From f47e1abac351ed10110c9d982aea76ca73dd30a6 Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Wed, 31 Jan 2018 18:37:43 -0600
Subject: 2018-01-31 18:37

---
 MX2/chapter.tex | 153 ++++++++++++++++++++++++++++++++++++--------------------
 1 file changed, 98 insertions(+), 55 deletions(-)

(limited to 'MX2/chapter.tex')

diff --git a/MX2/chapter.tex b/MX2/chapter.tex
index 77cfe6e..68e87b7 100644
--- a/MX2/chapter.tex
+++ b/MX2/chapter.tex
@@ -1,6 +1,5 @@
 \chapter{MX2}
 
-
 We report the first coherent multidimensional spectroscopy study of a MoS\textsubscript{2} film.  %
 A four-layer sample of MoS\textsubscript{2} was synthesized on a silica substrate by a simplified
 sulfidation reaction and characterized by absorption and Raman spectroscopy, atomic force
@@ -81,19 +80,23 @@ vector for each beam and the subscripts label the excitation frequencies.  %
 Multidimensional spectra result from measuring the output intensity dependence on frequency and
 delay times.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=0.5\textwidth]{MX2/01}
-  \caption[CMDS tutorial]{(a) Example delays of the $\omega_1$, $\omega_2$, and
-    $\omega_{2^\prime}$ excitation pulses. (b) Dependence of the output intensity on the
-    $\tau_{22^\prime}$ and $\tau_{21}$ time delays for $\omega_1=\omega_2$. The solid lines define
-    the regions for the six different time orderings of the $\omega_1$, $\omega_2$, and
-    $\omega_{2^\prime}$ excitation pulses. We have developed a convention for numbering these time
-    orderings, as shown. (c) Diagram of the band structure of MoS\textsubscript{2} at the $K$
-    point. The A and B exciton transitions are shown. (d) Two dimensional frequency-frequency plot
+  \caption[CMDS tutorial]{
+    (a) Example delays of the $\omega_1$, $\omega_2$, and $\omega_{2^\prime}$ excitation pulses.
+    (b) Dependence of the output intensity on the $\tau_{22^\prime}$ and $\tau_{21}$ time delays
+    for $\omega_1=\omega_2$.
+    The solid lines define the regions for the six different time orderings of the $\omega_1$,
+    $\omega_2$, and $\omega_{2^\prime}$ excitation pulses.
+    We have developed a convention for numbering these time orderings, as shown.
+    (c) Diagram of the band structure of MoS\textsubscript{2} at the $K$ point.
+    The A and B exciton transitions are shown. (d) Two dimensional frequency-frequency plot
     labeling two diagonal and cross-peak features for the A and B excitons.}
   \label{fig:Czech01}
 \end{figure}
+\clearpage}
 
 \autoref{fig:Czech01} introduces our conventions for representing multidimensional spectra.  %
 \autoref{fig:Czech01}b,d are simulated data.  %
@@ -141,12 +144,14 @@ B exciton states.  %
 
 \section{Methods}  % ------------------------------------------------------------------------------
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/S1}
   \caption{Schemiatic of the synthetic setup used for Mo thin film sulfidation reactions.}
   \label{fig:CzechS1}
 \end{figure}
+\clearpage}
 
 MoS\textsubscript{2} thin films were prepared \textit{via} a Mo film sulfidation reaction, similar
 to methods reported by \textcite{LaskarMasihhurR2013a}.  %
@@ -178,16 +183,20 @@ with DI water, and transferred to a Cu-mesh TEM grid.  %
 TEM experiments were performed on a FEI Titan aberration corrected (S)TEM under 200 kV accelerating
 voltage.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/10}
-  \caption[Mask and epi vs transmissive.]{(a) Mask. (b) 2D delay spectra at the BB diagonal
-    ($\omega_1=\omega_2\approx1.95$ eV) for transmissive and reflective geometries. Transmissive
-    signal is a mixture of MoS\textsubscript{2} signal and a large amount of driven signal from the
-    substrate that only appears in the pulse overlap region. Reflective signal is representative of
-    the pure MoS\textsubscript{2} response.}
+  \caption[Mask and epi vs transmissive.]{
+    (a) Mask.
+    (b) 2D delay spectra at the BB diagonal ($\omega_1=\omega_2\approx1.95$ eV) for transmissive
+    and reflective geometries.
+    Transmissive signal is a mixture of MoS\textsubscript{2} signal and a large amount of driven
+    signal from the substrate that only appears in the pulse overlap region. Reflective signal is
+    representative of the pure MoS\textsubscript{2} response.}
   \label{fig:Czech10}
 \end{figure}
+\clearpage}
 
