavelengths.

76

Figure 3-3. Spatial chirp from anamorphic focusing NOPA generation is the result of a large sweep of phase matching angles inside the crystal. A) Collimated NOPA beam immediately after generation imaged on a diffuser, B) illustration of different phase matching angles inside the crystal, C) different phase matching angles will give different phase matching conditions inside the crystal. Figures adapted from Johnson, P. J.; Prokhorenko, V. I.; Miller, R. J. Enhanced bandwidth

noncollinear optical parametric amplification with a narrowband anamorphic pump Opt. Lett. 2011, 36, 2170-2172.

A

C

B

77

The beam profile shown in figure 3-3A shows the spatial chirp (horizontal)

immediately after generation. The NOPA generation is vertically polarized from type I

phase matching conditions in the NOPA BBO crystal. Our pulse shaper requires

horizontally polarized light (determined by AR coatings on the SLM arrays). To change

the polarization of our beam to meet our needs, a turning periscope immediately after

NOPA generation is used. Turning the beams polarization with a turning periscope also

turns the spatial chirp on its side (spatial chirp will now be in the vertical direction).

The spatial chirp of our NOPA beam was measured by imaging the beam after

first order diffraction onto a CCD. Figure 3-4A shows the spatial chip with wavelengths

resolved in the x-axis, and physical space in the y-axis. The spectral chirp we observe

matches the expectations from the different phase matching conditions, shown in Figure

3-3C. We compensate the negative spatial chirp of the NOPA beam (crescent shape),

by introducing opposite spatial chirp (upside down crescent shape) with the geometry of

the 4-f compressor (explained later). Figure 3-4B shows the spatial chirp of the NOPA

beam after the 4-f compressor.

Figure 3-4. Spatial chirp of NOPA beam measured by imaging first order diffraction on a CCD. A) Collimated NOPA after the turning periscope, before the 4-f compressor, B) collimated NOPA after travel through our tilted 4-f compressor. The wavelength difference is a result of day-to-day NOPA spectrum changes, not from the 4-f compressor.

A

B

78

Pulse Shaping

There are two major components involved with pulse shaping: (1) diffracting the

beam into wavelength components and collimating into the Fourier plane using a 4-f

compressor, and (2) applying a modulation mask, by changing the phase and

amplitudes of individual wavelengths with a spatial light modulator. Figure 3-5 shows a

simplified illustration of pulse shaping.

Figure 3-5. Simplified illustration of pulse shaping. A) the beam is diffracted into wavelength components using a grating then collimated into the Fourier plane. B) The pulse can me modulated by changing individual wavelength phase and amplitude. This figure is not accurate representation and only an illustration to simplify understanding. Part A is adapted from Nuernberger, P.; Vogt, G.;

Brixner, T.; Gerber, G. Femtosecond quantum control of molecular dynamics in the condensed phase Phys. Chem. Chem. Phys. 2007, 9, 2470-2497.. Part B was produced by Valeria D. Kleiman and reproduced with permission.

Tilted 4-f Compressor

A 4-f compressor uses a diffraction grating to disperse wavelength components

of a beam in space. The dispersed beam is then collimated with a focusing optic,

effectively taking a pulse from the time domain to the frequency domain (called the

Fourier plane because wavelengths are separated in space and the phase of each

wavelength determines the pulse in the time domain). The SLM-640 we use is a double

pass configuration (there is a mirror at the end to reverse propagate the beam back

through the SLM). Travelling through the SLM twice doubles the dynamic range of the

SLM by doubling the effect of each pixel array, but it requires a folded 4-f compressor

A B

79

design which can distinguish the beam entering the shaper from the beam exiting the

shaper. An innovative design by Kuroda30, uses polarization changes to distinguish

between incoming and outgoing beams to minimize spatial chirp and pulse front tilt. The

design does not work for us because the design is for 800 nm pulses, and our spectrum

is in the blue-green of the visible, where optics for bandwidths of ~100 nm don’t exist for

polarization separation.

Figure 3-6. Tilted folded 4-f compressor design. Optics described in text.

80

Being unable to use polarization led us to go back to the standard method for

extracting pulses from a folded 4-f compressor, using tilt in the beam propagation (see

Figure 3-6). A small angle between the incoming and outgoing beam will lead to spatial

separation after a long path, allowing a pick-off mirror to separate the beams. A known

issue of a tilted 4-f compressor is resulting spatial chirp, because the incoming and

outgoing beam cannot share the true focal point of the focusing optic. The resulting

spatial chirp is crescent shaped because of focal point mismatch. By choosing whether

the incoming or outgoing beam matches the focal point of the focusing optic the beam

can have spatial chirp crescent concave up (incoming matches focus) or concave down

(outgoing matches focus). The spatial chirp of the NOPA beam entering the shaper is

concave down (see Figure 3-4A) choosing the incoming beam to match the focus of the

optics effectively cancels spatial chirp (see Figure 3-4B). The tilt angle was determined

experimentally. Our tilted 4-f design, depicted in Figure 3-6, has an incoming and

outgoing beam separated by ~6 mm after 250.4 cm of travel (distance to and from pick-

off mirror). The grating has grove density 1800 𝑔𝑟

𝑚𝑚, with a protected aluminum coating,

nominal blaze of 21.1°, and ~80% -1 order reflectivity for 400-600 nm horizontally

polarized light (Richardson Grating, catalog number 53-*-289R). The focusing mirror is

a 15.24 cm round concave protected aluminum mirror, with a focal length of 30.48 cm

(Edmunds optics, catalog number 32-839). The polarizer is a thin sheet polarizer with

an extinction ratio of 6000:1 dB (Newport, catalog number 5511). A calcite polarizer

cannot be used, because the NOPA pulse generates white light in the calcite. All other

optics are flat protected silver mirrors. The optics chosen for the 4-f compressor are

determined by SLM, discussed further below.

81

Using a concave spherical mirror is not ideal in a 4-f compressor because it

focuses the beam vertically as well as collimating the colors horizontally. The unneeded

focus in the vertical direction makes the distance from the SLM to the focusing mirror

critical, if the SLM back mirror is not at the exact focus of the focusing mirror, the beam

leaving the 4-f compressor will not be collimated. We have no choice but the use a

spherical mirror in our design because the SLM-640 pixel arrays are deformed30, not

focusing the beam onto the SLM face would result in serious spatial chirp (shown in

Figure 3-7). Focusing onto the SLM array minimizes spectral distortion on the beam

(like how a person with astigmatism can see sharper images by squinting, minimizing

the d).

The wavelength dispersion of the 4-f compressor on the SLM-640 is important

because the system is pixelated and a continuous phase function in wavelength is not

possible, leading to pixilation issues in modulation masks. The optimal 4-f configuration

and wavelength dispersion in the Fourier plane for an SLM-640, has been previously

calculated30, an 1800 𝑔𝑟

𝑚𝑚 grating is needed to disperse the beam with a focusing mirror

of focal length ~30.48 cm to collimate the beam into the Fourier. Pixilation effects in a

phase mask are covered in detail by Kuroda30 and Damrauer31. The most important

result from pixilation is that there is maximum phase difference between two adjacent

pixels of 2𝜋, limiting the dynamic range a pulse can be moved in time. For a pulse

centered at 520 nm (NOPA spectrum center) with the above grating-focus optic combo,

the dynamic range is ~2 ps.

82

Figure 3-7. Spatial aberrations introduced by the SLM-640 when a cylindrical mirror is used. Each panel shows the spatial distortions at different SLM-640 positions in the focal plane of the 4-f compressor. A) Center of SLM array at ~ 500 nm in the Fourier plane, B) ~520 nm C) and ~540 nm.

Figure 3-8 shows the spectral bandwidth allowed through the SLM by a 4-f

compressor with the grating-focal combo described above is shown in orange. The

dash-black lines show where the beam gets cut off by the edges of the SLM array. Only

intensity in the spectral range allowed through the SLM is relevant for an experiment, all

other wavelengths get blocked. Therefore, it is not important to maximize the bandwidth

of the NOPA generation, only ensure that the spectrum covers the full range of the

SLM. The blue spectrum is the NOPA spectral bandwidth before the shaper to compare

with the spectrum after the shaper.

Figure 3-8. Spectral bandwidth of the pump pulse allowed through the SLM-640 array, with the 4-f compressor design used. Black lines show the edges of the pixel arrays, were spectrum hits the edges of the SLM-640 device. Blue is spectrum before the shaper, and orange is the spectrum after the shaper. The difference in intensity distribution is a result of optic efficiency not being equal at all spectral wavelengths.

B C A u

83

The efficiency of the 4-f compressor, including the SLM, is measured at ~11%

(energy in over energy out). The difference in intensity profile between pre-post shaper

spectrum (shown in Figure 3-8) is the result of optics having different efficiencies for

transmission and reflectivity as a function of wavelength. The SLM-640 is the major loss

component of the shaper having ~40% transmission per propagation.

The native pulse width of an anamorphic focusing NOPA we built (or similar,

non-anamorphic NOPA) has not been previously reported. The 4-f compressor we built

combined with an SLM-640 allows a dynamic range of ~2 ps for temporal correction

(discussed earlier). Characterizing the native NOPA pulse to ensure it was shorter than

2 ps was performed with X-FROG, a frequency resolved crosscorrelation method

developed by Trebino10.

A BBO crystal has poor phase matching conditions when mixing wavelengths

that will generate a wavelength below 300 nm (the index of refraction of BBO becomes

non-linear bellow 300 nm). BBO cannot be used to autocorrelated the NOPA pulse

because 520 nm + 520 nm sum-frequency generates 260 nm (cannot be

autocorrelated). However, 520 nm + 800 nm sum-frequency generates 315 nm (just

above the cut off, allowing crosscorrelation). By mixing a pulse we could characterize

(800 nm fundamental) with a pulse we could not independently characterize, the

temporal profile of the NOPA pulse could be measured.

84

Figure 3-9. Phase matching bandwidth for SFG between NOPA beam and 800 nm beam at various phase matching angles for 100 𝜇𝑚 thick BBO. A) Phase matching bandwidth at different angles of the BBO, B) illustration of how the phase matching angle is tuned to meet different phase matching conditions.

The NOPA spectrum + 800 nm bandwidth that can be simultaneously phase

matched at a single phase-matching angle of a 100 𝜇𝑚 BBO crystal is ~10 nm, meaning

only 10 nm of the NOPA spectrum could be phase matches to generate sum-frequency

at a single time. Figure 3-9A shows how much spectrum of the NOPA can be

simultaneously phase matches at a single BBO angle (experimentally collected data,

not calculated), each colored line corresponds to a different BBO angle depicted by

Figure 3-9B. Knowing that it is possible to phase match the whole NOPA spectrum at

different angles, allows to piecewise generate an X-FROG Trace of the entire NOPA

spectrum by changing the BBO phase matching angle between scans. A piece wise

generated X-FROG trace of the native NOPA pulse shown in figure 3-10 appear like

“islands” because it’s the addition of traces taken at different BBO angles. Figure 3-10A

shows the X-FROG trace of the NOPA pulse which travels through the 4-f compressor,

without the SLM in the Fourier plane. The temporal width of the native NOPA pulse is

measured at ~400 fs, well within the dynamic range of the SLM-640. Figure 3-10B

shows an X-FROG trace of the NOPA pulse after the SLM has been added in the

A B u

85

Fourier plane, showing that the SLM adds a non-trivial phase distortion making the

pulse unworkable because it is spread out over more than 2 ps. The SLM-640 adds

more phase distortions than it can compensate. The non-trivial phase is a result of

deformations which are brought out by cylindrical focusing (discussed earlier). The

aberrations were characterized in detail by a previous student 30, which failed to

communicate that the aberrations in the mask are a significant problem.

