2018-02-26 17:07

9 files changed, 376 insertions, 245 deletions

diff --git a/PEDOT:PSS/agreement.png b/PEDOT:PSS/agreement.png
new file mode 100644
index 0000000..1a7df33
--- /dev/null
+++ b/PEDOT:PSS/agreement.png
diff --git a/PEDOT:PSS/chapter.tex b/PEDOT:PSS/chapter.tex
index 9138972..8bb1510 100644
--- a/PEDOT:PSS/chapter.tex
+++ b/PEDOT:PSS/chapter.tex
@@ -67,8 +67,11 @@ processing.  %
 
 \section{Transmittance and reflectance}
 
-\afterpage{
-\begin{figure}
+\autoref{fig:PEDOTPSS_linear} shows the transmission, reflectance, and extinction spectrum of the
+thin film used in this work.  %
+
+\clearpage
+\begin{dfigure}
   \centering
 	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/linear"}
 	\caption[PEDOT:PSS transmission and reflectance spectra.]{
@@ -77,27 +80,10 @@ processing.  %
     Extinction is $\log_{10}{\mathsf{(transmission)}}$.  %
   }
 	\label{fig:PEDOTPSS_linear}
-\end{figure}
-\clearpage}
-
-\autoref{fig:PEDOTPSS_linear} shows the transmission, reflectance, and extinction spectrum of the
-thin film used in this work.  %
+\end{dfigure}
+\clearpage
 
-\section{Three-pulse echo spectroscopy}
-
-\afterpage{
-\begin{figure}
-  \centering
-	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/mask"}
-	\caption[PEDOT:PSS 3PE phase matching mask.]{
-    Phase matching mask used in this experiment.
-    Each successive ring subtends 1 degree, such that the excitation pulses are each angled one
-    degree relative to the mask center.
-    The two stars mark the two output poyntings detected in this work.
-  }
-	\label{fig:PEDOTPSS_mask}
-\end{figure}
-\clearpage}
+\section{Three-pulse echo spectroscopy}  % --------------------------------------------------------
 
 Two dimensional $\tau_{21}, \tau_{22^\prime}$ scans were taken for two phase matching
 configurations: (1) $k_{\mathsf{out}} = k_1 - k_2 + k_{2^\prime}$ (3PE) and (2) $k_{\mathsf{out}} =
@@ -110,60 +96,208 @@ All data was modeled using numerical integration of the Liouville-von Numann equ
 Continuously variable ND filters (THORLABS NDC-100C-4M, THORLABS NDL-10C-4) were used to ensure
 that all three excitation pulse powers were equal within measurement error.  %
 
-\afterpage{
-\begin{figure}
-  \centering
-	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/raw"}
+\autoref{fig:PEDOTPSS_mask} diagrams the phase matching mask used in this set of experiments.  %
+
+\begin{dfigure}
+	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/mask"}
+	\caption[PEDOT:PSS 3PE phase matching mask.]{
+    Phase matching mask used in this experiment.
+    Each successive ring subtends 1 degree, such that the excitation pulses are each angled one
+    degree relative to the mask center.
+    The two stars mark the two output poyntings detected in this work.
+  }
+	\label{fig:PEDOTPSS_mask}
+\end{dfigure}
+
+\autoref{fig:PEDOTPSS_raw} shows the ten raw 2D delay-delay scans that comprise the primary dataset
+described in this section.  %
+The rows correspond to the two phase matching conditions, as labeled.  %
+
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/raw"}
 	\caption[PEDOT:PSS 3PE raw data.]{
     CAPTION TODO
   }
 	\label{fig:PEDOTPSS_raw}
-\end{figure}
-\clearpage}
+\end{dfigure}
 
+\subsection{Assignment of zero delay}  % ----------------------------------------------------------
 