 The coherent multidimensional spectroscopy system used a 35 fs seed pulse, centered at 800 nm and
 generated by a 1 kHz Tsunami Ti-sapphire oscillator.  %
@@ -200,12 +209,14 @@ Signal and idler were not filtered out, but played no role due to their low phot
 Pulse $\omega_2$ was split into pulses labeled $\omega_2$ and $\omega_{2^\prime}$ to create a total
 of three excitation pulses.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/S4}
   \caption{OPA outputs at each color explored.}
   \label{fig:CzechS4}
 \end{figure}
+\clearpage}
 
 In this experiment we use motorized OPAs which allow us to set the output color in software.  %
 OPA1 and OPA2 were used to create the $\omega_1$ and $\omega_2$ frequencies, respectively.  %
@@ -222,12 +233,14 @@ focused onto the sample surface by a 1 meter focal length spherical mirror in a
 geometry to form a 630, 580, and 580 $\mu$m FWHM spot sizes for $\omega_1$, $\omega_2$, and
 $\omega_{2^\prime}$, respectively.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/S5}
   \caption{Spectral delay correction.}
   \label{fig:CzechS5}
 \end{figure}
+\clearpage}
 
 \autoref{fig:CzechS5} represents delay corrections applied for each OPA.  %
 The corrections were experimentally determined using driven FWM output from fused silica.  %
@@ -262,25 +275,35 @@ signal id is the geometry chosen for this experiment.  %
 This discrimination between a film and the substrate was also seen in reflective and transmissive
 CARS microscopy experiments. \cite{VolkmerAndreas2001a}  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/11}
-  \caption[MoS\textsubscript{2} post processing.]{Visualization of data collection and processing.
+  \caption[MoS\textsubscript{2} post processing.]{
+    Visualization of data collection and processing.
     With the exception of (c), each subsequent pane represents an additional processing step on top
-  of previous processing. The color bar of each image is separate. (a) Voltages read by the
-  detector at teach color combination. The large vertical feature is $\omega_1$ scatter; the shape
-  is indicative of the power curve of the OPA. MoS\textsubscript{2} response can be barely seen
-  above this scatter. (b) Data after chopping and active background subtraction at the boxcar (100
-  shots). (c) The portion of chopped signal that is not material response. This portion is
-  extracted by averaging several collections at very positive $\tau_{21}$ values, where no material
-  response is present due to the short coherence times of MoS\textsubscript{2} electronic states.
-  The largest feature is $\omega_2$ scatter. Cross-talk between digital-to-analog channels can also
-  be seen as the negative portion that goes as $\omega_1$ intensity. (d) Signal after (c) is
-  subtracted. (e) Smoothed data. (f) Amplitude level (square root) data. This spectrum corresponds
-  to that at 0 delay in \autoref{fig:Czech03}. Note that the color bar's range is different than in
-  \autoref{fig:Czech03}.}
+    of previous processing.
+    The color bar of each image is separate.
+    (a) Voltages read by the detector at teach color combination.
+    The large vertical feature is $\omega_1$ scatter; the shape is indicative of the power curve of
+    the OPA.
+    MoS\textsubscript{2} response can be barely seen above this scatter.
+    (b) Data after chopping and active background subtraction at the boxcar (100 shots).
+    (c) The portion of chopped signal that is not material response.
+    This portion is extracted by averaging several collections at very positive $\tau_{21}$ values,
+    where no material response is present due to the short coherence times of MoS\textsubscript{2}
+    electronic states.
+    The largest feature is $\omega_2$ scatter.
+    Cross-talk between digital-to-analog channels can also be seen as the negative portion that
+    goes as $\omega_1$ intensity.
+    (d) Signal after (c) is subtracted.
+    (e) Smoothed data.
+    (f) Amplitude level (square root) data.
+    This spectrum corresponds to that at 0 delay in \autoref{fig:Czech03}.
+    Note that the color bar's range is different than in \autoref{fig:Czech03}.}
   \label{fig:Czech11}
 \end{figure}
+\clearpage}
 
 Once measured, the FWM signal was sent through a four-stage workup process to create the data set
 shown here.  %
@@ -303,19 +326,23 @@ processing and plotting in this work.
 