A trick was used to compensate the phase distortions added by the SLM-640. By

purposefully miss-aligning the 4-f compressor, linear temporal chirp could be added to

compensate some of the distortions added by the SLM array. The linear chirp was

added by adding an angle to the folding mirror immediately after the grating (purple

optic in figure 3-6). Linear chirp was added, while monitoring the pulse width using X-

FROG, to achieve the shortest possible pulse without using SLM dynamic range. Figure

3-10C shows the compensated pulse is spread over ~1 ps, within the dynamic range of

the SLM-640.

The phase distortions we observe added by the SLM-640 are not the result of

material dispersion. We preform X-FROG measurements at the sample position, as

such, the timing convention is the same used for pump-probe spectroscopy. The NOPA

pulse is our “pump”, and the 800 nm we use for crosscorrelation is the “probe” (no white

light generation). If the pump arrives before the probe, time is positive; if probe arrives

before the pump, time is negative. From Figure 3-10B, the short wavelength (high

energy) components arrive at negative times, and the long wavelength (low energy)

components arrive at positive time, thus the dispersion by the SLM is positive (see

figure 3-11 for a simple illustration explaining the statement). Normal dispersion in a

86

Figure 3-10. X-FROG traces of the NOPA pulse + 800 nm generated piecewise at

different BBO angles (discussed in text) showing that the SLM-640 destroys the phase

of a pulse. A) Native temporal profile of NOPA pulse, with no SLM in Fourier plane, B)

temporal profile after addition of SLM-640, C) compensated temporal profile after

temporal chirp was introduced.

Figure 3-10. X-FROG traces of the NOPA pulse + 800 nm generated piecewise at different BBO angles (discussed in text) showing that the SLM-640 destroys the phase of a pulse. A) Native temporal profile of NOPA pulse, with no SLM in Fourier plane, B) temporal profile after addition of SLM-640, C) compensated temporal profile after temporal chirp was introduced.

A

B

C

87

medium always results in negative chirp (red wavelengths traveling ahead of blue

wavelengths) because the index of refraction of materials increases with shorter

wavelengths (increasing energy). The SLM is 2.45 mm thick, with only 0.02 mm of liquid

crystal thickness, majority of the thickness is BK7 glass and index matched epoxy. In a

double pass configuration, the chirp added by ~6 mm of BK7 glass leads to a temporal

delay of ~100 fs for NOPA spectrum from the shortest to longest wavelength.

Figure 3-11. Simple illustration to explain how we know the SLM-640 adds positive dispersion from an X-FROG Trace.

On a side note, Figure 3-11 can be adapted to explain why blue wavelengths

arrive first in TA experiments with white light as the probe, shown in Figure 3-12 (red

wavelengths travel ahead of blue in normal dispersion).

Figure 3-12. Simple illustration of why temporal chirp in a white light probe leads to blue TA signals arriving before red signals in time.

88

Phase and Amplitude Control Using SLM-640

The first step in phase and amplitude control is calibrating the phase response of

the SLM-640 liquid crystal array as a function of voltage. A step-by-step explanation for

SLM-640 calibration is reported elsewhere.30 Each pixel in an array behaves differently

because of inhomogeneity, but we showed that that a single calibration curve can be

used to predict the phase response as a function of voltage for the entire array, with a

pixel-by-pixel correction factor.30

Once a calibration is in place, the following equations dictate the resulting phase

and amplitude of the pulse for a given frequency:

𝐴𝑆𝐿𝑀(𝜔) = |𝑐𝑜𝑠 (𝛥𝜑1 − 𝛥𝜑0

2)|

(3-1)

𝛷𝑆𝐿𝑀(𝜔) = (𝛥𝜑1+𝛥𝜑0)

2 (3-2)

The phase change added by each of the masks, Δ𝜑𝑖, can thus make a phase

only change if the same phase is applied to both mask, or amplitude only change if

opposite phase is applied to each mask.

To test the quality of a calibration, we generated double pulses (discussed later)

with delay 𝜏 separation from 0.1 fs to 2 ps. X-FROG measurements of the double pulse

showed no difference between the predicted delay and the measured delay, until after

~1 ps, where the phase required for double pulses started reaching the dynamic range

of the SLM. Some of the 2 ps Dynamic range is consumed to compress the pulse

(discussed later), prior to making double pulses.

Over the course of several years, the SLM calibrations only needed to be redone

after major events, such as an optic change in the 4-f compressor.

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Pump pulse compression

Given that the pump pulse has complex temporal chirp (see Figure 3-10C), the

phase needed to compress is determined empirically. A genetic algorithm (GA) written

by a previous student,30 used for pulse compression by optimizing a chosen feedback

parameter over the course of evolving generations. Choosing the proper feedback

parameter to evolve the generations is the most critical component of the compression

procedure. Maximizing the intensity of a non-linear signal is an ideal feedback signal

because the shortest temporal profile also has the highest peak intensity, yielding the

highest non-linear signal. The non-linear signals we tried are:

• Two-photon absorption

• SFG of Pump + 800 nm in BBO

• SFG of Pump + 800 nm in KDP

Each was unable to independently compress the pulse for distinct reasons which

will be discussed in detail.

Two-Photon absorption was performed using a photo-diode with a bandgap

larger than the pump wavelengths, but lower than the doubled wavelengths, allowing to

have response from multi-photon absorption events. The detector we used was based

on a SiC photo-diode design described elsewhere.32 Two-photon absorption was tried

first because it is a phase matching-independent non-linear signal. As discussed earlier,

BBO cannot phase match the entire pump spectrum simultaneously.

Two-photon absorption of the pump pulse was unable to serve as a feedback for

the GA because the temporal chirp of the uncompressed pump pulse yields no

detectible two-photon absorption. If the uncompressed pump pulse is taken to the

detector, the only signal measured is a baseline shift from heating. We know that the

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detector works because a partially compressed pulse (discussed later) gives a voltage

response on an oscilloscope with better signal-to-noise than detecting SFG from a non-

linear crystal on a commercial photo-diode (DET210, ThorLabs).

We had no choice but to use a phase matching-dependent signal to compress

the pulse.

SFG of Pump + 800 nm in BBO was attempted despite knowing that the whole

pump spectrum could not be simultaneously phase matched in a thin BBO crystal. We

quickly learned that phase matching the entire region of interest is critical and cannot be

avoided when dealing with complex pulses.

Figure 3-13. Crosscorrelation of Pump pulse + 800 nm pulse before and after a compression mask obtained with a GA using SFG in BBO is applied. A) Crosscorrelation taken using the same phase matching angle used for GA feedback, B) Cross Correlation taken using the next 10 nm increment of BBO phase matching angle, using a compression mask obtained at different phase matching angle.

Figure 3-13A shows a crosscorrelation of the pump pulse (blue) after a

compression using the same phase matching angle of the BBO used for GA feedback.

The uncompressed crosscorrelation (brown-dashed) is plotted simultaneously for

comparison of temporal profile and intensity between compressed and uncompressed.

Repeating the crosscorrelation with the same SLM phase mask, but changing the BBO

angle so the next ~10 nm of the pump pulse spectrum would phase match yields the

A A

B F

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crosscorrelation shown in Figure 3-13B. Regions of the spectrum which don’t phase

match during the GA, are made worse by applying compression mask generated

without feedback in that region. The “best” pulse in Figure 3-13B has less intensity, and

is thus broader in time than the unshaped pulse. The temporal profile of the “best” pulse

in Figure 3-13B would appear shorter compared to the unshaped if the plot of the

crosscorrelation was normalized, the fact that the “best” is worse than unshaped is lost

without the intensity dependence. The two plots shown are for two adjacent phase

matching regions, separated by 10 nm of pump spectrum, the resulting “best” pulse is

even worse further in spectrum from the phase matching conditions used for GA

feedback. Phase matching the entire spectrum of interest is critical to pulse

compression.

Figure 3-14. Phase matching acceptance bandwidth of KDP (Blue) compared with BBO (Green) at a single crystal phase matching angle.

SFG of Pump + 800 nm in KDP. Potassium dihydrogen phosphate (KDP), is a

lesser known non-linear crystal compared to BBO in optical spectroscopy. KDP has

significantly better spectral phase matching acceptance bandwidth compared to BBO

when mixing 520 nm with 800 nm. KDP can simultaneously phase match the entire

92

pump spectrum at a single-phase matching angle when mixing with 800 nm in a 100 𝜇m

crystal, as shown in Figure 3-14.

As discussed earlier, BBO can only phase match ~10 nm of pump at a single-

phase matching angle. KDP is ~500 times less polarizable than BBO and with a lower

damage threshold than BBO. KDP is only suitable for processes where the intensity of

the non-linear signal is not important, such as pulse characterization. Once a KDP

crystal was available, X-FROG characterization could be done in a single scan, instead

of piecewise in BBO (as discussed earlier).

Using the SFG signal generated in KDP as a feedback parameter for a pulse

compression allows for significant pulse improvement as seen in Figure 3-15. The “best”

pulse is not fully compressed however. There is wing structure with non-negligible

intensity, making the pulse unusable for a 2D-S experiment. The remaining wing

structure in the compressed pulse, can be related to the highly-structured part of the

uncompressed pulse (see X-FROG around SFG of at 320 nm in Figure 3-15).

93

Figure 3-15. X-FROG and cross correlation of pump + 800 nm pulse before and after compression mask obtained with a GA using SFG in KDP is applied. A) X-FROG of unshaped pulse, B) crosscorrelation of best and unshaped pulse, C) X-FROG of best compression mask obtained from GA.

A

B

C

94

Another trick was used to overcome the inability to simultaneously compress all

the wavelengths using SFG in KDP as feedback. The pump pulse is highly structured in

the long wavelength region as observed in X-FROG (see Figure 3-15A around 320 nm).

A compression GA can be biased to focus on the highly-structured region of the pulse

by blocking the pump spectrum in the Fourier plane for wavelength that generated SFG

signal above with shorter wavelength than 315 nm. Figure 3-16A shows the resulting

compressed pulse, by only focusing on the long wavelength component and blocking

shorter wavelengths. Phase masks are additive and can be mixed and combined, thus

the mask which compresses the long wavelengths, could be combined to the phase

mask which compresses the short wavelengths. Figure 3-16B shows the result of

combining to two phase masks, where one mask compresses the blue side and the

other the red side of the wavelengths. The semi-compressed pulses are short enough

for 2D-S experiments, but not ideal because the pulses have structure limiting the time

resolution of an experiment and making chirp correction in data harder because the

pump chirp needs to be deconvoluted from the probe chirp.

Compressed Pump Pulse. To achieve a compressed pulse, which is near-

transform limited, a pre-compressed pulse (shown in Figure 3-16B) was used as a

starting condition for a GA using two-photon absorption as feedback. Once a pulse is

short enough in time to generate two-photon absorption signal at all the wavelength

components of a pulse a the two-photon absorption detector sensitivity and improved

signal-to-noise can be used to remove the remaining structure and compress the pulse

to near-transform limited. The pulse characterized by X-FROG shown in figure 3-16C

cannot be used as a starting condition because the long wavelength region generates

95

no two-photon response. Figure 3-17A shows an X-FROG trace of a compressed pulse

using two-photon absorption as feedback. A compression mask is usable for ~1-2

months. Figure 3-17B shows an X-FROG trace collected using the same compression

mask as figure 3-17A, but 6 months after the compression GA was run. As time passes,

a compression mask is no longer usable because the energy in the wings starts to

become a problem, as seen in comparing the baseline of the crosscorrelation in Figure

3-17C and Figure 3-17D.

