From 4ddc0bcecdd172e6fbed0df2e80dfc7663b6ab73 Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Sun, 12 Nov 2017 18:51:13 -0600 Subject: structure --- BiVO4.tex | 3 - BiVO4/chapter.tex | 3 + MX2.tex | 1 - MX2/chapter.tex | 1 + PbSe.tex | 1 - PbSe/chapter.tex | 1 + colophon/chapter.tex | 4 + dissertation.pdf | Bin 9664415 -> 9667202 bytes dissertation.tex | 68 ++++++---- hardware.tex | 37 ----- hardware/auto/chapter.el | 7 + hardware/chapter.tex | 72 ++++++++++ instrument.tex | 150 --------------------- instrument/chapter.tex | 150 +++++++++++++++++++++ introduction.tex | 13 -- introduction/chapter.tex | 13 ++ materials.tex | 4 - materials/chapter.tex | 4 + procedures.tex | 1 - procedures/chapter.tex | 1 + public.tex | 120 ----------------- public/chapter.tex | 120 +++++++++++++++++ readme.tex | 4 - software.tex | 115 ---------------- software/chapter.tex | 115 ++++++++++++++++ spectroscopy.tex | 267 ------------------------------------- spectroscopy/auto/chapter.el | 9 ++ spectroscopy/chapter.tex | 311 +++++++++++++++++++++++++++++++++++++++++++ 28 files changed, 854 insertions(+), 741 deletions(-) delete mode 100644 BiVO4.tex create mode 100644 BiVO4/chapter.tex delete mode 100644 MX2.tex create mode 100644 MX2/chapter.tex delete mode 100644 PbSe.tex create mode 100644 PbSe/chapter.tex create mode 100644 colophon/chapter.tex delete mode 100644 hardware.tex create mode 100644 hardware/auto/chapter.el create mode 100644 hardware/chapter.tex delete mode 100644 instrument.tex create mode 100644 instrument/chapter.tex delete mode 100644 introduction.tex create mode 100644 introduction/chapter.tex delete mode 100644 materials.tex create mode 100644 materials/chapter.tex delete mode 100644 procedures.tex create mode 100644 procedures/chapter.tex delete mode 100644 public.tex create mode 100644 public/chapter.tex delete mode 100644 readme.tex delete mode 100644 software.tex create mode 100644 software/chapter.tex delete mode 100644 spectroscopy.tex create mode 100644 spectroscopy/auto/chapter.el create mode 100644 spectroscopy/chapter.tex diff --git a/BiVO4.tex b/BiVO4.tex deleted file mode 100644 index 604a75b..0000000 --- a/BiVO4.tex +++ /dev/null @@ -1,3 +0,0 @@ -\chapter{BiVO4} - -pass \ No newline at end of file diff --git a/BiVO4/chapter.tex b/BiVO4/chapter.tex new file mode 100644 index 0000000..604a75b --- /dev/null +++ b/BiVO4/chapter.tex @@ -0,0 +1,3 @@ +\chapter{BiVO4} + +pass \ No newline at end of file diff --git a/MX2.tex b/MX2.tex deleted file mode 100644 index 2914e65..0000000 --- a/MX2.tex +++ /dev/null @@ -1 +0,0 @@ -\chapter{MX2} \ No newline at end of file diff --git a/MX2/chapter.tex b/MX2/chapter.tex new file mode 100644 index 0000000..2914e65 --- /dev/null +++ b/MX2/chapter.tex @@ -0,0 +1 @@ +\chapter{MX2} \ No newline at end of file diff --git a/PbSe.tex b/PbSe.tex deleted file mode 100644 index 6d59c72..0000000 --- a/PbSe.tex +++ /dev/null @@ -1 +0,0 @@ -\chapter{PbSe} \ No newline at end of file diff --git a/PbSe/chapter.tex b/PbSe/chapter.tex new file mode 100644 index 0000000..6d59c72 --- /dev/null +++ b/PbSe/chapter.tex @@ -0,0 +1 @@ +\chapter{PbSe} \ No newline at end of file diff --git a/colophon/chapter.tex b/colophon/chapter.tex new file mode 100644 index 0000000..e0ace85 --- /dev/null +++ b/colophon/chapter.tex @@ -0,0 +1,4 @@ +\chapter{Colophon} + +This chapter lays out the technical aspects of this dissertation as a software and data product, +including instructions for obtaining the source and regeneration of figures and documents. % \ No newline at end of file diff --git a/dissertation.pdf b/dissertation.pdf index 1b27c74..1011949 100644 Binary files a/dissertation.pdf and b/dissertation.pdf differ diff --git a/dissertation.tex b/dissertation.tex index 1282485..52f040a 100644 --- a/dissertation.tex +++ b/dissertation.tex @@ -34,6 +34,7 @@ \setlength\parindent{0pt} \setlength{\parskip}{1em} \usepackage{enumitem} +\setlist{noitemsep, topsep=0pt, parsep=0pt, partopsep=0pt} \renewcommand{\familydefault}{\sfdefault} \newcommand{\RomanNumeral}[1]{\textrm{\uppercase\expandafter{\romannumeral #1\relax}}} \usepackage{etoolbox} @@ -95,13 +96,23 @@ \makeglossaries \include{glossary} + +\usepackage{tocloft} + +\setlength\cftparskip{0pt} +\setlength\cftbeforechapskip{-5pt} +\setlength\cftbeforesecskip{-7pt} +\setlength\cftbeforesubsecskip{-10pt} + \begin{document} +% pre --------------------------------------------------------------------------------------------- + \begin{centering} \thispagestyle{empty} % TITLE PAGE -Strategies for Coherent Multidimensional Spectroscopy of Semiconductors \\ +\textbf{Spectroscopy and Such (Working Title)} \\ \vspace{80 pt} By \\ Blaise Jonathan Thompson \\ @@ -136,8 +147,6 @@ This dissertation is approved by the following members of the Final Oral Committ \listoffigures \listoftables -\doublespacing % double spacing required for body of paper - % ACKNOWLEDGEMENTS \cleardoublepage \chapter*{Acknowledgments} @@ -152,46 +161,55 @@ This dissertation is approved by the following members of the Final Oral Committ \pagenumbering{gobble} \cleardoublepage -\begin{singlespace} - \setlength{\parskip}{\baselineskip} \vspace*{2 cm} -\noindent \emph{The explanatory stories that people find compelling are simple; are concrete rather than abstract; assign a larger role to talent, stupidity and intentions than to luck; and focus on a few striking events that happened rather than on the countless events that failed to happen.} +\noindent \emph{The explanatory stories that people find compelling are simple; are concrete rather + than abstract; assign a larger role to talent, stupidity and intentions than to luck; and focus + on a few striking events that happened rather than on the countless events that failed to + happen.} -\noindent \emph{The ultimate test of an explanation is whether it would have made the event predictable in advance.} +\noindent \emph{The ultimate test of an explanation is whether it would have made the event + predictable in advance.} -\noindent \emph{Paradoxically, it is easier to construct a coherent story when you know little, when there are fewer pieces to fit into the puzzle. Our comforting conviction that the world makes sense rests on a secure foundation: our almost unlimited ability to ignore our ignorance.} +\noindent \emph{Paradoxically, it is easier to construct a coherent story when you know little, + when there are fewer pieces to fit into the puzzle. Our comforting conviction that the world + makes sense rests on a secure foundation: our almost unlimited ability to ignore our ignorance.} \hfill -- Daniel Kahneman \cite{KahnemanDaniel2013.000} \cleardoublepage -\end{singlespace} - \pagebreak +\doublespacing % double spacing required for body of paper \pagenumbering{arabic} -%chapters -\include{introduction} -\include{spectroscopy} -\include{materials} -\include{software} -\include{instrument} -\include{PbSe} -\include{MX2} -\include{BiVO4} - -%appendix +% chapters ---------------------------------------------------------------------------------------- + +\include{introduction/chapter} +\include{spectroscopy/chapter} +\include{materials/chapter} +\include{software/chapter} +\include{instrument/chapter} +\include{PbSe/chapter} +\include{MX2/chapter} +\include{BiVO4/chapter} + +% appendix ----------------------------------------------------------------------------------------- + \begin{appendix} -\include{public} -\include{procedures} -\include{hardware} -\include{readme} +\include{public/chapter} +\include{procedures/chapter} +\include{hardware/chapter} +\include{colophon/chapter} \end{appendix} +% post -------------------------------------------------------------------------------------------- + +\pagenumbering{gobble} + \singlespacing \renewcommand{\arraystretch}{2} % there is probably a better way... \printglossaries