 \section{Results and discussion}  % ---------------------------------------------------------------
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=0.75\textwidth]{MX2/02}
-  \caption[Few-layer MoS\textsubscript{2} thin film characterization.]{Characterization of the
-    few-layer MoS\textsubscript{2} film studied in this work. Optical images of the
+  \caption[Few-layer MoS\textsubscript{2} thin film characterization.]{
+    Characterization of the few-layer MoS\textsubscript{2} film studied in this work.
+    Optical images of the
     MoS\textsubscript{2} thin film on fused silica substrate in (a) transmission and (b)
-    reflection. (c) Raman spectrum of the $E_{2g}^1$ and $A_{1g}$ vibrational
-    modes. (d) High-resolution TEM image and its corresponding FFT shown in the inset. (e)
-    Absorption (blue), photoluminescence (green), Gaussian fits to the A and B excitons, along with
-    the residules betwen the fits and absorbance (dotted), A and B exciton centers (dotted) and
-    representative excitation pulse shape (red).}
+    reflection.
+    (c) Raman spectrum of the $E_{2g}^1$ and $A_{1g}$ vibrational modes.
+    (d) High-resolution TEM image and its corresponding FFT shown in the inset.
+    (e) Absorption (blue), photoluminescence (green), Gaussian fits to the A and B excitons, along
+    with the residules betwen the fits and absorbance (dotted), A and B exciton centers (dotted)
+    and representative excitation pulse shape (red).}
   \label{fig:Czech02}
 \end{figure}
+\clearpage}
 
 The few-layer MoS\textsubscript{2} thin film sample studied in this work was prepared on a
 transparent fused silica substrate by a simple sufidation reaction of a Mo thin film using a
@@ -323,7 +350,7 @@ procedure modified from a recent report. \cite{LaskarMasihhurR2013a}  %
 \autoref{fig:Czech02}a and b show the homogeneous deposition and surface smoothness of the sample
 over the centimeter-sized fused silica substrate, respectively.  %
 The Raman spectrum shows the $E_{2g}^1$ and $A_{1g}$ vibrational modes (\autoref{fig:Czech02}c)
-that are characteristic of MoS\textsubscript{2}. \cite{LiSongLin2012a}  %
+that are characteristic of MoS\textsubscript{2}. \c ite{LiSongLin2012a}  %
 The transmission electron micrograph (TEM) in \autoref{fig:Czech02}d shows the lattice fringes of
 the film with an inset fast Fourier transform (FFT) of the TEM image indicative of the hexagonal
 crystal structure of the film corresponding to the 0001 plane of MoS\textsubscript{2}.
@@ -334,7 +361,8 @@ corresponds to approximately four monolayers.  %
 and B excitonic line shapes that were extracted from the absorption spectrum. A representative
 excitation pulse profile is also shown in red for comparison.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/S3}
   \caption[MoS\textsubscript{2} absorbance.]{Extraction of excitonic features from absorbance
@@ -343,6 +371,7 @@ excitation pulse profile is also shown in red for comparison.  %
     (black), Gaussian fits (blue and red), and remainder (black dotted).}
   \label{fig:CzechS3}
 \end{figure}
+\clearpage}
 
 Extracting the exciton absorbance spectrum is complicated by the large ``rising background'' signal
 from other MoS\textsubscript{2} bands.  %
@@ -366,7 +395,8 @@ In order to compare the FWM spectra with the absorption spectrum, the signal has
 the square root of the measured FWM signal since FWM depends quadratically on the sample
 concentration and path length.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/03}
   \caption[MoS\textsubscript{2} frequency-frequency slices.]{2D frequency-frequency spectra of the
@@ -380,6 +410,7 @@ concentration and path length.  %
     of the A and B excitons, as designated from the absorption spectrum.}
   \label{fig:Czech03}
 \end{figure}
+\clearpage}
 
 The main set of data presented in this work is an $\omega_1\omega_2\tau_{21}$ ``movie'' with
 $\tau_{22\prime}=0$. 
@@ -393,7 +424,8 @@ In contrast, we see no well-defined excitonic peaks along the $\omega_2$ ``pump'
 Instead, the signal amplitude increases toward bluer $\omega_2$ values.  %
 The decrease in FWM above 2.05 eV is caused by a drop in the $\omega_2$ OPA power.
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=0.75\textwidth]{MX2/04}
   \caption[MoS\textsubscript{2} $\omega_1$ Wigner progression.]{Mixed $\omega_1$---$\tau_{21}$
@@ -403,8 +435,10 @@ The decrease in FWM above 2.05 eV is caused by a drop in the $\omega_2$ OPA powe
     marked as dashed lines within each spectrum.}
   \label{fig:Czech04}
 \end{figure}
+\clearpage}
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=0.75\textwidth]{MX2/05}
   \caption[MoS\textsubscript{2} $\omega_2$ Wigner progression.]{Mixed $\omega_2$---$\tau_{21}$
@@ -414,6 +448,7 @@ The decrease in FWM above 2.05 eV is caused by a drop in the $\omega_2$ OPA powe
     marked as dashed lines within each spectrum.}
   \label{fig:Czech05}
 \end{figure}
+\clearpage}
 