Figure 3-16. Mixing compression mask can allow for pulse with better temporal profile than that achievable directly. A) X-FROG of Compression with the short wavelength region blocked, B) a mixed of the phase mask used for long wavelength compression and short wavelength compression, C) short wavelength compression used for part B.

A

B

C

96

A crosscorrelation temporal resolution is limited by the longest of the two pulses

used. The X-FROG trace of the compressed pump pulse (shown in figure 3-17A)

measures a full width at half max (FWHM) of ~68 fs. X-FROG is achieved by mixing

pump pulse with an 800 nm pulse with ~64 fs FWHM (measured by autocorrelation).

This allows us to conclude that the pump pulse is shorter than 64 fs, because an

autocreation of two 64 fs pulses would measure ~90 fs (√2 ⋅ 64).

Figure 3-17. X-FROG and crosscorrelation of pump pulse + 800 nm pulse before and after compression mask obtained with a GA using two-photon absorption is applied. A) A compressed pulse near transform limited, B) drift in a compression mask collected ~6 months after GA was run, C) crosscorrelation of compressed and unshaped pulse, D) crosscorrelation of a pulse no longer suitable for experiments because of wings.

To fully characterize the pump pulse used for experiments, an interferogram was

measured by generating double pulses with the SLM and scanning over double pulse

delay using SHG signal. The resulting interferogram is shown in Figure 3-18. The lines

connecting the data points are not a fit, but straight lines to show the fringe pattern.

From the interferogram, we measured a pulse width for our pump of ~28 fs.

A B

C D i

97

Figure 3-18. Interferogram generated by generating pulse pairs with the SLM-640 to generate a convolution spectrum. The lines are not a fit, they are lines connecting data points to emphasize the fringe pattern indicative of coherent pulse mixing.

It took 2 years after the 2D-S instrument was built to figure out all the problems

generated by the deformation of the SLM-640 and generate a compressed pump pulse

for 2D-S experiments. The SLM-640 is no longer sold for ultra-fast applications because

the added phase distortions from deformation render the unit essentially useless for its

intended purpose.

Double pulses

Double pulses can be generated through a phase and amplitude change on the

SLM such that the final field, �� 𝐹, becomes two identical clones of the original pulse, �� 0,

with a relative delay 𝜏, given by equation 3-3.

�� 𝐹(𝑡) =1

2(�� 0(𝑡 − 𝜏) + �� 0(𝑡))

(3-3)

The phase and amplitude mask, 𝑀(𝜔), needed to generate �� 𝐹(𝑡) is simple in the

frequency domain, given by equation 3-4 and 3-5. We introduce an arbitrary phase, 𝜙𝑖,

for each pulse in equation 3-4 because it is needed for phase-cycling (discussed later).

It is important to distinguish between the phase of a pulse, given by 𝜙𝑖, and the applied

phase of an SLM mask, given by Δ𝜑𝑖.

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𝑀(𝜔) =1

2(𝑒−𝑖𝜔𝜏+𝑖𝜙1 + 𝑒𝑖𝜙2)

(3-4)

�� 𝐹(𝜔) = 𝑀(𝜔) ⋅ �� 0(𝜔) (3-5)

In equation 3-5, 𝑀(𝜔) is a modulation mask, a term used in Fourier Theory to

describe a function to change one field into another. We use the SLM pixel array to

generate the mask, 𝑀(𝜔). Using Euler’s formula, equation 3-4 can be rewritten in a

form given by equation 3-6, that has a clear amplitude and phase component.

𝑀(𝜔) = 𝑐𝑜𝑠 (−𝜔𝜏+𝜙1−𝜙2

2) ⋅ 𝑒

𝑖 (−𝜔𝜏+𝜙1+𝜙2)

2 (3-6)

Looking back at equations 3-1 and 3-2, there is a simple solution to apply a

phase change on the SLM to generate a mask with the form given in equation 3-6.

Δ𝜑0 = −𝜔𝜏 + 𝜙1 (3-7)

𝛥𝜑1 = 𝜙2 (3-8)

The solutions shown in equation 3-7 and 3-8 are not unique, which SLM array

applies the 𝜔𝜏 term is invariant. However, the SLM pixel arrays are not equal, each has

a different amount of leakage (ability to apply desired phase). Figure 3-19 shows a 500

fs delay pulse pair measured by X-FROG generated by a 𝜔𝜏 phase change with

different SLM arrays. mask0 will generate a pulse with more intensity for the delayed

pulse (shown in Figure 3-19A), while Mask1 keeps more intensity at the non-delayed

pulse (shown in Figure 3-19B).

To see whether having different intensity pump pulses effects 2D-S experiments,

we collected 2D-S data for the molecule DASPI. One experiment, by making double

pulses with Mask0, and another with Mask1. The two 2D-S data sets were

indistinguishable, so further effort was put into the issue of pump pulse intensity.

99

Figure 3-19. Difference in intensity of a pulse pair measured by X-FROG because of SLM array leakage. A) Pulse pair applied using mask0, B) pulse pair applied using mask1.

Broadband Seed/Probe Pulse

Figure 3-20. Typical white light spectrum generated in sapphire with different pump (800 nm) fluence. The fluence range shown is that for stable white light spectrums. The intensity is not normalized.

Broadband spectrum pulses are used for both seeding NOPA generation and as

a probe pulse for 2D-S spectroscopy. The broad band spectrum (white light) generated

in sapphire is pump fluence dependent, the range shown for stable spectral white light

generation in Figure 3-20. White light generation is a high-order non-linear process24

making generation very sensitive to the phase of the fundamental pulse. NOPA

generation becomes unstable if great care is not taken to generate a white light seed

with no detectible color difference in the beam except an intensity profile (seen by eye

A B

-

100

on a cotton business card). The ability to control the focal point, fluence, and overlap in

sapphire of the 800 nm beam is critical to generate stable white light to seed the NOPA.

The optics used to generate the NOPA seed are described in chapter 2.

The white light probe is generated with a 3 mm waist beam of 800 nm focused

using a 25.4 mm focus round singlet lens onto a 2 mm thick sapphire window. The

sapphire window is uncoated with 𝜆/10 surface flatness and 10/5 scratch/dig (CVI). The

white light generated in sapphire is collimated with protected aluminum coated off-axis

parabolic mirror with EFL of 25.4 mm (ThorLabs, catalog number MPD019-G01). For

both NOPA seed and 2D-S probe, we specifically choose to generate the spectrum

shown with less fluence (Figure 3-20), because it allows for more wavelength range with

less chirp. Less chirp and more spectral range is a must to generate a broadband

NOPA pulse. However, the probe spectrum should be determined by the experiment. If

low wavelengths are not of interest, the spectrum generated with more fluence is more

stable in spectral intensity, improving signal to noise.

As mentioned earlier white light is very sensitive to the fundamental beams

phase stability. Air currents are enough to change the spectrum, phase and intensity of

the white light. It is important that the region around white-light generation is isolated.

Even with isolation the white-light generated has short (shot-to-shot) fluctuations and

long time (hours) fluctuations. The oscillations effect 2D-S data, because they add noise

to the Fourier Transform required for data processing. To help reduce the noise we use

self-referencing, where a part of the probe is split off with a beam splitter (thin wedge)

and propagates nearly the same path as the probe, except reaching a region of the

sample that is not excited by the pump (~1.5 mm separation at the sample). Self-

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referencing allows to distinguish between white-light oscillations from noise and

oscillations from 2D-S signal.

Pump-Probe Overlap

2D-S signal is generated when the pump and probe overlap in space and time.

The SLM controls the pump-pump delay (𝜏), and a commercial delay stage, DDS220

(ThorLabs) is used to control probe delay (𝑇). The reproducibility of the probe delay

stage is ~± 0.45 fs for a signal retroreflection configuration. Spatial geometry for overlap

was determined so a 10 cm by 10 cm footprint optical cryostat with 25.4 mm windows

could be places at the sample position. A long 15 cm EFL off-axis parabolic mirror

(OAPM) with a protected aluminum coating (Janos) is used for pump and probe overlap

to allow room for a large sample holder. The beams travel parallel to reach the OAPM

with a separation of ~6 mm and are thus focused at the same point without chromatic

aberrations. The beams travel with a small separation angle of ~2º to the sample

because of focusing. Focusing spots sizes were measured to ensure that the probe was

smaller than the pump, such that the probe did not detect any region of the sample not

excited by the pump. The probe spot size at the sample is 80 𝜇𝑚 and the pump spot

size is 170 𝜇𝑚 at sample, meeting the rule of thumb for pump-probe overlap (that the

pump be at least twice as large as the probe).

Sample Holder

Work done to bench mark our new instrument employed a liquid sample inside a

2 mm optical path length cuvette with a PTFE coated magnetic stir bar to prevent

thermal heating effects from the laser.

In the case of merocyanine-540 (MC540), stirring the solution was insufficient to

avoid detection of a long-lived isomer state (4 ms). Instead a commercial laser-dye

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pump (Spectra-physics) was used to flow solution through a home built flow cell with 2

mm optical path length. Cavitation from the pump was avoided using a gravity fed

reservoir with larger diameter feed tubing.

Measuring Signal

Once the 2D-S signal has been generated at the sample, it co-propagates with

the probe pulse (described in detail in chapter 2). A multi-core fiber with four individual

inputs and one output designed to place at the entrance slit of a spectrograph is used to

pick up the probe and reference beams after the sample (Andor, catalog number SR-

OPT-8027). AR coated fiber couplers were used to collect the beams into the fibers

(Newport, catalog number F-C5-S3-543).

The white-light beam has residual 800 nm and a fiber coupler has a tight focus,

thus the 800 nm left over has enough fluence to burn an optical fiber and/or generate

white-light in the fiber. A high-pass filter is required to remove wavelengths longer than

700 nm before entering the fibers, but after the sample. It is important to not filter 800

nm before the sample because, even a thin 1 mm filter will add a significant amount of

GVD to the white-light.

A CCD camera with 1300x1030 pixels (Roper, MicroMax 1300Y), and

spectrograph (Oriel, MS260i) were used to disperse the probe and reference into

frequency components to be measured. The CCD has a chip depth of 20 mm from the

face of the camera, and the spectrograph has an imaging length of 10 mm from the exit

slit, making it impossible to place the CCD at the correct location. Although the CCD

could not be used to image, it could be used to collect a spectrum which is what is

needed for 2D-S. Since the imaging points are not coincident, the wavelength

dispersion on the camera from the spectrograph is not linear at the chip position, thus a

103

careful calibration is required. Four spectral lines are used for calibration, 3 from Hg-Ar,

and one from a He-Ne laser. Three points from Hg-Ar lines in the visible are not enough

points for a good calibration.

Instrument Control

Control of the instruments was achieved through a LabView interface. A program

was written by our group to allow coordinated control of the SLM-640, the probe delay

stage, the spectrograph, and the CCD camera. There are two independent parameters

in 2D-S, 𝜏 and 𝑇. The data can be collected by holding one parameter fixed, and

scanning all the 2nd parameter, then repeating for every value of the 1st parameter.

Which parameter, 𝜏 or 𝑇, is fixed while the other is scanned depends only on

experimental factors. It is better to scan 𝜏 and hold 𝑇 if a fast pulse shaper is used with

a slow stage. This procedure minimizes the number of times the stage needs to be

moved. In our setup, the pulse shaper is slower (response in seconds) so it is better to

scan 𝑇 and hold 𝜏. The current program scans 𝜏 and holds 𝑇, the next user can reduce

data collection time by modifying the program to scan 𝑇 and hold 𝜏. A non-trivial change

in the logic of the program, but worth the eventual saved time, a rough calculation

estimates that a 28 hour experiment (current average collection time) could be cut down

to ~18 hours.