diff --git a/hardware.tex b/hardware.tex deleted file mode 100644 index b5a02d7..0000000 --- a/hardware.tex +++ /dev/null @@ -1,37 +0,0 @@ -\chapter{Hardware} % ----------------------------------------------------------------------------- - - -\section{Adjustable periscopes} % ---------------------------------------------------------------- - - -Our light sources take on horizontal or vertical polarizations according to which tuning process is -used. % -Our experiments are opinionated about polarization, so some strategy for aligning polarization is -necessary. % -Desire fully reflective, easy to switch without changing path length (delay) etc... For several -years, we used brewster-angle polarization unifiers... % -These worked by... % -But these were very difficult to align, and they were too lossy for some of the weaker tuning -processes. % -As an alternative, we designed a more traditional periscope with adjustability for our unique -needs. % - -\begin{figure}[htp!] - \centering - \includegraphics[scale=0.1]{"hardware/periscope"} - \label{f:periscope} - \caption{CAPTION TODO} -\end{figure} - -\begin{enumerate} - \item in flipped polarization: - \begin{itemize} - \item stage near - \item upper mirror far - \end{itemize} - \item in kept polarization: - \begin{itemize} - \item stage x and upper mirror height near - \item lower mirror far - \end{itemize} -\end{enumerate} diff --git a/hardware/auto/chapter.el b/hardware/auto/chapter.el new file mode 100644 index 0000000..bff5926 --- /dev/null +++ b/hardware/auto/chapter.el @@ -0,0 +1,7 @@ +(TeX-add-style-hook + "chapter" + (lambda () + (LaTeX-add-labels + "f:periscope")) + :latex) + diff --git a/hardware/chapter.tex b/hardware/chapter.tex new file mode 100644 index 0000000..c1b505d --- /dev/null +++ b/hardware/chapter.tex @@ -0,0 +1,72 @@ +\chapter{Hardware} % ----------------------------------------------------------------------------- + +In this chapter I collect some of the specific hardware contribution details that do not belong in +the body of the dissertation. % + +\section{Adjustable periscopes} % ---------------------------------------------------------------- + +OPAs output horizontal or vertical polarizations according to which tuning process is used. % +Our experiments are opinionated about polarization, so some strategy for aligning polarization is +necessary. % TODO: cite opinionated about polarization +In addition, it is useful to bring all excitation beams to the same height. % +To this end, I designed and constructed two adjustable periscopes. % +Each periscope is designed to bring OPA output to table height standard (5 inches) while either +keeping or switching polarization. % +Both polarization configurations take the same path length, so source polarization can be switched +without large changes to zero delay. % +All of this is done with just two (switched polarization) or three (kept polarzation) +reflections. % +A picture of these periscopes is shown in \ref{f:periscope}. % + +\begin{figure}[htp!] + \centering + \includegraphics[width=\textwidth]{"hardware/periscope"} + \label{f:periscope} + \caption{CAPTION TODO} +\end{figure} + +While these periscopes are easy to align, their unique design means that it is not necessarily +obvious what the correct strategy is. % +The following strategy will always converge: +\begin{enumerate} + \item use two ``magic'' apertures along the output beamline + \item in flipped polarization (two mirror configuration): + \begin{itemize} + \item use the stage (green X, Y) to align near aperture + \item use the upper mirror (yellow TA, TB) to align far aperture + \item iterate above + \end{itemize} + \item in kept polarization (three mirror configuration): + \begin{itemize} + \item use stage X (green X) and upper mirror height (yellow TC) to align near aperture + \item use lower mirror (pink SA, SB) to align far aperture + \item iterate above + \end{itemize} +\end{enumerate} +The kept polarization alignment is derivative of the fixed polarization alignment. % +One must ensure that the fixed polarization is correctly aligned at all times. % + +Mirror B (aqua) is magnetically mounted to switch between polarization conditions. % +Ensure that the lower turning mirror (pink) does not bump into mirror B (aqua) in polarization +swtiching configuration. % +The lower turning mirror is on a rail (pink SC). % +This rail is a rough adjust for the same degree of freedom as pink SA. % +Adjust the rail only to ensure that the beam is roughly centered on the free aperture of the +turning mirror. % + +The first reflection is often accomplished using a wedge, as OPA output may be strong enough to +damage downstream optics. % +This optic can and should be replaced if more of the OPA output is desired on the table (keeping +damage thresholds in mind). % + +\subsection{Wedge polarization preference} + +TODO: wedges will be more efficent at reflecting horizontal / vertical at 45 degrees + +\section{Automated transmissive filters} % ------------------------------------------------------- + +TODO + +\section{Electronics} % -------------------------------------------------------------------------- + +TODO \ No newline at end of file diff --git a/instrument.tex b/instrument.tex deleted file mode 100644 index 6eee6e8..0000000 --- a/instrument.tex +++ /dev/null @@ -1,150 +0,0 @@ -% TODO: BerkTobyS1975.000 people trust computers too much - -\chapter{Instrumental Development} - -\section{Hardware} - -\subsection{Delay Stages} - -% TODO: discuss _all 3_ delay configurations.... implications for sign conventions etc - -\section{Signal Acquisition} - -Old boxcar: 300 ns window, ~10 micosecond delay. Onset of saturation ~2 V. - -\subsection{Digital Signal Processing} - -% TODO: - - - -\section{Artifacts and Noise} - -\subsection{Scatter} - -Scatter is a complex microscopic process whereby light traveling through a material elastically changes its propagation direction. In CMDS we use propagation direction to isolate signal. Scattering samples defeat this isolation step and allow some amount of excitation light to reach the detector. In homodyne-detected 4WM experiments, -\begin{equation} -I_{\mathrm{detected}} = |E_{\mathrm{4WM}} + E_1 + E_2 + E_{2^\prime}|^2 -\end{equation} -Where $E$ is the entire time-dependent complex electromagnetic field. When expanded, the intensity will be composed of diagonal and cross terms: -\begin{equation} -\begin{split} -I_{\mathrm{detected}} = \overline{(E_1+E_2)}E_{2^\prime} + (E_1+E_2)\overline{E_{2^\prime}} + |E_1+E_2|^2 + (E_1+E_2)\overline{E_{\mathrm{4WM}}} \\ + (E_1+E_2)\overline{E_{\mathrm{4WM}}} + \overline{E_{2^\prime}}E_{\mathrm{4WM}} + E_{2^\prime}\overline{E_{\mathrm{4WM}}} + |E_{\mathrm{4WM}}|^2 -\end{split} -\end{equation} -A similar expression in the case of heterodyne-detected 4WM is derived by \textcite{BrixnerTobias2004.000}. The goal of any `scatter rejection' processing procedure is to isolate $|E_{\mathrm{4WM}}|^2$ from the other terms. - -% TODO: verify derivation - -\subsubsection{Abandon the Random Phase Approximation} - -\subsubsection{Interference Patterns in TrEE} - -TrEE is implicitly homodyne-detected. Scatter from excitation fields will interfere on the amplitude level with TrEE signal, causing interference patterns that beat in delay and frequency space. The pattern of beating will depend on which excitation field(s) reach(es) the detector, and the parameterization of delay space chosen. - -First I focus on the interference patterns in 2D delay space where all excitation fields and the detection field are at the same frequency. - -\begin{figure}[p!] \label{fig:scatterinterferenceinTrEEold} - \centering - \includegraphics[scale=0.5]{"instrument/scatter/scatter interference in TrEE old"} - \caption[Simulated interference paterns in old delay parameterization.]