 Figures \ref{fig:Czech04} and \ref{fig:Czech05} show representative 2D frequency-delay slices from
 this movie, where the absicissa is the $\omega_1$ or $\omega_2$ frequency, respectively, the
@@ -440,7 +475,8 @@ Both the line shapes and the dynamics of the spectral features are very similar.
 \autoref{fig:Czech05} is an excitation spectrum that shows that the dynamics of the spectral
 features do not depend strongly on the $\omega_1$ frequency.
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=0.5\textwidth]{MX2/06}
   \caption[Pathway V, VI liouville pathways.]{Liouville pathways for \autoref{fig:Czech04}. gg and
@@ -450,6 +486,7 @@ features do not depend strongly on the $\omega_1$ frequency.
     either A or B excitonic states.}
   \label{fig:Czech06}
 \end{figure}
+\clearpage}
 
 The spectral features in Figures \ref{fig:Czech03}, \ref{fig:Czech04} and \ref{fig:Czech05} depend
 on the quantum mechanical interference effects caused by the different pathways.  %
@@ -541,15 +578,18 @@ $\omega_2$ is lower than the A exciton frequency (the top subplot).  %
 If population transfer of holes from the B to A valence bands occurred during temporal overlap, the
 B/A ratio would be independent of pump frequency at $\tau_21<0$.
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/07}
-  \caption[MoS\textsubscript{2} transients.]{Transients taken at the different $\omega_1$ and
-    $\omega_2$ frequencies indicated by the colored markers on the 2D spectrum. The dynamics are
-    assigned to a 680 fs fast time constant (black solid line) and a slow time constant represented
-    as an unchanging offset over this timescale (black dashed line).}
+  \caption[MoS\textsubscript{2} transients.]{
+    Transients taken at the different $\omega_1$ and $\omega_2$ frequencies indicated by the
+    colored markers on the 2D spectrum.
+    The dynamics are assigned to a 680 fs fast time constant (black solid line) and a slow time
+    constant represented as an unchanging offset over this timescale (black dashed line).}
   \label{fig:Czech07}
 \end{figure}
+\clearpage}
 
 \autoref{fig:Czech07} shows the delay transients at the different frequencies shown in the 2D
 spectrum.  %
@@ -565,7 +605,8 @@ offset that represents the long time decay.  %
 The 680 fs decay is similar to previously published pump-probe and transient absorption
 experiments. \cite{NieZhaogang2014a, SunDezheng2014a, DochertyCallumJ2014a}  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{MX2/08}
   \caption[MoS\textsubscript{2} frequency-frequency slices near pulse overlap.]{2D
@@ -573,6 +614,7 @@ experiments. \cite{NieZhaogang2014a, SunDezheng2014a, DochertyCallumJ2014a}  %
     normalized to the brightest features in each spectrum.}
   \label{fig:Czech08}
 \end{figure}
+\clearpage}
 
 The spectral features change quantitatively for delay times near temporal overlap.  %
 \autoref{fig:Czech08} shows a series of 2D spectra for both positive and negative $\tau_{21}$ delay
@@ -584,7 +626,8 @@ The spectra also develop more diagonal character as the delay time moves from ne
 values.  %
 The AB cross-peak is also a strong feature in the spectrum at early times.  %
 
-\begin{figure}[!htb]
+\afterpage{
+\begin{figure}
   \centering
   \includegraphics[width=0.5\textwidth]{MX2/09}
   \caption[Pathways I, III Liouville pathways.]{Liouville pathways for the $\omega_1$, $\omega_2$,
@@ -592,6 +635,7 @@ The AB cross-peak is also a strong feature in the spectrum at early times.  %
     A or B excitonic states.}
   \label{fig:Czech09}
 \end{figure}
+\clearpage}
 
 The pulse overlap region is complicated by the multiple Liouville pathways that must be
 considered.  %
@@ -654,5 +698,4 @@ complex MoS\textsubscript{2} and other TMDC heterostructures with quantum-state
 The frequency domain based multiresonant CMDS methods described in this paper will play a central
 role in these measurements.  %
 They use longer, independently tunable pulses that provide state-selective excitation over a wide
-spectral range without the requirement for interferometric stability.  %
-
+spectral range without the requirement for interferometric stability.  %
\ No newline at end of file
-- 
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