-\afterpage{
-\begin{figure}
-  \centering
-	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/processed"}
+The absolute position of complete temporal overlap of the excitation pulses (zero delay) is a
+crucial step in determining the magnitude of th epeak shift and therefore the total rephasing
+ability of the material.  %
+The strategy for assigning zero delay relies upon the intrinsic symmetry of the two-dimensional
+delay space.  %
+\autoref{fig:PEDOTPSS_delay_space} labels the six time-orderings (TOs) of the three pulses that are
+possible with two delays.  %
+The TO labeling scheme follow from a convention first defined my Meyer, Wright and Thompson.
+[CITE]  %
+[CITE] first discussed how these TOs relate to traditional 3PE experiments.  %
+Briefly, spectral peak shifts into the rephasing TOs \RomanNumeral{3} and \RomanNumeral{5} when
+inhomogeneous broadening creates a photon echo in the \RomanNumeral{3} and \RomanNumeral{5}
+rephasing pathways colored orange in \autoref{fig:PEDOTPSS_delay_space}.  %
+For both phase-matching conditions, there are two separate 3PE peak shift traces (represented as
+black arrows in \autoref{fig:PEDOTPSS_delay_space}), yielding four different measurements of the
+photon echo.  %
+Since both 3PE and 3PE* were measured using the same alignment on the same day, the zero delay
+position is identical for the four photon echo measurements.  %
+We focus on this signature when assigning zero delay---zero is correct only when all four peak
+shifts agree.  %
+Conceptually, this is the two-dimensional analogue to the traditional strategy of placing zero such
+that the two conjugate peak shifts (3PE and 3PE*) agree. [CITE]  %
+
+We found that the 3PEPS traces agree best when the data in \autoref{fig:PEDOTPSS_raw} is offset by
+19 fs in $\tau_{22^\prime}$ and 4 fs in $\tau_{21}$.  %
+\autoref{fig:PEDOTPSS_processed} shows the 3PEPS traces after correcting for the zero delay
+value.  %
+The entire 3PEPS trace ($\tau$ vs $T$) is show for regions \RomanNumeral{1}, \RomanNumeral{3}
+(purple and light green traces) and \RomanNumeral{5}, \RomanNumeral{6} (yellow and light blue
+traces) for the [PHASE MATCHING EQUATIONS] phase matching conditions, respectively.  %
+Peak-shift magnitudes were found with Gaussian figs on the intensity level, in accordance with
+3PEPS convention. [CITE]
+The bottom subplot of \autoref{fig:PEDOTPSS_overtraces} shows the agreement between the four traces
+for $T > 50$ fs where pulse-overlap effects become negligible.  %
+These pulse-overlap effects cause the 3PEPS at small $T$ even without inhomogeneous broadening.
+[CITE]  %
+At long $T$, the average static 3PEPS is 2.5 fs.  %
+
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/delay space"}
+	\caption[PEDOT:PSS 3PE delay space.]{
+    CAPTION TODO
+  }
+	\label{fig:PEDOTPSS_delay_space}
+\end{dfigure}
+
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/processed"}
 	\caption[PEDOT:PSS 3PE processed data.]{
     CAPTION TODO
   }
 	\label{fig:PEDOTPSS_processed}
-\end{figure}
-\clearpage}
+\end{dfigure}
 
-\afterpage{
-\begin{figure}
-  \centering
-	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/delay_space"}
-	\caption[PEDOT:PSS 3PE delay space.]{
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/overtraces"}
+	\caption[PEDOT:PSS 3PE traces.]{
     CAPTION TODO
   }
-	\label{fig:PEDOTPSS_delay_space}
-\end{figure}
-\clearpage}
+	\label{fig:PEDOTPSS_overtraces}
+\end{dfigure}
 
-\afterpage{
-\begin{figure}
-  \centering
-	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/traces"}
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/traces"}
 	\caption[PEDOT:PSS 3PE traces.]{
     CAPTION TODO
   }
 	\label{fig:PEDOTPSS_traces}
-\end{figure}
-\clearpage}
+\end{dfigure}
 