{Numerically simulated interference patterns between scatter and TrEE for the old delay parametrization. Each column has scatter from a single excitation field. The top row shows the measured intensities, the bottom row shows the 2D Fourier transform, with the colorbar's dynamic range chosen to show the cross peaks.} -\end{figure} -Here I derive the slopes of constant phase for the old delay space, where $\mathrm{d1}=\tau_{2^\prime1}$ and $\mathrm{d2}=\tau_{21}$. For simplicity, I take $\tau_1$ to be $0$, so that $\tau_{21}\rightarrow\tau_2$ and $\tau_{2^\prime1}\rightarrow\tau_{2^\prime}$. The phase of signal is then -\begin{equation} -\Phi_{\mathrm{sig}} = \mathrm{e}^{-\left((\tau_{2^\prime}-\tau_2)\omega\right)} -\end{equation} -The phase of each excitation field can also be written: -\begin{eqnarray} -\Phi_{1} &=& \mathrm{e}^0 \\ -\Phi_{2} &=& \mathrm{e}^{-\tau_2\gls{omega}} \\ -\Phi_{2^\prime} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} -\end{eqnarray} -The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$ and $\Phi_\mathrm{scatter}$. The cross terms are: -\begin{eqnarray} -\Delta_{1} = \Phi_{\mathrm{sig}} &=& \mathrm{e}^{-\left((\tau_{2^\prime}-\tau_2)\omega\right)} \\ -\Delta_{2} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_2\omega} &=& \mathrm{e}^{-\left((\tau_{2^\prime}-2\tau_2)\omega\right)}\\ -\Delta_{2^\prime} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_{2^\prime}\omega} &=& \mathrm{e}^{-\tau_{2}\omega} -\end{eqnarray} -Figure \ref{fig:scatterinterferenceinTrEEold} presents numerical simulations of scatter interference as a visual aid. See Yurs 2011 \cite{YursLenaA2011.000}. -% TODO: Yurs 2011 Data - -\begin{figure}[p!] \label{fig:scatterinterferenceinTrEEcurrent} - \centering - \includegraphics[width=7in]{"instrument/scatter/scatter interference in TrEE current"} - \caption[Simulated interference paterns in current delay parameterization.]{Numerically simulated interference patterns between scatter and TrEE for the current delay parametrization. Each column has scatter from a single excitation field. The top row shows the measured intensities, the bottom row shows the 2D Fourier transform, with the colorbar's dynamic range chosen to show the cross peaks.} -\end{figure} - -Here I derive the slopes of constant phase for the current delay space, where $\mathrm{d1}=\tau_{22^\prime}$ and $\mathrm{d2}=\tau_{21}$. I take $\tau_2$ to be $0$, so that $\tau_{22^\prime}\rightarrow\tau_{2^\prime}$ and $\tau_{21}\rightarrow\tau_1$. The phase of the signal is then -\begin{equation} -\Phi_{\mathrm{sig}} = \mathrm{e}^{-\left((\tau_{2^\prime}+\tau_1)\omega\right)} -\end{equation} -The phase of each excitation field can also be written: -\begin{eqnarray} -\Phi_{1} &=& \mathrm{e}^{-\tau_1\omega} \\ -\Phi_{2} &=& \mathrm{e}^{0} \\ -\Phi_{2^\prime} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} -\end{eqnarray} -The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$ and $\Phi_\mathrm{scatter}$. The cross terms are: -\begin{eqnarray} -\Delta_{1} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_1\omega} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} \\ -\Delta_{2} = \Phi_{\mathrm{sig}} &=& \mathrm{e}^{-\left((\tau_2+\tau_1)\omega\right)} \\ -\Delta_{2^\prime} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_{2^\prime}\omega} &=& \mathrm{e}^{-\tau_1\omega} -\end{eqnarray} -Figure \ref{fig:scatterinterferenceinTrEEcurrent} presents numerical simulations of scatter interference for the current delay parameterization. - -\subsubsection{Instrumental Removal of Scatter} - -The effects of scatter can be entirely removed from CMDS signal by combining two relatively straight-forward instrumental techniques: \textit{chopping} and \textit{fibrillation}. Conceptually, chopping removes intensity-level offset terms and fibrillation removes amplitude-level interference terms. Both techniques work by modulating signal and scatter terms differently so that they may be separated after light collection. - -\begin{table}[h] \label{tab:phase_shifted_parallel_modulation} - \begin{center} - \begin{tabular}{ r | c | c | c | c } - & A & B & C & D \\ - signal & & & \checkmark & \\ - scatter 1 & & \checkmark & \checkmark & \\ - scatter 2 & & & \checkmark & \checkmark \\ - other & \checkmark & \checkmark & \checkmark & \checkmark - \end{tabular} - \end{center} - \caption[Shot-types in phase shifted parallel modulation.]