\chapter{Introduction} \label{cha:int}

\begin{dquote}
  Experience has shown that the experimental implementation of three laser FWM is a formidable task
  which is far from complete.  %
  Characterization and improvement of existing apparatus must be a integral part of future research
  if FWM is to become a viable spectroscopic technique.  %
  To this end, it would be helpful to stimulate an atmosphere within the scientific community in
  which the method of measurement is considered to be as important as the result of the
  measurement.  %
  
  \dsignature{Roger Carlson (1988) \cite{CarlsonRogerJohn1988a}}
\end{dquote}
  
\clearpage

Coherent multidimensional spectroscopy (CMDS) is a family of experimental strategies capable of
providing unique insights into microscopic material physics.  %
It is similar to more familiar multidimensional NMR experiments \cite{KeustersDorine1999a,
  ZhaoWei2000b, PakoulevAndreiV2006a}, although the implementation is different due to differences
between the behavior of nuclear spin states (probed by NMR) and electronic and vibrational states
(probed by CMDS).  %
CMDS can resolve couplings between states, and can decongest spectra by taking advantage of
dimensionality and selection rules.  %
With the advent of ultrafast lasers, CMDS can resolve dynamics in excited states and the coupling
between them. \cite{RentzepisPM1970a}  %

CMDS is most often performed in the time domain, where multiple broadband pulses are scanned in
time (phase) to collect a multidimensional interferogram. \cite{MukamelShaul2009a,
  GallagherSarahM1998a}  %
This technique is fast and robust---it has even been performed on a single shot.
\cite{HarelElad2010a}  %
However time-domain CMDS has some fundamental limitations:
\begin{ditemize}
  \item The frequency bandwidth must be contained within the excitation pulse---and ultrabroadband
    pulses are hard to make and control. \cite{SpencerAustinP2015a}  %
  \item A phase-locked local oscillator is required, and preparing a local oscillator for experiments
    with unique output colors is challenging.
\end{ditemize}
Scientists in the time-domain CMDS community are taking both of these challenges head-on, pushing
the envelope in excitation pulse bandwidth \cite{KearnsNicholasM2017a} and performing two-stage
experiments in which excitation pulses are used to generate a local oscillator in non-resonant
media \cite{XiongWei2011a}.  %

An alternative strategy is frequency domain ``multi-resonant'' CMDS (MR-CMDS).  %
Rather than using a single broadband excitation pulse, MR-CMDS employs a relatively narrow-band
source with a tunable frequency.  %
Motorized optical parametric amplifiers (OPAs) are typically used to provide this tunability.
\cite{CerulloGiulio2003a}  % 
In MR-CMDS, frequency axes are resolved directly by scanning these motorized OPAs.  %
This process is time intensive, and it can be challenging to ensure that the OPAs are well
calibrated and that the experiment is not affected by the motion of crystals and other optics
inside these automated OPAs.  %
Despite these challenges, MR-CMDS is an incredibly flexible strategy that could become a powerful
analytical tool. \cite{PakoulevAndreiV2009a}  %
Because MR-CMDS does not require that all frequencies be contained within one broadband source,
there is no theoretical limit to the frequency range that can be resolved in this way.  %
MR-CMDS can be homodyne-detected, so experiments with unique output colors are much more
accessible.  %
Finally, because the components are more self-contained, MR-CMDS instruments tend to be more
flexible in the kinds of experiments that they can perform.  %

This dissertation contains several projects undertaken to improve the reliability and accessibility
of MR-CMDS.  %
While MR-CMDS will never be a single-shot experiment, there are many improvements that can improve
data collection speed.  % JCW: NOT SO SURE IT CAN'T BE SINGLE SHOT
Necessary calibration, especially OPA calibration, can be made robust and fully automatic.  %
Common artifacts can be addressed through relatively simple modifications in hardware and
software.  %
Finally, the complexity that arises from finite pulses with ``marginal'' resolution in frequency
and time can be understood and accounted for through numerical simulation.  %
Taken together, these improvements represent a significant improvement in the accessibility of
frequency-domain coherent multidimensional spectroscopy.  %

Due to its diversity and dimensionality, MR-CMDS data is challenging to process and represent.  %
The data processing tools that a scientist develops to process one experiment may not work when she
attempts to process an experiment where different experimental variables are explored.  %
Historically, this processing strategy has resulted in MR-CMDS practitioners have using custom,
one-off data processing workflows that need to be changed for each particular experiment.  %
These changes take time to implement, and can become stumbling blocks or opportunities for
error.  %
Even worse, the challenge of designing a new processing workflow may dissuade a scientist from
creatively modifying their experimental strategy, or comparing their data with data taken from
another group.  %
This limit to creativity and flexibility defeats one of the main advantages of the MR-CMDS
strategy.  %
Chapter \ref{cha:pro} describes a new software package, WrightTools, that greatly simplifies CMDS
data processing.  %
WrightTools defines a \emph{universal format} that is capable of representing any CMDS dataset,
regardless of dimensionality or the axes scanned.  %
A set of simple functions are used to convert raw data into this universal format.  %
Once converted, the data can be manipulated with a set of powerful methods that encompass the
majority of operations needed to process such data.  %
Finally, simple tools are defined to quickly and beautifully represent the datasets.  %
WrightTools is made to be extended, so it will continue to evolve along with its users.  %