-\afterpage{
-\begin{figure}
-  \centering
-	\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/overtraces"}
+There is a deviation of the TO \RomanNumeral{1}-\RomanNumeral{3} 3PEPS* trace (green line) from the
+other traces.  %
+It is attributed to a combination of excitation pulse distortions and line shape differences
+between OPA1 and OPA2 (see \autoref{fig:PEDOTPSS_linear}) and small errors in the zero delay
+correction.  %
+\autoref{fig:PEDOTPSS_traces} shows what the four 3PEPS traces would llike like for different
+choices of zero-delay.  %
+The inset numbers in each subplot denote the offset (from chosen zero) in each delay axis.  %
+
+\subsubsection{Numerical model}  % ----------------------------------------------------------------
+
+We simulated the 3PEPS response of PEDOT:PSS through numerical integration of the Liouville-von
+Neumann Equation.  %
+Integration was performed on a homogeneous, three-level system with coherent dynamics described by
+
+\begin{equation}
+  \frac{1}{T_2} = \frac{1}{2T_1} + \frac{1}{T_2^*},
+\end{equation}
+
+where $T_2$, $T_1$ and $T_2^*$ are the net dephasing, population relaxation, and pure dephasing
+rates, respectively.  %
+A three-level system was used because a two-level system cannot explain the population relaxation
+observed at long populations times, $T$.  %
+This slow delcay may be the same as the slowly decaying optical nonlinearities in PEDOT:PSS.
+[CITE]  %
+Inhomogeneity was incorporated by convolving the homogeneous repsonse with a Gaussian distribution
+function of width $\Delta_{\mathsf{inhom}}$ and allowing the resultant polarization to interfere on
+the amplitude level.  %
+This strategy captures rephasing peak shifts and ensemble dephasing.  %
+
+It is difficult to determine the coherence dephasing and the inhomogeneous broadening using 3PE if
+both factors are large.  %
+To extract $T_2^*$ and $\Delta_{\mathsf{inhom}}$, we focused on two key components of the dataset,
+coherence duration and peak shift at large $T$.  %
+Since dephasing is very fast in PEDOT:PSS, we cannot directly respove an exponential free induction
+decay (FID).  %
+Instead, our model focuses on the FWHM of the $\tau$ trace to determine the coherence duration.  %
+At $T > 50$ fs, the transient has a FWHM of $\sim$ 80 fs (intensity level).  %
+For comparison, our instrumental response is estimated to be 70-90 fs, depending on the exact value
+of our puse duration $\Delta_t$ (35-45 fs FWHM, intensity level).  %
+An experimental peak shift of 2.5 fs was extracted using the strategy described above.  %
+Taken together, it is clear that both pure dephasing and ensemble dephasing influence FWHM and peak
+shift so it is important to find valuse of $T_2^*$ and $\Delta_{\mathsf{inhom}}$ that uniquely
+constrain the measured response.  %
+
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/parametric"}
 	\caption[PEDOT:PSS 3PE traces.]{
     CAPTION TODO
   }
-	\label{fig:PEDOTPSS_overtraces}
-\end{figure}
-\clearpage}
+	\label{fig:PEDOTPSS_parametric}
+\end{dfigure}
+
+We simulated the $\tau$ trance for a variety of $\Delta_{\mathsf{inhom}}$ and $T_2$ values.  %
+The results for $\Delta_t = 40$ fs are summarized in \autoref{fig:PEDOTPSS_parametric}.  %
+The lines of constant $T_2$ span from $\Delta_{\mathsf{inhom}} = 0$ (green left ends of curves) to
+the limit $\Delta_{\mathsf{inhom}} \rightarrow \infty$ (blue right ends of curves).  %
+The lines of constant $T_2$ demonstrate that ensemble dephasing reduces the transient duration and
+introduces a peak shift.  %
+The influence of inhomogeneity on the observables vanishes as $T_2 \rightarrow \infty$. % 
+
+We preformed simulations analogus to those in \autoref{fig:PEDOTPSS_parametric} for pulse durations
+longer and smaller than $\Delta_t = 40$ fs.  %
+Longer pulse durations create solutions that do not intersect our experimental point (see
+right-most subplot of \autoref{fig:PEDOTPSS_parametric}), but shorter pulse durations do.  %
+[TABLE] summarizes the coherence dephasing time and inomogeneous broadening values that best
+matches the experimental FWHM and inhomogeneous broadening value for $\Delta_t = 35, 40$ and 45
+fs.  %
+Clearly, there is no upper limit that can provide an upper limit for the inhomogeneous
+broadening.  %
+
+\begin{dtable}
+ \begin{tabular}{ c | c c c }
+  $\Delta_t$ (fs) & $T_2$ (fs) & $\hbar T_2^{-1}$ (meV) & $\Delta_{\mathsf{inhom}}$ (meV) \\ \hline
+  45 & --- & --- & --- \\
+  40 & 10 & 66 & $\infty$ \\
+ \end{tabular}
+ \caption[]{
+   CAPTION TODO
+ }
+ \label{tab:PEDOTPSS_table}
+\end{dtable}
+
+\begin{dfigure}
+	\includegraphics[width=\linewidth]{"PEDOT:PSS/agreement"}
+	\caption[PEDOT:PSS 3PE traces.]{
+    CAPTION TODO
+  }
+	\label{fig:PEDOTPSS_agreement}
+\end{dfigure}
+
+Our model system does ans excellent job of reproducing the entire 2D transient within measurement
+error (\autoref{fig:PEDOTPSS_agreement}).  %
+The most dramatic disagreement is in the upper right, where the experiment decays much slower than
+the simulation.  %
+Our system description does not account for signal contributions in TOs \RomanNumeral{2} and
+\RomanNumeral{4}, where double quantum coherence resonances are important.  %
+In additon, excitation pulse shapes may cause such distortions.  %
+Regardless, these contributions do not affect our analysis.  %
+
+Extremely fast (single fs) carrier scattering time constants have also been observed for PEDOT-base
+conductive films. [CITES]
+
+\section{Frequency-domain transient grating spectroscopy}  % --------------------------------------
+
+This section describes preliminary, unpublished work accomplished on PEDOT:PSS.  %
+
 
