From cd162fef9d9f3145c1e29c63439759636ba62c41 Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Mon, 26 Feb 2018 17:08:07 -0600 Subject: 2018-02-26 17:07 --- PEDOT:PSS/agreement.png | Bin 0 -> 648749 bytes PEDOT:PSS/chapter.tex | 246 ++++++++++++++++++++++++++++++++++++----------- PEDOT:PSS/parametric.pdf | Bin 0 -> 15815 bytes dissertation.cls | 133 +++++++++++++++++++++++++ dissertation.pdf | Bin 3303728 -> 34266858 bytes dissertation.syg | 3 + dissertation.tex | 134 +++----------------------- mixed_domain/chapter.tex | 100 ++++++------------- spectroscopy/chapter.tex | 5 +- 9 files changed, 376 insertions(+), 245 deletions(-) create mode 100644 PEDOT:PSS/agreement.png create mode 100644 PEDOT:PSS/parametric.pdf create mode 100644 dissertation.cls diff --git a/PEDOT:PSS/agreement.png b/PEDOT:PSS/agreement.png new file mode 100644 index 0000000..1a7df33 Binary files /dev/null and b/PEDOT:PSS/agreement.png differ 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 Binary files /dev/null and b/PEDOT:PSS/parametric.pdf differ diff --git a/dissertation.cls b/dissertation.cls new file mode 100644 index 0000000..2d2ebc8 --- /dev/null +++ b/dissertation.cls @@ -0,0 +1,133 @@ +\ProvidesClass{dissertation} + +% --- basic --------------------------------------------------------------------------------------- + +% required: 10 to 12 point font + +\LoadClass[11pt, twoside, openright]{report} +\RequirePackage[letterpaper, margin=1in]{geometry} % 1 inch margins required +\RequirePackage{setspace} +\RequirePackage{afterpage} +\RequirePackage{color} +\RequirePackage{array} + 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a/dissertation.syg +++ b/dissertation.syg @@ -0,0 +1,3 @@ +\glossaryentry{\ensuremath {N}?\glossentry{N}|setentrycounter[]{page}\glsnumberformat}{8} +\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 -\usepackage{setspace} -\usepackage{afterpage} -\usepackage{color} -\usepackage{array} - -% headers (required: page number in upper right, nothing else) 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-\AtBeginEnvironment{verse}{\singlespacing} -\AtBeginEnvironment{tabular}{\singlespacing} - -% code highlighting -%\usepackage{minted} -\definecolor{light-gray}{gray}{0.90} -\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} -\usepackage{fixltx2e} -\usepackage{pdfpages} -\usepackage[utf8]{inputenc} - -% hyperref -\usepackage[colorlinks=true, linkcolor=black, urlcolor=blue, citecolor=black, anchorcolor=black]{hyperref} -\usepackage[all]{hypcap} % helps hyperref work properly - -% bibliography -\usepackage[backend=biber, natbib=true, sorting=none, maxbibnames=99]{biblatex} -\bibliography{bibliography} - -% glossary -\usepackage[acronym, nopostdot, nogroupskip]{glossaries} -\newcommand{\comma}{,\penalty \exhyphenpenalty} -\newlength\glsnamewidth -\setlength{\glsnamewidth}{0.3\hsize} -\setlength{\glsdescwidth}{1\hsize} -\newglossarystyle{myglossarystyle}{ - \setglossarystyle{super} - \renewenvironment{theglossary}{ - \tablehead{} - \tabletail{} - \begin{supertabular}{p{\glsnamewidth}p{\glsdescwidth}}}{\end{supertabular}} - \renewcommand{\glossentry}[2]{ - \raggedleft - \glsentryitem{##1}\glstarget{##1}{\glossentryname{##1}} & - \glossentrydesc{##1}\glspostdescription\space ##2\tabularnewline}} -\renewcommand{\arraystretch}{1} -\setglossarystyle{myglossarystyle} -\newglossary[slg]{symbolslist}{syi}{syg}{Symbols} -\makeglossaries -\include{glossary} - -\usepackage{tocloft} - -\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 -- cgit v1.2.3