From an instrumental perspective, MR-CMDS is a problem of calibration and coordination.  % 
Within the Wright Group, each of our two main instruments are composed of roughly ten actively
moving component hardwares. %
Many of these components are purchased directly from commercial vendors, while others are created
or heavily modified by graduate students.  %
The Wright Group has always maintained custom acquisition software packages which control the
complex, many-stepped dance that these components must perform to acquire MR-CMDS spectra.  %

When I joined the Wright Group, I saw that acquisition software was a barrier to experimental
progress and flexibility.  %
Graduate students had ideas for instrumental enhancements that were infeasible because of the
challenge of incorporating the new components into the existing software ecosystem.  %
At the same time, students were spending much of their time in lab repeatedly calibrating optical
parametric amplifiers by hand, a process that sometimes took days.  %
I chose to spend a significant portion of my graduate career focusing on solving these problems
through software development.  %
At first, I focused on improving the existing LabVIEW code.  %
Eventually, I developed a vision for a deeply modular acquisition software that could not be
practically created with LabVIEW.  %
Using Python and Qt, I created a brand new acquisition software PyCMDS: built from the ground up to
fundamentally solve historical challenges in the Group.  %
PyCMDS offers a modular hardware model that can ``re-configure'' itself to flexibly control a
variety of component hardware configurations.  %
This has enabled graduate students to add and remove hardware whenever necessary, without worrying
about a heavy additional programming burden.  %
PyCMDS is now used to drive both MR-CMDS instruments in the Group, allowing for easy sharing of
component hardware and lessening the total amount of software that the Group needs to maintain.  %
Besides being more flexible than prior software, PyCMDS solves a number of other problems.  %
It offers fully automated strategies for calibrating component hardwares, making calibration less
arduous and more reproducible.  %
It offers more fine-grained control of data acquisition and timing, enabling more complex
algorithms to quickly acquire artifact-free results.  %
In conjunction with other algorithmic and hardware improvements that I have made, PyCMDS has
decreased acquisition times by up to two orders of magnitude.  %

Like any analytical technique, MR-CMDS is subject to artifacts: features of the data that are
caused by instrumental imperfections or limitations, and do not reflect the intrinsic material
response that is of interest.  %
For example, consider well-known artifacts such as absorptive effects \cite{CarlsonRogerJohn1989a},
pulse effects \cite{SpencerAustinP2015a}, and window contributions \cite{MurdochKiethM2000a}.  %
Since MR-CMDS is a very active experiment, with many moving motors, an active approach to artifact
correction is particularly appropriate.  %
Chapter \ref{cha:act} describes strategies for implementing such corrections.  %
Spectral delay correction can be applied to account for the fact that not all output colors arrive
at the same time.  %
Dual chopping can correct for scatter and other unwanted processes, ensuring that the observed
signal depends on all of the excitation beams.  %
Fibrillation can wash out interference between desired and undesired processes, and is
complementary to chopping.  %
Automated poynting correction and power correction can account for non-idealities in OPA
performance.  %

MR-CMDS instruments rely on OPAs as tunable light sources.  %
OPAs are very sensitive to changes in upstream lasers and lab conditions, so OPA tuning is
regularly required.  %
Manual OPA tuning can easily take a full day of human effort. %
Furthermore, manual tuning typically results in inferior tuning curves, since it is difficult for
humans to consider all available information simultaneously.  %
Automated OPA tuning makes OPA upkeep easier, faster and more reproducible, facilitating higher
throughput, higher quality frequency domain experiments. %
Chapter \ref{cha:opa} describes fully automated tuning algorithms which I have developed.  %

The theory that is used to describe CMDS is typically derived in one of two limits.  %
In the impulsive limit, pulses are broad in frequency and short in time compared to material
resonances.  %
Resonant responses are impulsive, like a hammer hitting a bell.  %
The impulsive limit is particularly well suited for describing time domain experiments.  %
In the driven limit, pulses are narrow in frequency and long in time compared to material
response.  %
Resonant responses are driven, like jiggling jello dessert sitting on a washing machine.  %
The expected spectrum in both of these limits can be computed analytically.  %
Things get more complicated in the mixed domain, where pulses have similar bandwidth as the
material response. %
Experiments in this domain are a practical necessity as CMDS addresses systems with very fast
dephasing times. \cite{SmallwoodChristopherL2016a, PerlikVaclav2017a}
% BJT: connect bw and dephasing
At the same time, the marginal resolution in frequency \emph{and} time that the mixed domain
possess promises huge potential in pathway resolution and decongestion.
\cite{PakoulevAndreiV2009a}  %
Chapter \ref{cha:mix} describes the pitfalls and opportunities contained in the mixed domain
approach.  %
An intuitive description of mixed-domain experiments is given.  %
False signatures of material correlation are discussed, and strategies for resolving true material
correlation are defined.  %