-\section{Frequency-domain transient grating spectroscopy}
\ No newline at end of file
diff --git a/PEDOT:PSS/parametric.pdf b/PEDOT:PSS/parametric.pdf
new file mode 100644
index 0000000..a3b50fa
--- /dev/null
+++ b/PEDOT:PSS/parametric.pdf
diff --git a/dissertation.cls b/dissertation.cls
new file mode 100644
index 0000000..2d2ebc8
--- /dev/null
+++ b/dissertation.cls
@@ -0,0 +1,133 @@
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+
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+
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+
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+
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+
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+
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+
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+
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+
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diff --git a/dissertation.pdf b/dissertation.pdf
index 7cfeb9a..c66f292 100644
--- a/dissertation.pdf
+++ b/dissertation.pdf
diff --git a/dissertation.syg b/dissertation.syg
index e69de29..fc6ad1e 100644
--- a/dissertation.syg
+++ b/dissertation.syg
@@ -0,0 +1,3 @@
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+\glossaryentry{\ensuremath {N}?\glossentry{N}|setentrycounter[]{page}\glsnumberformat}{8}
+\glossaryentry{\ensuremath {\omega }?\glossentry{omega}|setentrycounter[]{page}\glsnumberformat}{82}
diff --git a/dissertation.tex b/dissertation.tex
index 4bc47a2..8c16976 100644
--- a/dissertation.tex
+++ b/dissertation.tex
@@ -1,113 +1,11 @@
 % https://grad.wisc.edu/currentstudents/doctoralguide/

 % TODO: cool quote: God made the bulk; surfaces were invented by the devil. https://en.wikiquote.org/wiki/Wolfgang_Pauli

 

-% document

-\documentclass[11 pt, twoside, openright]{report}  % 10 to 12 pt font required

-\usepackage[letterpaper, margin=1in]{geometry}  % 1 inch margins required

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-

-% headers (required: page number in upper right, nothing else)

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-

-% ensure that floats appear in the section they are defined in (http://tex.stackexchange.com/a/235312)

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-

-% text

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-

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-\newcommand{\code}[1]{\colorbox{light-gray}{\texttt{#1}}}

-

-% graphics

-\usepackage{graphics}

-\usepackage{graphicx}

-\usepackage{epsfig}

-\usepackage{epstopdf}

-\usepackage{etoc}

-\usepackage{tikz}

-

-% math

-\usepackage{amssymb}

-\usepackage{amsmath}

-\usepackage[cm]{sfmath}

-\usepackage{bm} % bold mathtype

-\DeclareMathOperator{\me}{e}

-

-% misc / ?