Data Collection

Data collection must adhere to the Nyquist limit of the highest frequency

oscillation we want to detect. The high frequency edge of the pump pulse spectra is

~470 nm, which corresponds to a period of ~1.57 fs, thus a sample of Δ𝜏 = 0.784 fs is

required to overserve oscillation resulting from 470 nm excitation. The range of 𝜏 delays

104

which needs to be measure is determined by the dephasing time of the system (needs

to be empirically determined, explained later). Data must be collected until the signal

decays—at least decays into the noise. Truncating a decaying oscillation leads to “sinc-

wiggles”, shown in Figure 3-21D, a well-known artifact in NMR. However, collecting

unneeded data past when the signal has decayed into the noise leads to a nosier 2D-S

plot, because baseline noise transfers into the FFT, as shown in figure 3-22. Before

collecting a full 2D-S data set on a new system, a scouting experiment must be

performed to figure out the range of 𝜏 that needs to be scanned.

Figure 3-21. Effects of truncating data and Hamming windows on the resulting FFT. Figure adapted from Ref 13.

A common method used to expedite the collection of data when only the peak

location matters and not the line-width, involves collecting less data than the range

needed to ensure the signal has decayed and using a Hamming window to force the

signal to zero to prevent sinc-wiggles, as shown in Figure 3-21E. Windowing the data

this way leads to broadening of the FFT, as shown in Figure 3-21F. Artificially

broadening the FFT leads to 2D-S plot that lose the physical meaning. A slice of 2D-S

Time Frequency

A B

C D

E F

FFTሱሮ

105

data would no longer match an equivalent TA spectrum collected at the corresponding

excitation wavelength.

Figure 3-22. Effect of collecting unneeded data past the signal decay on the FFT signal-to-noise. Figure generated by James Keeler and reproduced with permission.

Improving Signal-to-Noise

The low signal intensities from 2D-S result in low S/N. Techniques have been

adopted to raise signal and reduce noise. One method proposed by Zanni, called

phase-cycling20 is based on the phase dependence of the 2D-S signal. It allows

distinguishing phase dependent from non-phase dependent processes, and removing

unwanted non-phase dependent signals. In pump-probe geometry the probe carries the

2D-S signal, as well as all other signals measured by the probe (i.e. TA and Raman).

Phase invariant signals, are noise in 2D-S Spectroscopy. The phase dependence of the

2D-S signal to pump phase can be explained by looking back to equation 2-10, and

introducing a phase dependence to the pump pulses given by the difference in phase

between the first and second pulse, Δ𝜙12:

𝑅(3) ∝ 𝑒𝑖Δ𝜙12 ⋅ 𝑒𝑖𝜔𝐵𝐴𝜏 ⋅ 𝑒−Γ𝜏 ⋅ 𝑒−𝑇𝜏𝐵

(3-9)

The phase dependence on the response, given by equation 3-9, results in a sign

change if Δ𝜙12 = 𝜋. Figure 3-23 shows the result of phase cycling a 2D-S experiment

with a Δ𝜙12 = 0 and 𝜋 pulse pair signal. The detected signal by a Δ𝜙12 = 0 scan (shown

Time

Frequency

106

in red), can be subtracted from the signal generated by a Δ𝜙12 = 𝜋 scan (shown in

blue). The 2D-S response is equal for both experiments, but with opposite sign. The

transient absorption signal is phase invariant, so it remains the same. By subtracting the

two scans, the TA signal can be subtracted, and the 2D-S signals are additive, result of

subtraction is shown in green.

Figure 3-23. Phase cycling data shown in green results from subtracting signal collected with zero phase (red line), and difference in phase of 𝜋 (green line). Figure

reproduced from Ref 20 with permission of the PCCP Owner Societies.

The scheme used in our instrument is that suggested by Zanni,20 shown in

equation 3-10.

𝑆𝑃𝐶 = 𝑆(𝜙1 = 0, 𝜙2 = 0) − 𝑆(𝜙1 = 0,𝜙2 = 𝜋)

+𝑆(𝜙1 = 𝜋, 𝜙2 = 𝜋) − 𝑆(𝜙1 = 𝜋,𝜙2 = 0)

(3-10)

𝑆𝑃𝐶 represents the signal obtained by phase cycling. The scheme from equation

3-10, takes full advantage of the phase control provided by the SLM. In the article by

Zanni presenting phase-cycling,20 the claim is made that phase-cycling also removes

scatter because scattered light is not phase dependent. However, we discovered that

this method does not remove scatter, it only reduces it. The amplitude of a given

107

frequency component in a pulse-pair is phase dependent, resulting in phase

dependence in the scatter. To understand, we need to go back to the modulation mask

applied to make double pulses with arbitrary phase 𝜙1 and 𝜙2 on the SLM, from

equations 3-1, 3-7 and 3-8. We get

𝐴𝑆𝐿𝑀(𝜔) = |cos (−𝜔𝜏 + 𝜙1 − 𝜙2

2)|

(3-11)

For Δ𝜙12 = 0,

𝐴Δ𝜙12=0(𝜔) = |cos (−𝜔𝜏

2)| (3-12)

The maximum amplitude for frequency 𝜔 occur at,

𝜏max = 𝑁 ⋅ 𝑇𝑝𝑒𝑟, (3-13)

with N being 0 and an integer, and 𝑇𝑝𝑒𝑟 the period of the frequency 𝜔. The amplitude is

zero when,

𝜏zero = (𝑁 +1

2) ⋅ 𝑇𝑝𝑒𝑟

(3-14)

For Δ𝜙12 = 𝜋,

𝐴Δ𝜙12=𝜋(𝜔) = |cos (−𝜔𝜏 + Δ𝜙12

2)|

(3-15)

𝐴Δ𝜙12=𝜋(𝜔) = |sin (−𝜔𝜏

2)| (3-16)

Thus, the amplitude of a frequency component (intensity available to scatters) will

oscillate as a cosine and sine pair between a signal collected with Δ𝜙12 = 0 and 𝜋.

When one is maximized, the other is zero. Scatter cannot be subtracted by phase

dependence because when one pulse pair has maximum scatter, the subtracted pulse

pair will have zero scatter at that frequency. Leading to an oscillation in the scatter

signal for each 𝜔 in a pulse pair, at its own frequency, which will get picked up by an

FFT. The scatter is wavelength resolved onto the CCD, so an individual pixel will only

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see scatter from the wavelength it corresponds to. The oscillation frequency will

oscillate at the same frequency of the scatter wavelength; thus, scatter will only appear

on the diagonal of 2D-S plot.

This is a significant advantage to TA, where scatter is detected everywhere that

scatter occurs. 2D-S allows systems with high scatter to be studied, limited only by not

being able to remove scatter from the diagonal. Intuitively it might seem like rotating the

frame of the 2D-S signal would eliminate scatter because the sampling frequency would

not match the frequency of the scatter, but this is not the case. Scatter will always follow

the relationship shown above, even if 𝜔 is shifted to 𝜔𝑟𝑓 = 𝜔 − 𝜔𝑖, the scatter will

appear at 𝜔𝑟𝑓 instead and still be on the diagonal of a 2D-S plot.

Data Processing and Management

Data sets are large 3D matrices, with a 𝜏 axis, 𝑇 axis, and 𝜆𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛 axis. A data

file would be ~1.3 GB if data was saved in double precision as a text file with minimal

formatting. Time was spent to reduce file sizes such that our computers would not take

30 mins to import data files into MatLab. We focus on ease of data storage and

reducing the file size without reducing the information. The filetype we settled on is tab

delimited with the first line containing the dimensions of the 3D matrix, and the second

line containing all the elements of the matrix. This file is easy to import into MatLab by

using the commands:

>> fid = fopen('DataFile'); % opens the file (don't forget the extension and path)

>> arraySize = str2num(fgetl(fid)); % reads the first line

>> data = str2num(fgetl(fid)); % reads the second line

>> data = reshape(data,arraySize); % reshape the data into a 3D matrix

>> fclose(fid); % closes the file to clear space

Once the data was processed in MatLab, the results were saved as ‘.m’ files.

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New versions of LabVIEW allow MatLab to be run within the LabVIEW

environment, allowing the 3D data to be saved as a “.m” directly. The file type is very

efficient at storing matrices (e.g. a ‘.txt’ file in the format above would be ~100 MB, while

the same information in a ‘.m’ file already stored as a 3D matrix, with variable names

and headers would be ~40 MB). Some of our instrument drivers are not supported on

new LabView versions, so we could not directly implement this saving option.

The output of the data collection program is a differential transmission,

ΔT =Iprobe

𝐼𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒− 1

(3-17)

The best instrument sensitivity will not be below a 1×10−6 Δ𝑇, which corresponds

to a Δ𝐴 of 0.4 𝑚𝑖𝑐𝑟𝑜𝑂𝐷. keeping only 6 decimal places of precision in our data files

greatly reduce the file size without loss of information.

Expectation Versus Reality

Looking back at Figure 2-23 and 2-24, the pump-probe 2D-S plots don’t match

with expectation from the concept of 2D spectroscopy when introduced in books or

lectures. We don’t observe well defined “blobs” of on/off-diagonal elements that show

coupling. In electronic 2D-S, there are many overlapping signals; making it difficult to

assigned signals to certain transitions. The advantage of 2D-S vs TA experiments,

includes the reduction of scatter as described earlier, and overcoming the limitation of

temporal bandwidth and spectral bandwidth of a pulse being coupled, Δ𝑡 ⋅ Δ𝜔 ≥ 2𝜋 ⋅

0.441 (for a Gaussian pulse). For example, a TA experiment cannot independently

excite and probe two transitions separated by less than the bandwidth of the pump,

because both states will be simultaneously excited. This is not a problem in 2D-S

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allowing for the possibility of observing coherent coupling between two similar

chromophores

111

CHAPTER 4 MEROCYANINE-540

“If we spent more time doing experiments than making figures, we could change the world; but a good figure speaks a thousand words—”

Valeria D. Kleiman

Merocyanine-540 (MC540), as introduced in Chapter 1, has been studied for

over 40 years but the mechanism for isomerization and triplet state formation is still

elusive. Using the newly built 2D instrument we hoped to shed light into the excited

state dynamics.

Merocyanine-540 (MC540), shown in Figure 4-1, was designed as a molecular

probe to stain cells33. The functional groups of MC540 allow it to integrate into a lipid

membrane and to be soluble in both polar34 to non-polar35 solvents. The absorption and

fluorescence of MC540 are dependent on local environments, making it suitable for

probing micro-environments36 such as the charged surface of a nerve axon firing37.

Figure 4-1. Chemical structure of Merocyanine-540 in trans-isomer configuration, with red arrow showing carbon double bond assigned to rotation for cis-isomer configuration.