In \hyperref[prt:applications]{Part III: Applications}, four projects in which MR-CMDS was used to
answer chemical questions in materials systems are described.  %
These chapters do not directly address improvements to the MR-CMDS methodology, but instead serve
as case studies in the potential of MR-CMDS and the utility of the improvements described in
\autoref{prt:development}.  %

In \autoref{cha:pss}, we employ transient grating MR-CMDS to interrogate the photophysics of
lead selenide (PbSe) quantum dots (QDs).  %
PbSe QDs are an interesting semiconductor system with many appealing properties for basic method
development work.  %
They are easy to synthesize, store and prepare in the solution phase, and they have bright and
relatively narrow band-edge excitons which are easy to interrogate using MR-CMDS.  %
In \autoref{cha:pss}, we describe a simple approach to extracting the quantitative third-order
susceptibility of PbSe quantum dots using MR-CMDS.  %
Using standard dilutions, we define this susceptibility in ratio to the known well-quantified
susceptibility of our solvent and cuvette windows.  %
A few-parameter model is employed to extract this ratio.  %
We are optimistic that this approach will be generally applicable, making it simple to perform
quantitative solution-phase MR-CMDS.  %

In \autoref{cha:psg} we continue to investigate PbSe QDs.  %
Here we combine transient grating and transient absorption MR-CMDS to learn more about the
nonlinear spectrum near the band edge, around the 1S exciton.  %
By combining both methods with the information from \autoref{cha:pss}, we are able to extract the
complete amplitude and phase of the non-linear susceptibility.  %
We develop a simulation that relates the microscopic physics of PbSe electronic states to transient
grating and transient absorption spectra, and fit our model to both spectra simultaneously.  %
Our model reveals the presence of continuum transitions, mostly invisible in typical transient
absorption experiments.  %
We show that our model is able to describe spectra from two different syntheses with two different
sizes of quantum dot.  %

In \autoref{cha:mx2} we report the first MR-CMDS study performed on a molybdenum disulfide thin
film.  %
MoS\textsubscript{2} is a member of a class of materials called transition metal dichacolgenides
which have recently attracted a large amount of attention for their unique photophysical
properties. \cite{MakKinFai2010a, XuXiaodong2014a, XiaoDi2012a}  %
These thin films have relatively low optical density and are highly scattering, making them
particularly challenging for MR-CMDS experiments.  %
We employed several strategies to overcome these challenges, and performed three dimensional
frequency-frequency-delay transient grating spectroscopy to understand the basic coupling and
dynamics of MoS\textsubscript{2}.  %
We show that the band-edge excitons of MoS\textsubscript{2} are not easily resolved, and the
dynamics of MoS\textsubscript{2} are fast.  %
We describe a picture of MoS\textsubscript{2} electronic states that is consistent with our
results.  %

In \autoref{cha:pps} we use MR-CMDS to interrogate the dynamics of electronic states of
PEDOT:PSS.  %
PEDOT:PSS is a transparent, electrically conductive polymer.  %
The exact origin of the conductivity is not well understood, so it is unclear how to improve the
conductivity or synthesize other conductive polymers.  %
We performed photon echo experiments on PEDOT:PSS, directly interrogating the electronic states
that are speculated to participate in conductivity.  %
Using a sophisticated model extended from the work in \autoref{cha:mix}, we constrain the pure and
ensemble dephasing lifetimes of PEDOT:PSS.  %
These lifetimes can be directly related to the homogeneous and inhomogeneous broadening parameters
in PEDOT:PSS.  %
Amazingly, we find that PEDOT:PSS has very broad homogeneous \emph{and} inhomogeneous
linewidths.  %
We cannot fully determine either quantity, but we can put lower limits on both.  %
This basic information is complementary to other experiments in the ongoing effort to fully
understand PEDOT:PSS.  %

Despite challenges in software, hardware, and theory MR-CMDS is a crucial tool in the hands of
scientists.  %
This dissertation describes several ways to make MR-CMDS more accessible through software and
hardware development.  %
PyCMDS has enabled new experiments, and has made data collection faster and more artifact-free.  %
WrightTools has trivialized data processing, tightening the loop between idea and execution.  %
Theory can be used to guide experimental insight in the promising, if challenging, mixed domain.  %
Applications of these ideas in three material systems are presented.  %