-\usepackage[nottoc]{tocbibind}

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-\usepackage{pdfpages}

-\usepackage[utf8]{inputenc}

-

-% hyperref

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-\usepackage[all]{hypcap}  % helps hyperref work properly

-

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-\usepackage[backend=biber, natbib=true, sorting=none, maxbibnames=99]{biblatex}

-\bibliography{bibliography}

-

-% glossary

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- 

-\setlength\cftparskip{0pt}

-\setlength\cftbeforechapskip{-5pt}

-\setlength\cftbeforesecskip{-7pt}

-\setlength\cftbeforesubsecskip{-10pt}

+\documentclass{dissertation}

 

 \begin{document}

 

-% pre ---------------------------------------------------------------------------------------------

+% --- preamble ------------------------------------------------------------------------------------

 

 \begin{centering}

 \thispagestyle{empty}

@@ -192,30 +90,30 @@ This dissertation is approved by the following members of the Final Oral Committ
 \include{introduction/chapter}

 

 \part{Background}

-%\include{spectroscopy/chapter}

-%\include{materials/chapter}

-%\include{mixed_domain/chapter}

+\include{spectroscopy/chapter}

+\include{materials/chapter}

+\include{mixed_domain/chapter}

 

 \part{Instrumental Development}

-%\include{software/chapter}

-%\include{instrument/chapter}

+\include{software/chapter}

+\include{instrument/chapter}

 

 \part{Applications}

-%\include{PbSe/chapter}

-%\include{MX2/chapter}

+\include{PbSe/chapter}

+\include{MX2/chapter}

 \include{PEDOT:PSS/chapter}

-%\include{pyrite/chapter}

-%\include{BiVO4/chapter}

+\include{pyrite/chapter}

+\include{BiVO4/chapter}

 

 % appendix -----------------------------------------------------------------------------------------

 

 \part{Appendix}

 \begin{appendix}

-%\include{public/chapter}

-%\include{procedures/chapter}

-%\include{hardware/chapter}

-%\include{errata/chapter}

-%\include{colophon/chapter}

+\include{public/chapter}

+\include{procedures/chapter}

+\include{hardware/chapter}

+\include{errata/chapter}

+\include{colophon/chapter}

 \end{appendix}

 

 % post --------------------------------------------------------------------------------------------

diff --git a/mixed_domain/chapter.tex b/mixed_domain/chapter.tex
index 308146b..7f8a8b4 100644
--- a/mixed_domain/chapter.tex
+++ b/mixed_domain/chapter.tex
@@ -137,9 +137,7 @@ from these measurement artifacts.  %
 

 \section{Theory}

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=0.5\linewidth]{"mixed_domain/WMELs"}

 	\caption[Sixteen triply-resonant Liouville pathways.]{

 		The sixteen triply-resonant Liouville pathways for the third-order response of the system used

@@ -149,8 +147,7 @@ from these measurement artifacts.  %
     are yellow, excitations with $\omega_2=\omega_{2'}$ are purple, and the final emission is gray.

 	}

 	\label{fig:WMELs}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 We consider a simple three-level system (states $n=0,1,2$) that highlights the multidimensional

 line shape changes resulting from choices of the relative dephasing and detuning of the system and

@@ -234,8 +231,7 @@ this paper.  %
 The steady state and impulsive limits of Equation \ref{eq:rho_f_int} are discussed in Appendix

 \ref{sec:cw_imp}.  %

 

-\afterpage{

-\begin{figure}

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{"mixed_domain/simulation overview"}

 	\caption[Overview of the MR-CMDS simulation.]{

 		Overview of the MR-CMDS simulation. 