There are a few properties known about MC540, that have strong experimental

support: (1) MC540 forms aggregates in water,38 and dimers when on a lipid

membrane37, both aggregation and dimers are concentration dependent. (2) MC540

forms a triplet state upon visible light irradiation that can be quenched by saturating the

solution with oxygen.3 (3) In the ground-state at room temperature in ethanol, only one

isomer configuration of MC540 is detected by 2D-NMR.3 (4) A model system of MC540

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shows a similar TA spectrum when isomerized from trans to cis configuration, thus trans

configuration is assumed for MC540 in the ground state.39. (5) Isomerization and

emission are competing excited state deactivation pathways; if one goes up, the other

goes down and the ratio of the yields is temperature dependent.40 (6) the cis-isomer

absorption spectrum is red shifted and has a lifetime that depends on temperature.34 (7)

Solvent polarity greatly affects the isomerization rate and yield, but the values for

ethanol and methanol are similar.41

The seven properties listed above have strong experimental support. Pinning

down which carbon double bond isomerizes experimentally has been a matter of debate

for some time, but because cyanine is the chromophore of MC540, a large spectral shift

on the chromophore absorptions would not occur if an isomerization occurred at one of

the end double bonds. Working assumptions about MC540 will be based on the above

seven properties: from 7, methanol and ethanol have similar values for solvent polarity,

thus, considering point 3 and 4, we can assume that the trans-isomer configuration is

also the ground state in methanol. The highest isomer yield and lowest emission yield at

room temperature is observed in methanol34, making it the best solvent to look for a

spectral signature of excited state isomerization because overlap of signals is minimized

(explained below).

Overlapping Signals

Figure 4-2 show the transient differential absorption of MC540 10 𝜇𝑠 after

excitation3 in the top panels, along with the steady state absorption spectrum (blue line)

and emission spectrum (red line) in the bottom panels for comparison. Figure 4-2A and

4-2B show the differential absorption in a deoxygenated solution and oxygenated

solution respectively. The cis-isomer spectral signature (isolated in Figure 4-2B by

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quenching the triplet with oxygen) overlaps with the ground state bleach and expected

stimulated emission in a differential absorption experiment (i.e. pump-probe 2D-S and

transient absorption). Making it difficult to isolate excited state dynamics for different

species. Methanol was used in all our experiments to minimize the effect of overlap by

maximizing the isomer generation, and minimizing the overlapping stimulated emission

(red line).

Figure 4-2. Spectral signature of long lived transients top panel, 10 𝜇𝑠 after excitation with a 10 ns pulse of 532 nm. Normalized absorption (blue) and Emission (red) shown in bottom panel. A) Cis-isomer and triplet state spectral signatures in deoxygenated ethanol, B) cis-isomer spectral signature isolated in oxygenated ethanol. The top panels are reproduced from Ref 3 with permission of The Royal Society of Chemistry.

Method

Merocyanine at ~99% purity, purchased from ThermoFisher was used without

further purification. The solvent, Methanol, Extra Dry, 99.9% purchased from Fisher,

was further distilled to prevent water aggregates when doing experiments to observe

aggregates and the triplet state. After we established there was no triplet and no

aggregation (discussed later), HPLC grade methanol (Fisher) exposed to Florida

humidity without degassing was used for ultrafast experiments. Being able to use

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atmosphere exposed solvent was critical to allow a high flow cell (described in chapter

3) to avoid measuring MC540 long lived isomer signals (discussed later).

Steady-state absorption measurements were performed on a UV-VIS Jaz

spectrometer (Ocean Optics), and emission and excitation spectra were collected on a

Fluorolog-3 (Spex). When optical densities bellow 0.05 needed to be measured a Cary

50 Probe (Varian) UV-VIS was used. Steady state measurements were performed with

and without flowing comparing spectra we concluded the light sources for absorption

and emission were not intense enough to make any detectible amount of cis-isomer or

triplet for a steady-state measurement. Steady state absorption was collected for

various optical densities in a 2 mm cuvette. Steady state emission and excitation

spectra were collected with a 1 cm path length cuvette at ~0.005 OD sample to

minimize self-absorptions.

Throughout ultrafast experiments, a ~0.3 optical density sample was used. The

spot size of the pump for 2D-S experiments is measured at 170 𝜇𝑚 (beam waist) and a

pump energy of 20 nJ/pulse (10 nJ/pulse of a pulse pair) is used for excitation. We

measured 2D-S and TA up to 200 nJ/pulse (maximum without attenuation) without

observing non-linear absorption, but pump scatter needs to be considered because

scatter intensity transfers into TA and 2D-S data, settling on 20 nJ as a compromise

between signal intensity from the sample and noise from scatter intensity.

The pump-probe 2D-S instrument is home built with pump spectrum from 475 nm

to 565 nm and pulse width of ~28 fs (instrument described in chapters 2 and 3).

Transient absorption data was collected using a commercial TA instrument, Helios

(Coherent). The pump energy used for TA was 50 nJ/pulse, picked to match the fluence

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used for 2D-S. TA spot size was not measured, fluence was estimated by the focal

length and beam size.

2D-S data collection and processing is discussed in Chapter 2 and 3.

SVD/MCR-ALS: TA data was processed using singular value decomposition

(SVD) and multivariate curve resolution-alternating least squares (MCR-ALS)42 in

MatLab. SVD breaks a signal down to its basic components, or “eigen spectra”; if TA

data is the input, SVD will determine the minimum number of spectral components

needed to reproduce the TA data. Once the eigen spectra are determined, the TA signal

is fit using a linear combination of the eigen spectra, where the eigen spectra determine

the profile of the signal, and the time dependent constants (amplitudes) determine the

time evolution. Eigen spectra depend on the basis set used and SVD has no constraint

on the basis set leading to rotational ambiguity which means solutions are not unique

and often converge in a basis without physical interpretation. Finding the correct basis

set to show the eigen spectral components is achieved through MCR-ALS by applying

constraints to the SVD eigen components and amplitudes to conform to the physical

interpretation of the data. For example, non-negativity in the amplitude components

used for the linear combination is critical for TA data because TA spectral profiles can

have negative Δ𝐴(𝜆) values (i.e. ground state bleach and stimulated emission), but the

species generating the negative signal always has real and positive amplitude

(corresponds to the population of the state generating the spectral signal). Even if the

molecule absorbing the TA pulse is destroyed through the absorption of a photon

(photo-bond breaking for example) such that the ground state is not recovered, the

physical amplitudes will still be non-negative because the lack of recovery of the bleach

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is a spectral signature of the new species population. SVD and MCR-ALS cannot deal

with shifts in wavelength seen in TA and 2D-S from vibrational cooling and solvent

reorganization because each vibrational state gives a spectral signature different

enough to require its own spectral eigen component, and each vibrational eigen

component contributes so little to the overall signal (it rises and decays very quickly)

that the component is lost in the noise of an SVD fit.

Results

Steady-State

Merocyanine-540 is in a family of chromophores that is known to show

photodegradation over time. 2D experiments often take several days of continuous laser

excitation and detection to generate good S/N data sets because of the weak nature of

2D signals arising from a 3rd order weak perturbation. To ensure samples would not

photodegrade (or show no evidence) over the course of the experiment, a large volume

(~0.5 L) of dye was prepared to flow through the flow cell, and the absorption spectrum

of a sample from the reservoir was tested daily to ensure no detectable amount of

degradation.

Figure 4-3 shows the absorption spectrum (black) and emission spectrum (red)

of MC540 in methanol along with the pump spectrum (green) used in the 2D-S

experiments. The absorption spectrum (black line) has three bands/shoulders indicated

with arrows (determined by looking at the change in spectrum as function of wavelength

inflection points) with the maximum at ~555 nm, a band at ~518 nm the and a shoulder

at ~480 nm. The emission spectrum appears as a mirror image of the absorption,

indicative of similar Franck-Condon character of the ground state and excited state

vibrational states. The emission is red-shifted to absorption with a maximum at 580 nm.

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The pump spectrum (green) is the spectrum after pulse shaping (discussed in Chapter

3) and covers the three absorption bands/shoulders. The pump spectrum was

specifically chosen to have more intensity at short wavelengths components to ensure a

detectible 2D-S signal from the low absorption region of MC540.

Figure 4-3. Steady state spectra collected for MC540 in methanol. Absorption is shown in black, emission in red, and the pump spectrum used for 2D-S is shown in green

The excitation spectrum of MC540 was collected with detection at 600 nm

(negligible absorption from MC540) and at 660 nm to ensure that emission and

absorption had no excitation wavelength dependence. Figure 4-4 shows the excitation

spectra collected at 600 nm (blue) and 660 (orange) normalized to the absorption

spectrum (red dashed).

MC540 is reported to form dimers and aggregates in water.38 A dilution study of

MC540 was performed in wet methanol (HPLC grade methanol left exposed to high

humidity environment) to see if the water concentration would cause problems with

aggregation. Absorption spectra were collected at dilutions from 0.005 OD to 2.0 OD to

look for signatures of aggregations. Figure 4-5 shows the normalized absorption spectra

of the high optical density samples (where aggregation should be more apparent) with

Pump

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the unnormalized data shown below. For comparison, the absorption spectrum of

MC540 with optical density ~0.005 prepared in extra dry methanol (described earlier) is

superimposed (dashed black line) on the normalized spectra. From Figure 4-5 we can

conclude that “wet” methanol does not lead to aggregation, and from the extensive

range of optical densities we probed, if there is a dimer configuration in methanol it has

no observable concentration dependence in the limit of optical spectroscopy

concentrations.

Figure 4-4. Excitation Spectrum of MC540 in methanol with detection at 600 nm (blue) and 660 nm (orange). Sample optical density of ~0.005 OD in 1 cm cuvette was used. Spectra are normalized to absorption spectrum (dashed red).

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Figure 4-5. Dilution study of MC540 absorption prepared in atmospherically wet methanol. The top panel shows normalized absorption spectra collected in wet methanol, superimposed with the normalized absorption of MC540 prepared in extra dry methanol with ~0.005 optical density (black-dashed).

Long Lived Isomer

MC540 has a long lived cis-isomer with a reported lifetime of ~6 ms in methanol

at room temperature.3 The rep-rate of an experiment becomes a consideration when

measuring signals that persist longer than the time between excitation pulses (1 ms for

1 kHz laser). Figure 4-6 shows the TA signal observed before “time-zero” when stirring

is used to mix the solution (green). The signal measured is the difference between the

probe and reference signals because the sample in the vicinity of the probe pulse does

not have enough time to relax to the ground state trans conformation before the next

Concentration

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pump pulse arrives to re-excite the sample. The data in red shows the result of not

mixing the sample, bringing out the spectral signature of the cis-isomer reported in the

literature. The absorption spectrum is shown as a dashed black line for comparison,

along with pump pulse spectrum (20 nJ/pulse) used for TA as blue dashed line.

Figure 4-6. Transient signal detected before time-zero when the sample is not refreshed between pump pulses. Not stirring is shown in red and with stirring in green. Dashed lines are the absorption spectrum of MC540 (Black dashed) and pump spectrum with 20 nJ/pulse (blue dashed).

Starting a 2D-S or TA experiment with a combination of a ground state and

excited state increases the complexity of data analysis because the signals will overlap

and the ground state cannot be assumed.

Figure 4-7 shows TA collected before “time-zero” when using a high rate flow cell

(described in Chapter 3) to refresh the sample in-between laser excitations for 2D-S

experiments with no detectible difference between probe and reference. Figure 4-7A

shows one spectrum, and figure 4-8B shows spectra for many several times before

time-zero, to emphasize that the small off-set signal away from Δ𝐴 = 0 is not isomer

signal but an experimental artifact of not using a pump-off scenario to isolate differences

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between probe and references spectrum (2D-S does not need a pump-off case,

because the artifact is a “TA signal” which is subtracted by phase cycling).

Figure 4-7. Transient signal observed before “time-zero” when adequately refreshing sample between consecutive excitation pulses. A) One time before zero, B) many times before zero for comparison.

A home built optical cell and a commercial optical cell (Starna Cells, catalog

number 48-Q-2) were used for flowing experiments. Figure 4-8 shows the difference in

flow between the two, where the blue arrows are flow directions and the red arrow is

laser propagation direction. Both cell have a sample path of 2 mm. The home built cell

(Figure 4-8A) would flow the solution without a direction change, while the commercial

cell (Figure 4-8B) would flow the solution with a 90 degree turn. Use of the commercial

cell results in pump scatter picked up in an FFT of the data (discussed in chapter 3).