@@ -253,8 +249,7 @@ The steady state and impulsive limits of Equation \ref{eq:rho_f_int} are discuss
     help introduce our delay convention.  

 	}

 	\label{fig:overview}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 Fig. \ref{fig:overview} gives an overview of the simulations done in this work.  %

 Fig. \ref{fig:overview}a shows an excitation pulse (gray-shaded) and examples of a coherent

@@ -491,8 +486,7 @@ The driven limit holds for large detunings, regardless of delay.  %
 

 \subsection{Convolution Technique for Inhomogeneous Broadening}\label{sec:convolution}

 

-\afterpage{

-\begin{figure}

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{mixed_domain/convolve}

   \caption[Convolution overview.]

   {Overview of the convolution.

@@ -501,8 +495,7 @@ The driven limit holds for large detunings, regardless of delay.  %
     (c) The resulting ensemble line shape computed from the convolution.

     The thick black line represents the FWHM of the distribution function.}

 	\label{fig:convolution}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 Here we describe how to transform the data of a single reference oscillator signal to that of an

 inhomogeneous distribution.  %

@@ -588,8 +581,7 @@ pulse delay times, and inhomogeneous broadening.  %
 

 \subsection{Evolution of single coherence}\label{sec:evolution_SQC}

 

-\afterpage{

-\begin{figure}

+\begin{dfigure}

   \centering

 	\includegraphics[width=0.5\linewidth]{"mixed_domain/fid vs dpr"}

 	\caption[Relative importance of FID and driven response for a single quantum coherence.]{

@@ -601,8 +593,7 @@ pulse delay times, and inhomogeneous broadening.  %
     slightly detuned (relative detuning, $\Omega_{fx}/\Delta_{\omega}=0.1$).

 	}

 	\label{fig:fid_dpr}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 It is illustrative to first consider the evolution of single coherences, $\rho_0 \xrightarrow{x}

 \rho_1$, under various excitation conditions.  %

@@ -639,8 +630,7 @@ We note that our choices of $\Gamma_{10}\Delta_t=2.0, 1.0,$ and $0.5$ give coher
 mainly driven, roughly equal driven and FID parts, and mainly FID components, respectively.  %

 FID character is difficult to isolate when $\Gamma_{10}\Delta_t=2.0$.  %

 

-\afterpage{

-\begin{figure}

+\begin{dfigure}

   \centering

 	\includegraphics[width=0.5\linewidth]{"mixed_domain/fid vs detuning"}

 	\caption[Pulsed excitation of a single quantum coherence and its dependance on pulse detuning.]{

@@ -661,8 +651,7 @@ FID character is difficult to isolate when $\Gamma_{10}\Delta_t=2.0$.  %
 		In all plots, the gray line is the electric field amplitude. 

 	}

 	\label{fig:fid_detuning}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 Fig. \ref{fig:fid_detuning}a shows the temporal evolution of $\rho_1$ at several values of $\Omega_{1x}/\Delta_{\omega}$ with $\Gamma_{10}\Delta_t=1$.\footnote{

 	See Supplementary Fig. S3 for a Fourier domain representation of Fig. \ref{fig:fid_detuning}a.

@@ -729,8 +718,7 @@ $\Gamma_{10}\Delta_t=1$.  %
 

 \subsection{Evolution of single Liouville pathway}

 

-\afterpage{

-\begin{figure}

+\begin{dfigure}

   \centering

 	\includegraphics[width=\linewidth]{"mixed_domain/pw1 lineshapes"}

 	\caption[2D frequency response of a single Liouville pathway at different delay values.]{

@@ -743,8 +731,7 @@ $\Gamma_{10}\Delta_t=1$.  %
     compare 2D spectrum frame color with dot color on 2D delay plot.

 		}

 	\label{fig:pw1}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 We now consider the multidimensional response of a single Liouville pathway involving three pulse

 interactions.  %

@@ -783,11 +770,10 @@ Since $E_1$ is not the last pulse in pathway I$\gamma$, the tracking monochromat
 	See Supplementary Fig. S5 for a representation of Fig. 5 simulated without monochromator frequency filtering ($M(\omega-\omega_1)=1$ for Equation \ref{eq:S_tot}).

 }

 

-\begin{table*}

-  \centering

+\begin{dtable}

 	\caption{\label{tab:table2} Conditions for peak intensity at different pulse delays for pathway

     I$\gamma$.}

-	\begin{tabularx}{0.7\linewidth}{c c | X X X X}

+	\begin{tabular}{c c | c c c c}

 		\multicolumn{2}{c}{Delay} & \multicolumn{4}{|c}{Approximate Resonance Conditions} \\

 		$\tau_{21}/\Delta_t$ & $\tau_{22^\prime}/\Delta_t$ & $\rho_0\xrightarrow{1}\rho_1$ &

     $\rho_1\xrightarrow{2}\rho_2$ & $\rho_2\xrightarrow{2^\prime}\rho_3$ & $\rho_3\rightarrow$

@@ -800,8 +786,8 @@ Since $E_1$ is not the last pulse in pathway I$\gamma$, the tracking monochromat
     $\omega_1=\omega_{10}$ \\

 		2.4 & -2.4 & $\omega_1=\omega_{10}$ & $\omega_2=\omega_{10}$ & $\omega_2=\omega_{10}$ &

     $\omega_1=\omega_2$ \\

-	\end{tabularx}

-\end{table*}

+	\end{tabular}

+\end{dtable}

 

 When the pulses are all overlapped ($\tau_{21}=\tau_{22^\prime}=0$, lower right, orange), all

 transitions in the Liouville pathway are simultaneously driven by the incident fields.  %

@@ -875,9 +861,7 @@ in unexpected ways.  %
 

 \subsection{Temporal pathway discrimination}

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{"mixed_domain/delay space ratios"}

 	\caption[2D delay response for different relative dephasing rates.]{

 		Comparison of the 2D delay response for different relative dephasing rates (labeled atop each

@@ -892,8 +876,7 @@ in unexpected ways.  %
     (purple), and III or I (teal).

 	}

 	\label{fig:delay_purity}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 In the last section we showed how a single pathway's spectra can evolve with delay due to pulse

 effects and time gating.  %

@@ -943,9 +926,7 @@ vanishing signal intensities; the contour of $P=0.99$ across our systems highlig
 

 \subsection{Multidimensional line shape dependence on pulse delay time}

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{"mixed_domain/spectral evolution"}

 	\caption[Evolution of the 2D frequency response.]{

 		Evolution of the 2D frequency response as a function of $\tau_{21}$ (labeled inset) and the

@@ -960,8 +941,7 @@ vanishing signal intensities; the contour of $P=0.99$ across our systems highlig
     $\tau_{22^\prime}=0$.

 	}

 	\label{fig:hom_2d_spectra}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 In the previous sections we showed how pathway spectra and weights evolve with delay.  %

 This section ties the two concepts together by exploring the evolution of the spectral line shape

@@ -1036,17 +1016,14 @@ only the absorptive line shape along $\omega_2$.  %
 This narrowing, however, is unresolvable when the pulse bandwidth becomes broader than that of the

 resonance, which gives rise to a vertically elongated signal when $\Gamma_{10}\Delta_t=0.5$.  %

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{"mixed_domain/wigners"}

 	\caption[Wigners.]{

 		Transient ($\omega_1$) line shapes and their dependence on $\omega_2$ frequency.  

 		The relative dephasing rate is $\Gamma_{10}\Delta_t=1$ and $\tau_{22^\prime}=0$.  