The pump scatter resulting from commercial flow cell is low enough to not be observed

on the detector, unless the probe light is blocked (only background noise) and the

averaging typical for experiments is used. We know the scatter results from the flow

direction and not the quality of the glass, because when the flow is turned off, no scatter

is observed. Time constraints left us not choice but to use the commercial cell for

experiments on MC540 when the home built cell became unusable from a solvent-

gasket mismatch that required replacement of all the components (note to future

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student, replacement parts are in the lab and the cell needs to be rebuilt). As such, 2D-

S data presented has scatter along the diagonal which is picked up as extra intensity on

the detector (negative Δ𝐴).

Figure 4-8. Solvent flow difference between home build flow cell and commercial flow cell used. A) home built cell flow leads to no scatter, B) commercial flow cell leads to scatter from flow path.

Two-Dimensional Spectroscopy

Experimental conditions are described in chapter 3 and in the methods section of

this chapter. All 2D-S plots of MC540 we present are normalized to the absorption

spectrum of MC540 allowing differences in excitation wavelength to be more easily

observed because the number of photons absorbed contribution to the signal intensity is

removed (equivalent to assuming, the sample absorbs the same number of photons at

every excitation wavelength, so the data can be read as “if photons are absorbed at

excitation… the system will show a response at the detection wavelength…”). Data

collection takes a long time (~30 continuous hours for the 2D-S presented here), and is

limited by how long the laser is stable. Therefore, non-uniform time steps for 𝑇 are used:

fine time delay steps for early times, to observer fast dynamics and larger steps with

longer delay time.

2D-S data for MC540 has fast early time (instantaneous to 4 ps) dynamics, that

is different from longer excited state dynamics (4 ps to 1 ns). The early and “long” time

dynamics will be discussed separately. At all times, there will be a negative signal on

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the diagonal (black line) arising from pump pulse scatter. Scatter does not decay with 𝜏

so there will be sinc wiggles around the scatter peak (see chapter 3) and scatter is not

constant, so it will change in intensity randomly in time and spectrum.

Three regions of the 2D-S plot will dominate the changes in the signal observed

over time, 𝑇. Figure 4-9 is one 2D-S plot (left panel) for 𝑇 = 0.3 ps, after solvent Raman

has dissipated, which will be used to explain what each region represents and how to

follow the data before we go into how the 2D-S signal changes in time. The right panel

shows the expected signals from the excited states of MC540 (where 2D-S signal

should appear). The horizontal axis is excitation wavelength, the vertical axis is

detection wavelength. A region of the plot can be read as “what is the signal observed

when exciting at 𝜆𝑒𝑥𝑐𝑖𝑡𝑎𝑎𝑡𝑖𝑜𝑛 and detecting at 𝜆𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”. As described in chapters 2 and

3, pump-probe 2D-S leads to absorptive signals so the intensity in the z-axis is a

differential absorption observed by the probe. The colors used to represent intensity on

the 2D-S plots are RGB for negative signals (less absorbed light means more light

reaching detector), and grey-scale for positive signals (more absorption means less light

reaching detector). This convention was chosen because positive signals give us little

information from the data we collect (except for very specific things which will be pointed

out), so emphasis is place on the negative signals with this color convention.

MC540 has maximum absorption at 555 nm (see figure 4-3), so we expect a

negative signal to be detected in this region from ground state depletion (purple in

Figure 4-9). The emission spectra of MC540 is maximized at 580 nm (see figure 4-3),

so we expect a negative signal from stimulated emission in this region (magenta in

Figure 4-9). From Figure 4-2 and 4-6, we can expect to see a positive signal from

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absorption of the cis-isomer (cyan spectrum in right panel) once it is formed around 580

nm detection, the same region as a negative signal from stimulated emission (cyan

circle in figure 4-9 shows the only region of the 2D-S data where the cis-isomer signal

will be detected).

Figure 4-9. 2D-S signal for MC540 at 𝑇 = 0.3 ps. Figure is described in text.

Early time 2D-S

Figure 4-10 shows the early time evolution of MC540 up to 4ps. The changes

observed, are: (1) an increase of negative signal detected at 580 axis, which appears as

a negative signal growing in the vertical direction; (2) a positive signal at early times

detected at 580 nm with excitation at 490 nm, quickly disappears in 1 ps and is replaced

by a negative signal; (3) The most intense negative signal (blue color) grows in size and

intensity and is not at the peak of the absorption spectrum of MC540 but at ~535 nm

excitation wavelength (this result requires spectral component analysis to separate

overlapping signals to understand, discussed later after TA experiments are preformed).

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Later time 2D-S

Figure 4-11 shows the later time evolution of the 2D-S signal. Two changes

dominate the signal: (1) intensity profile of the negative signal is shifting horizontally

along the excitation direction (use green color contour as a reference with purple guide

lines). The data is plotted vertically in time to emphasize the shift of the negative

absorption signal in excitation wavelength (leftwards along horizontal axis); (2) the peak

signal intensity of the negative signal (blue color) begins to decay. The 2D-S data is

hard to interpret and relate back to a physical process; the overlap of all the signals

make it difficult to conclude anything other than the excited state dynamics for MC540

are excitation wavelength dependent.

Our 2D-S data has too much noise to preform SVD and global fitting to isolate

overlapping signals. A TA experiment coincides to a vertical slice of the 2D-S data at

the same excitation wavelength. Therefore, three TA experiments were performed to

probe MC540 at the regions of interest observed from 2D-S. Excitation at 490 nm gives

a positive signal at early times where we expect the cis-isomer signature and excitation

at 517 nm and 555 nm absorption bands show different dynamic, so TA was also

performed at these wavelengths.

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Figure 4-10. Snap shots of the time evolution of the 2D-S signal of MC540 in methanol at early times. 𝑇 time of 2D-S plot is indicated in white in each panel.

127

Figure 4-11. 2D-S data for later times of MC540 in methanol. Negative numbers are shown in color scale, and positive numbers in grey scale, with black set to zero; Black dashed line across is the diagonal. Grey vertical lines are guide lines to allow the shift in the excitation axis to be observed.

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Transient Absorption

Transient absorption data was desired at the three excitation wavelengths of

interest: 490 nm, 517 nm, and 555 nm. The three wavelengths collected were 480 nm

(easier to generate OPA with more stability), 515 nm (commercial instrument would

generate OPA centered at 515 nm when 517 nm was entered) and 555 nm. All three

excitation wavelengths were attenuated to a power of 50 nJ/pulse at the sample

position. TA was collected out to 4 ns, with steps size of 0.5 ps until 1 ns, and 2 ps

steps until 4 ns. As discussed earlier, SVD cannot fit a shift in spectrum, which we

observe in 2D-S at early times (see Figure 4-10 for detection around 590 nm). We know

this signal to be vibrational cooling from previous time resolved emission studies.43

Once complete data sets for each excitation wavelength were collected with high S/N,

SVD was performed to isolate overlapping signals. Figure 4-12 shows a TA spectrum of

data collected at 480 nm excitation to give an idea of the quality of TA data needed to

get excellent fits acquired from SVD/MCR-ALS analysis (next section).

Figure 4-12. TA data collected for MC540 in methanol with excitation at 480 nm (blue arrow). Each spectrum is a 5 ps step starting at (red) to 4 ns (blue). Pump scatter is blocked in the spectra shown.

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SVD / MCR-ALS

SVD is tricky to understand because it looks like TA data, someone familiar with

TA but not SVD, might confuse a spectral component with a TA spectra, and an

amplitude temporal evolution with a kinetic trace of a TA spectrum at a single

wavelength. If you skipped the method section of this chapter and are not an expert in

SVD, please go back and read parts concerning SVD and MCR-ALS, before this

section. TA data after 5 ps was used for SVD (after vibrational cooling has finished).

Figure 4-13 shows the results for SVD using the TA data collected at 555 nm

excitation. There are only 2 significant spectral components. Meaning two eigen spectra

can be used to reproduce the data set with minimal error deviation from the data. All

three TA data sets at different excitation wavelengths had only two significant spectral

components.

Figure 4-13. Singular Value Decomposition values of TA data for MC540 in methanol excited at 555 nm. Inset shows all singular values of the TA data matrix.

MCR-ALS was used to place constraints on the SVD spectral components, to

show the components in a basis which would allow physical interpretation

corresponding with TA experiments. The only constraint used was non-negativity in the

spectral amplitudes (see Appendix if it is not clear why), so that spectral components

could not change sign (discussed in methods), only decay and/or rise. We also forced

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the optimization to continue until the error improvement was less than 0.01 percent

between iterations; the default error convergence is 1%. Increasing the convergence

constraint was critical because we noticed that two convergence runs would result in

spectral components with different spectral profile and amplitude evolution, even though

the error between the MCR-ALS fit was less than 1% error with TA data. Once the

convergence constraint was raised, all three TA data sets converged to the same two

spectral components shown in Figure 4-13A. Although all three TA data sets share the

same two spectral components, though the time evolution of the corresponding

amplitudes is quite different. Figure 4-13B shows the time evolution of the first spectral

component, for the three different pump wavelengths, which are color coded. Figure 4-

13C shows the time evolution of the second spectral component, for the three different

pump wavelengths. The black curves are fits of the data (discussed later).

Using only the two eigen spectra shown in Figure 4-14, along with their amplitude

components as a function of time, the TA data sets can be reproduced with no structure

in the residuals when the data is subtracted from the fit for all the wavelengths detected

in TA, from 450 nm to 700 nm. Figure 4-15 shows the residuals for all times and

wavelengths after 5 ps when SVD fits of 555 nm are subtracted from raw the raw TA

data. Only residuals for 555 nm excitation is shown because it is the nosiest data set.

The two spectral components from SVD/MCR-ALS were assigned as a cis-

isomer species (red from Figure 4-15A.), and an excited state species (blue from figure

4-15A). The assignment was straight forward considering component I (red) is the only

signal after 1.5 ns and matches the profile of the spectral signature of the cis-isomer in

solution in literature3 (see Figure 4-2B), and we observe the same spectral signature

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after 1 ms if care is not taken to refresh the sample volume between excitations (see

figure 4-6).

Figure 4-14. Spectral components and spectra from MCR-ALS for TA data collected at three different excitation wavelengths along with multi-exponential fit (black curve). A) Two significant spectral components from MCR-ALS, B) time evolution of red component at three different excitation wavelengths, C) time evolution of blue component at three different excitation wavelengths.

Figure 4-16 explains the composition of each SVD/MCR-ALS spectral

component shown in Figure 4-15A. A simplified Jablonski diagram is included above the

spectrum to help explain the spectral signatures of having population in an excites state.

Figure 4-16A shows the spectral component assigned to the isomer species which is

the spectral signature (differential absorptions) of having population in the cis-isomer

state. The profile will include ground state bleach (missing absorption because some of

A

C B

I II

132

the molecules are in the cis-isomer configuration, and not absorbing like the trans-

isomer), and the cis-isomer absorption (a new positive absorption resulting from the cis-

isomer having a different absorption spectrum than the trans-isomer). The predicted cis-

isomer spectrum (dashed line) is obtained by subtracting the profile of the ground state

absorption of MC540 (solid black line) from the SVD component. Figure 4-16B shows

the composition of the excited state species spectral signature. The spectral profile

observed from having populating in the excited state will include a ground state bleach

(explained earlier), stimulated emission (a negative signal because more photons reach

the detector), and excited state absorption (a positive new absorption because the

excited state can absorb into another excited state). The predicted excited state

absorption shown in Figure 4-16B is generated by using the MC540 absorption and

emission spectra as the bleach and stimulated emission and subtracting from the SVD

component obtained from Figure 4-14A (assuming equal oscillator strength for ground

state absorption and stimulated emission).