 		For each plot, the corresponding $\omega_2$ value is shown as a light gray vertical line.}

 	\label{fig:wigners}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 It is also common to represent data as ``Wigner plots,'' where one axis is delay and the other is

 frequency.\cite{Kohler2014, Aubock2012,Czech2015,Pakoulev2007}  %

@@ -1063,12 +1040,9 @@ This representation also highlights the asymmetric broadening of the $\omega_1$
 pulse overlap when $\omega_2$ becomes non-resonant.  %

 Again, these features can resemble spectral diffusion even though our system is homogeneous.  %

 

-\subsection{Inhomogeneous broadening}

+\subsection{Inhomogeneous broadening} \label{sec:res_inhom}  % ------------------------------------

 

-\afterpage{

-\label{sec:res_inhom}

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=0.5\linewidth]{"mixed_domain/inhom delay space ratios"}

 	\caption[2D delay response with inhomogeneity.]{

 		2D delay response for $\Gamma_{10}\Delta_t=1$ with sample inhomogeneity.  %

@@ -1083,8 +1057,7 @@ Again, these features can resemble spectral diffusion even though our system is
     (purple), III (teal, dashed), and I (teal, solid).  %

 	}

 	\label{fig:delay_inhom}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 With the homogeneous system characterized, we can now consider the effect of inhomogeneity.  %

 For inhomogeneous systems, time-orderings III and V are enhanced because their final coherence will

@@ -1138,9 +1111,7 @@ distortion has not been investigated previously.  %
 Peak-shifting due to pulse overlap is less important when $\omega_1\neq\omega_2$ because

 time-ordering III is decoupled by detuning.  %

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{"mixed_domain/inhom spectral evolution"}

 	\caption[Spectral evolution of an inhomogenious system.]{

 		Same as Fig. \ref{fig:hom_2d_spectra}, but each system has inhomogeneity

@@ -1157,8 +1128,7 @@ time-ordering III is decoupled by detuning.  %
     time-orderings V and VI unequal.

 	}

 	\label{fig:inhom_2d_spectra}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 In frequency space, spectral elongation along the diagonal is the signature of inhomogeneous

 broadening.  %

@@ -1241,9 +1211,7 @@ Only time-orderings V and VI are relevant.  %
 The intermediate population resonance is still impulsive but it depends on

 $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space.  %

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=\linewidth]{"mixed_domain/steady state"}

 	\caption[Conditional validity of the driven limit.]{

 		Comparing approximate expressions of the 2D frequency response with the directly integrated

@@ -1256,14 +1224,11 @@ $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space.  %
 		Third column:  The directly integrated response.  %

 	}

 	\label{fig:steady_state}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

-\subsection{Extracting true material correlation}

+\subsection{Extracting true material correlation}  % ----------------------------------------------

 

-\afterpage{

-\begin{figure}

-  \centering

+\begin{dfigure}

 	\includegraphics[width=0.5\linewidth]{"mixed_domain/metrics"}

 	\caption[Metrics of correlation.]{

 		Temporal (3PEPS) and spectral (ellipticity) metrics of correlation and their relation to the

@@ -1280,8 +1245,7 @@ $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space.  %
     area are connected).  %

 }

 	\label{fig:metrics}

-\end{figure}

-\clearpage}

+\end{dfigure}

 

 We have shown that pulse effects mimic the qualitative signatures of inhomogeneity.  %

 Here we address how one can extract true system inhomogeneity in light of these effects.  %

diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex
index 3aa7ffc..21a233d 100644
--- a/spectroscopy/chapter.tex
+++ b/spectroscopy/chapter.tex
@@ -162,12 +162,11 @@ Transient absorbance (TA) spectroscopy is a self-heterodyned technique.  %
 Through chopping you can measure nonlinearities quantitatively much easier than with homodyne

 detected (or explicitly heterodyned) experiments.

 

-\begin{figure}[p!]

-	\centering

+\begin{dfigure}

 	\includegraphics[width=\textwidth]{"spectroscopy/TA setup"}

 	\label{fig:ta_and_tr_setup}

 	\caption{CAPTION TODO}

-\end{figure}

+\end{dfigure}

 

 \autoref{fig:ta_and_tr_setup} diagrams the TA measurement for a generic sample.  %

 Here I show measurement of both the reflected and transmitted probe beam \dots not important in