Figure 4-15. Residuals from TA data excited at 555 nm fit using the SVD/MCR-ASL results shown in Figure 4-15.

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Time evolution

The kinetic profiles of the spectral components obtained from SVD/MCR-ALS

were fit using a sum of exponentials which are the fits shown in black in Figures 4-14B

and 4-14C. The least number of exponentials needed to avoid structure in the residuals

was used. The lifetimes are found in Table 4-1, along with amplitude components

reported as a percentage of total signal.

Excitation at 515 nm can be fit with one exponential for fitting both SVD

components with no structure in the residuals. The excited state decay of 515 nm

excitation could be fit by 257 ps (±1 ps) lifetime, outside of those values, residuals

would have structure, while the isomer rise could be fit with 270 ps (±30 ps) without

structure in the residuals. 257 ps is inside the range that can fit the rise with no

residuals, so 257 ps was assigned for both 515 nm comports. The tight tolerance of 257

ps, led us to use this value for other excitation wavelengths when possible.

Excitation at 480 nm could also be fit with a single exponential sharing the

same rates used for 515 nm with no structure in the residuals. The difference is that

both are decay times.

Excitation at 555 nm required at least two rates to fit the data. Fitting time

constants when more than one exponential is involved can be tricky, because there is a

large tolerance range for rates and amplitude combinations which will give rise to a

good fit with no residual structure. A judgment call is needed to help constrain the range

of rates and amplitudes, keeping in mind the potential for physical interpretation, and

always trying to minimize the number of free variables.

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Figure 4-16. Composition of spectral signitures of SVD/MCR-ASL components. Black line is the absorption spectra of MC540 in methanol. Dashed line is predicted excited state absorbtion. Dash and dotted line is emission spectra of MC540 in methanol. A) Cis-isomer component composition, B) excited state component composition.

A B

135

The common lifetime from 480 nm and 515 nm of 257 ps, was used for 555 nm

pump wavelength data to constrain the second rate. The isomer state component is

easy to fit with an additional fast rise. The excited state can tolerate a second

component from 25 ps to 100 ps, a vast range for a small number. Which is chosen

would significantly affect the amplitude of the rates. We choose to report a lifetime of 30

ps because the physical interpretation is easier if the excited state feeds the cis-isomer

state (as one decays, the other rises).

Table 4-1. Lifetimes and amplitude percentages of SVD/MCR-ALS components. Excitation wavelength

[nm]

Excited state lifetime [ps]

Cis-isomer state lifetime* [ps]

480 257 +12/-24 100% 257 +4/-8 100%

515 257 ±1 100% (257) +33/-17 100%

555 257 fixed 30 +70/-5†

89% 11%

(257) fixed (30) +3/-3

55% 45%

* Long lived cis-isomer component not included. † Strange error explained in text. Note: Numbers in parenthesis are rise times.

Discussion

Using SVD/MCR-ALS to isolate overlapping spectral features facilitates

interpretation of the 2D-S data. The shift along the excitation axis in Figure 4-11

detected at 580 nm is the result of signal with positive Δ𝐴 contribution decaying for

excitations around 480 nm, while a signal with positive Δ𝐴 contribution rising faster at

555 nm excitation than at the center. The time resolution of the TA experiment (1 ps)

could not help to determine the character of the positive signal observed at early 2D-S

times, however, TA data supports the idea that the cis-isomer spectral signature forms

in less than 5 ps.

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Ultrafast Formation of Cis-isomer Spectral Signature

Ultrafast isomerization8 processes have been observed before, but MC540

isomerization has not previously been reported to occur on the time-scales we observe

for excitation at 480 nm, probably because no one thought to excite the molecule there.

Using the information from 2D and TA, we began to construct a model that would fit

these new findings and agree with previous data. To start, we suspected a surface

crossing or conical intersection was involved near the Franck-Condon region because

of the fast time scales observed in isomerization. MC540 is a large molecule and cannot

be modeled using a method that could accurately predict the Franck-Condon region

(absorptions spectra) and the excited state surfaces (conical intersections and surface

crossings), so we were limited to smaller model systems for insight.

Unfortunately, no simple model (and not so simple models) can explain

everything we observe. If we only needed a model to explain each of the excitations

independently, it would be trivial, but kinetics for excitation at 515 nm can’t be explained

by the models for 480 nm or 555 nm, or vice versa. We are missing a piece of the

puzzle to bridge the difference in kinetics between different excitation energies, but we

don’t know what that is. All the excited state population is accounted for in the two

spectral signatures from SVD/MCR-ALS. We know this because a dark state which

gave no spectral signatures other than a ground state depletion, would require its own

spectral component to fit the data (the signature of missing absorption of the grounds

state). SVD/MCR-ALS data matches the TA data with less than 1% error, which means

if we are missing a spectral component, less than 1% contributes to the transient

signals.

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Every kinetic model for MC540 we could find in literature fails when attempting to

explain the excitation wavelength dependence we observed. A model that cannot

predict an experimental result is wrong, so a new model is needed.

Excitation wavelength dependent cis-isomerization yield? The instantaneous

detection of the cis-isomer spectral feature with excitation at 480 nm, and the faster

formation kinetics when exciting at 555 nm, compared to 515 nm, made us wonder if the

yield of the isomer was also excitation wavelength dependent. Emission is said to

compete with isomerization, so if the cis-isomer forms faster in some cases, the yield

can be expected to change. All the TA experiments were performed with the same

pump power, so the SVD/MCR-ALS results were normalized to the corresponding

absorption spectrum value (isolating the signal from optical density). The result being

normalized data independent of number of excited molecules. Figure 4-17 shows the

normalized cis-isomer component amplitude kinetics. The result of normalization shows

that the same amount of cis-isomer forms after ~1 ns, regardless of the excitation

wavelength. Combing this information with the lack of excitation wavelength

dependence of emission (discussed earlier) makes it a truly puzzling problem; there are

starkly different excitation wavelength dependent kinetics, but with the same overall

yields after all the excited state kinetics are settled.

Merocyanine-540 has proven to be a complicated system eluding even a

complex model able to explain all the observed behavior. Our research hoped to add

pieces to the puzzle to shed light on this curious system with real world importance, but

instead we discovered that the puzzle is bigger than previously imagined.

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Figure 4-17. Normalized cis-isomer component amplitude kinetics for 3 different excitation wavelengths.

Complicating things further, the well documented triplet state of MC540 was not

detected in our experiments, despite extensive efforts to try to observe it.

Triplet State

Not observing the triplet state in methanol, made us question our methods and

results, because its spectral signature and kinetics are heavily reported in literature.

After we finally convinced ourselves that our methods were valid by observing triplet

states in other systems, we did a deep literature search to figure out why we were not

measuring a triplet state. Having published work for over ~40 years of intense study on

MC540, made it possible to conclude that a triplet state is only measured, if the pump

power is high44,45 and the pulse width of the excitation source is long, above 100’s of ps.

We were not able to find a short pulse experiment with experimental evidence of

the Triplet. A single ultrafast paper by the Kamat group46 mentions the triplet, but their

ultrafast data is cut off starting at the wavelengths where triplet signature is expected.

The spectrum of the triplet they report to observe was collected using a 532 nm pulses

555 nm

480 nm

515 nm

139

with 6 ns temporal bandwidths and 10 mJ/pulse, not an ultrafast pulse. Every single

other paper that mentions the triplet state of MC540 (with experimental evidence, and

not just a reference to another paper) uses a CW laser, nanosecond laser, or

microsecond flash photolysis to discuss the triplet state.

Not measuring a triplet state with short pulses is compelling evidence that the

triplet state is the result of re-excitation of something other than the ground state. This

might be a way to finally settle the debate of whether MC540 kills leukemia by triplet

formation or isomerization. An ultrafast laser can be used to excite live leukemia cells

stained with MC540 in such a way that the same cell isn’t re-excited until well after the

cis-isomer has decayed. The laser would need to have a low rep-rate to allow for gentle

methods of displacing the sample from shot-to-shot, or the position of the laser pulse

from shot the shot can be changed using acoustic displacement of an optic to change

the focal position from shot-to-shot.

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CHAPTER 5 CONCLUSION

"A good experimentalist doesn't mean being able to collect beautiful low-noise data; it means when you measure something you don't expect you’re able to distinguish

whether there is mistake in your experimental methods or a mistake in the theory." Adrian Roitberg

Two-dimensional spectroscopy in the optical electronic region for pump-probe

geometry experiments is not yet a mature scientific method. The problems that plague

transient absorption (overlapping signatures of species) are also present in optical 2D-

S. Something that is neglected to be explained when the “amazing things which 2D-S

can show” part of a lectures, presentations, journal articles, and books is covered.

Signals overlap in 2D-S and TA spectroscopy, so SVD is used to figure out

independent components to isolate the kinetics of individual species (see Chapter 4

methods). SVD results have ABSOLUTLY no physical meaning without

constraining the basis set. Eigen components of a matrix only have physical meaning

if they are shown in a basis set with physical meaning. However, 2D-S fits using SVD

component analysis are justified in literature with global fitting of decay associated

spectra, to show that the SVD results “fit the data well”. If the SVD components didn’t

fit the data well, they would not have been picked up by the algorithm to

reproduce the data set—a good fit does not mean anything other than the 2D-S

data set has noise tolerable for the algorithm to converge on some non-unique

solution. Having a good fit of data is not science, because any unconstrained function

with unlimited parameters can reproduce data with a “good fit”. Except for things that

can’t be fit like random signals and chaotic behavior, but those are their own “beasts”.

Constraining 2D-S data from SVD to have physical meaning using MCR-ASL is

very challenging; SVD does not work on 3-D data sets, so slices of the 3-D matrix must

141

be done separately. 2D-S data is also much harder to collect than TA, making

generating a data set with low noise and enough time points for SVD analysis very

difficult. To compound the complexity of interpreting data, lots of the interesting

dynamics of systems occur on time scales where vibrational states are still “hot”,

meaning SVD cannot be used to separate overlapping signals; unless data set with

enough time and temporal resolution is collected for “hot” vibrational states to be

represented in the data long enough to not be considered noise by the algorithm.

Making 2D-S data have physical meaning, should be the top priority for the

optical 2D-S community, kinetics and fits discussed for data which might have no

physical interpretation is troubling.

Tensor decomposition47 (SVD in 3-D) is a promising method currently in

development which might allow optical 2D-S data to be processed to extract species

information from overlapping signals. Up to now, no successful application has been

used on data as complex as 2D-S data. However, the “deep-learning” community is

heavily interested in tensor decomposition because computers use SVD to break down

images; not being able to look at the time-evolution of images (i.e. movie, or real-time

visual input) prevents computers from interpreting time-dependent signals such as

understanding what action is being performed over time. The large amount of resources

being invested into deep-learning will hopefully lead to the development of a tensor

decomposition algorithm which can be used for 2D-S data.

There is significant advantage to a 2D-S experiment compared to a TA

experiment (discussed in Chapter 3). 2D-S will eventually replace TA as technology

142

advances because of the advantages, just as FT-IR is now the standard for vibrational

spectroscopy.

My contribution to the field was not building a new instrument that could perform

experiments no one else can (yet, a publication to help others access the blue-green

region of the visible spectrum for pump-probe 2D-S is in the works), or showing that

MC540 is an even more complicated system than what was previously known; my

contribution to the field is showing that pump-probe 2D-S measures real signals that

can be interpreted with fits corresponding to physical processes. The difficulty of the

experimental method and theory is not an acceptable excuse to not explain what the

signal means—if you can collect data, but not understand what it means, you’re a

skilled technician, not a scientist.

Merocyanine-540 Excited State Kinetics

The excitation wavelength dependence of the excited state dynamics of

merocyanine-540 (MC540), observed using 2D-S in the pump-probe geometry and

confirmed by TA experiments, described in Chapter 4 cannot be explained by any

current model of excited state MC540 in the literature. The trouble arises from observing

faster cis-isomer formation signature at both high energy (480 nm) and low energy (555

nm) component of the absorption spectrum.

Adding to the complexity is the lack of excitation wavelength dependence on

emission and cis-isomer yield. Accounting for starkly different dynamics while

maintaining emission yield and isomer yield with only two species with two rates

(extracted from SVD/MCR-ALS), is daunting for a kinetic model. Another complexity is

MC540 vibrationally cools in ~4 ps after excitation, from time resolved emission

studies43 and shifts observed in our data. The additional 30 ps rate for 555 nm excitation

143

compared to 515 nm, cannot be explained from being exciting to different vibration

states, because both should be in the same vibrational state after ~4 ps.

An extensive literature review on MC540 and similar molecules was performed to

see if similar dynamics have been previously observed.

Figure 5-1. Transient data for a model merocyanine which shows spectral signatures like those observed for merocyanine-540. Figure adapted with permission from Kahan, A.;

Wand, A.; Ruhman, S.; Zilberg, S.; Haas, Y. Solvent tuning of a conical intersection: direct experimental verification of a theoretical prediction J Phys Chem A 2011, 115, 10854-10861. Copyright (2011) American Chemical Society.

A simple merocyanine model (MCM), shown in Figure 5-1A, shows similar

kinetics to what we observe for MC540, except the differences in kinetics are from

different solvents, instead of different excitation wavelengths.9 Figure 5-1C shows the

TA spectra of MCM in toluene and Figure 5-1D in acetonitrile with spectra color coded

to time, and absorption spectrum (dashed line) and emission spectrum (dotted line) for

D

C

B

A

144

comparison. Figure 5-1B shows the kinetic profiles at 660 nm detection color coded to

solvent.

The molecule MCM does not form a trans-cis isomer in the ground state because

isomerization around the double bonds yield no difference, and the central bond is

unrestricted. From calculations on a similar simple merocyanine without the tertbutyl

moieties, the first excited state is predicted to be a zwitterion.48 The Valence Bond

theory calculation, assignments are shown in Figure 5-2. Combining the TA results

shown in Figure 5-1, with the calculated VB assignments, the excited state spectral

absorption signature around 660 nm, is assigned to the zwitterion excited state

absorption by Haas.48

Figure 5-2. VB structure used to assign transition from work by Haas on the MCM system. Figure reproduced with permission from Kahan, A.; Wand, A.; Ruhman, S.; Zilberg, S.;

Haas, Y. Solvent tuning of a conical intersection: direct experimental verification of a theoretical prediction J Phys Chem A 2011, 115, 10854-10861. Copyright (2011) American Chemical Society.

145

It’s a stretch, but applying the idea that the spectral signature of an excited state

zwitterion form has similar spectral profile as a ground state cis-isomer of MC540, it is

possible to assign some of the different kinetics observed for MC540 at different

excitations, to whether a zwitterion forms. The temporal response we observe between

different excitation could be a result of an overlapping zwitterion excited state

absorption signal. From figure 5-3B, amplitude profiles for the 480 nm excitation

component (blue) could be explained if lots zwitterion populations formed, and the

decay we observe is the decay of the zwitterion signal convoluted with the rise of the

isomer signal. The spectral profile of the signal assigned to cis-isomerization state in

Chapter 4, could be a mixture of cis-isomer absorption, and excited state zwitterion

absorption with profile so similar that they are mixed by SVD/MCR-ASL, and the kinetics

of the components keep track of the species, instead of the profile.

Figure 5-3. Reproduction of plots shown in Figure 4-15.

I purposefully choose to neglect zwitterions through the dissertation because

zwitterions predicted for MC540 is one of the properties discussed in Chapter 1, where

it is mentioned in literature so often that is assumed to be true. Tracking references

down to find an experiment which shows MC540 forms the zwitterion configuration, lead

to papers that are speculative about the possible formation of a zwitterion without any

555 nm

480 nm

515

ground state bleach

cis-isomer/zwitterion absorption?

A

B

146

experimental evidence. Refence chains for mentions of zwitterions of MC540 often end

at an article34 for which the evidence for a zwitterion presented is being able to draw a

resonance structure. An undergraduate chemist learns in physical chemistry that a

resonance structure does not mean that the two species will exist, only that the true

conformation is a combination of both. And indeed, the true ground state has some

zwitterion character, as discussed in interpretation of 2D-NMR experiments to

determine the ground state conformation.3

Complicating things even further when trying to see if there is experimental

evidence or at least strong tangential support reaches the problem of the “hot topic”

nature of zwitterions in the 90’s. Like how someone will have trouble when doing a

literature search for keyword “nano” for publications in the 2000’s. On top of being

difficult to research for directly in literature, MC540 is often clumped in work with other

similar dyes that make no mention of merocyanine. This means that there might be

convincing evidence somewhere, and I just can’t find it.

Zwitterion Evidence?

It is possible we generated experimental evidence of a zwitterion configuration

accidently by exciting at 480 nm, while looking for signature of the isomer. An elaborate

experiment would need to be performed to confirm the results.

2D-S/TA Experiments with other solvents would need to be performed. The

excited state vibrational band which couples to the zwitterion state can’t be assumed to

be the high frequency band like that is observed for MC540 in methanol. The surface

crossing location is dependent on polarity not the vibrational structure, so the absorption

band which couples is expected to shift around with solvent properties.

147

The surface crossing with a zwitterion is also predicted to shift with the

application of an external field48, allowing to stay with methanol because of the

favorable properties discussed in Chapter 4 for transient spectroscopy.

Looking at the problem with a background in physics, I would look for anisotropy

of the emission when excited at 490 nm, in varying external fields; the charge separated

state would want to align with the field. However, I have never done anisotropy

experiments and I only know the basic theory and not whether the experiments would

be possible on MC540 and methanol (high polarity solvent). The lack of emission yield

from excitation spectra shows that if the zwitterion exists it must fluoresce, or relax back

down to the state which emits to conserve the overall yield. Looking for a change in

anisotropy when applying an external field compared to anisotropy when exciting at a

wavelength with different kinetics would be evidence of a zwitterion.

Another experiment to probe for a zwitterion configuration would be to do 2D-

S/TA experiments with a visible wavelength pump pulse and IR wavelength probe

pulse. The vibrational signature of a charge separated species should be significantly

different form a neutral excited state-conformer because a polar solvent should perturb

the vibrations and shift the frequencies.

148

APPENDIX CONSTRAINING SVD

Constraining SVD results using MCR-ALS in MatLab is a significant part of data

analysis to ensure that the correct kinetics are being reported and discussed. The

kinetics of a SVD fit without putting the eigen spectra into a proper basis set leads to

confusion and erroneous results which do not relate to physical processes. Pump-probe

geometry 2D-S measures observables with physical meaning: the system is put into a

coherence by the first pump pulse; the coherence evolves for time 𝜏 after which the

second pump pulse puts the system into a population state. The population state

evolves for time 𝑇 until the third pulse arrives and puts the system back into a

coherence; the coherence is not allowed to evolve and is immediately measured by

heterodyning the third-order signal with the third pulse (probe) on the detector. The

signal measures purely absorptive signals as discussed in Chapter 2.

To observe the excited state signals generated by 2D-S and TA, measurements

are presented as a differential absorption by subtracting the absorption of the pure

ground state. As a result, when population is in an excited state, a bleach signal is

always present; if the negative signal expected for a bleach is not observed, it means

that it is masked by a positive signal (excited state absorption) with a larger oscillator

strength at the same spectral range.

Relating SVD results to a physical signal being measured has been a topic of

debate in the literature. Pre-packaged software for SVD analysis, such as KOALA and

MCR-ALS have many available constraints to change the basis set of an SVD fit to

have physical meaning. The constraints available to end-users of SVD analysis

software can be confusing, and it is critical that SVD analysis not be treated as a “black-

149

box” method to analyze data. If you do not understand what SVD does to a data matrix

and what it means to change the basis of a matrix, you should not use SVD—the results

are meaningless unless the correct constraints are applied.

Non-negativity of the amplitude components is a critical constraint for SVD

analysis so TA and 2D-S data have physical meaning. However, this constraint makes

TA very difficult to analyze because of experimental noise and spurious signals (i.e.

solvent Raman and pump scatter). Requiring the data to be high S/N and spurious

signal free is probably the reason that prevented others from realizing how simple it is to

extract information from overlapping TA signals. As a species approaches zero Δ𝐴

(decaying back to ground state) the noise of a measurement will result in the measured

signal oscillating from positive to negative amplitudes (see Figure A-1A of an

exponential decay (red) with 10% RMS noise data (blue)). The negative amplitudes

prevent SVD analysis to fit the data well because a non-negative amplitude constraint

was applied. Figure A-1B shows the results of fitting data using a non-negativity

constraint (orange). High, one sided residuals (between a fit and data) result from being

unable to generate negative amplitudes to match the experimental data.

Pump scatter and Raman are not TA signals from the sample and are thus not

associated with a population of an excited state. To use SVD on TA data, the data set

must be low noise and spurious signals free such that when the error from being unable

to produce negative amplitude values is negligible.

Some examples of excellent “fits” of MC540 TA data presented in Chapter 4 (see

Figure 4-12) with no physical meaning are shown in Figure A-2. TA measures the

spectral signature of having population in the excited state. The excited state population

150

will yield both positive and negative Δ𝐴 signals (bleach, stimulated emission, and

excited state absorption); the eigen spectra need to be free to be both positive and

negative. However, the amplitudes of the spectral components represent the population

of the excited state generating the spectrum measured by TA; populations must be non-

negative, so the amplitudes must be non-negative. TA measures differential absorption,

thus, if the bleach does not recover because the ground-state population is not

conserved (i.e. bond breaking), it does not mean there can be a negative population for

the ground state, instead it will be measured as a positive population of a species

whose spectral signature is a lack of ground state absorption.

A caveat for anyone attempting to reproduce my results is the following: MatLab

generates “initial guesses” each time the program is started and reuses the same

numbers until the program is restarted. Running the same unconstrained SVD/MCR-

ALS optimization back-to-back will yield the same results. To generate a new non-

unique solution, close and restart MatLab, then rerun the optimization. Different runs will

converge on different results because the initial guesses are different and SVD

solutions are not unique when unconstrainted. Data shown in Figure A-2 was generated

by two consecutive runs of unconstrainted SVD/MCR-ALS analysis of MC540 TA data

shown in Figure 4-12.

151

Figure A-1. Example of a decaying exponential signal with noise. Figure explained in text.

A

152

Figure A-2. Two unconstrained fits of MC540 TA data that fit the data well, but have no physical meaning. A) amplitudes change sign from positive to negative (bottom panel, orange line), B) fit showing that meaningless spectra and amplitudes can fit data well.

B

A

153

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BIOGRAPHICAL SKETCH

Jorge I. Medina received his Ph.D. in chemistry under the mentorship of Valeria

D. Kleiman at the University of Florida in the spring of 2017. His undergraduate

education was performed at California State University, Long Beach, where he obtained

a B.S. in physics and astronomy in the spring of 2009.