{Four shot-types in a general phase shifted parallel modulation scheme. The `other' category represents anything that doesn't depend on either chopper, including scatter from other excitation sources, background light, detector voltage offsets, etc.} -\end{table} - -We use the dual chopping scheme developed by \textcite{FurutaKoichi2012.000} called `phase shifted parallel modulation'. In this scheme, two excitation sources are chopped at 1/4 of the laser repetition rate (two pulses on, two pulses off). Very similar schemes are discussed by \textcite{AugulisRamunas2011.000} and \textcite{HeislerIsmael2014.000} for two-dimensional electronic spectroscopy. The two chop patterns are phase-shifted to make the four-pulse pattern represented in Table \ref{tab:phase_shifted_parallel_modulation}. In principle this chopping scheme can be achieved with a single judiciously placed mechanical chopper - this is one of the advantages of Furuta's scheme. Due to practical considerations we have generally used two choppers, one on each OPA. The key to phase shifted parallel modulation is that signal only appears when both of your chopped beams are passed. It is simple to show how signal can be separated through simple addition and subtraction of the A, B, C, and D phases shown in Table \ref{tab:phase_shifted_parallel_modulation}. First, the components of each phase: -\begin{eqnarray} -A &=& I_\mathrm{other} \\ -B &=& I_\mathrm{1} + I_\mathrm{other} \\ -C &=& I_\mathrm{signal} + I_\mathrm{1} + I_\mathrm{2} + I_\mathrm{other} \\ -D &=& I_\mathrm{2} + I_\mathrm{other} -\end{eqnarray} -Grouping into difference pairs, -\begin{eqnarray} -A-B &=& -I_\mathrm{1} \\ -C-D &=& I_\mathrm{signal} + I_\mathrm{1} -\end{eqnarray} -So: -\begin{equation} \label{eq:dual_chopping} -A-B+C-D = I_\mathrm{signal} -\end{equation} -I have ignored amplitude-level interference terms in this treatment because they cannot be removed via any chopping strategy. Interference between signal and an excitation beam will only appear in `C'-type shots, so it will not be removed in Equation \ref{eq:dual_chopping}. To remove such interference terms, you must \textit{fibrillate} your excitation fields. - -An alternative to dual chopping is single-chopping and `leveling'... this technique was used prior to May 2016 in the Wright Group... `leveling' and single-chopping is also used in some early 2DES work... \cite{BrixnerTobias2004.000}. - -\begin{figure}[p!] \label{fig:ta-chopping-comparison} - \centering - \includegraphics[scale=0.5]{"instrument/scatter/TA chopping comparison"} - \caption[Comparison of single, dual chopping.]{Comparison of single and dual chopping in a MoS\textsubscript{2} transient absorption experiment. Note that this data has not been processed in any way - the colorbar represents changes in intensity seen by the detector. The grey line near 2 eV represents the pump energy. The inset labels are the number of laser shots taken and the chopping strategy used.} -\end{figure} - -Figure \ref{fig:ta-chopping-comparison} shows the effects of dual chopping for some representative MoS\textsubscript{2} TA data. Each subplot is a probe wigner, with the vertical grey line representing the pump energy. Note that the single chopper passes pump scatter, visible as a time-invariant increase in intensity when the probe and monochromator are near the pump energy. Dual chopping efficiently removes pump scatter, but at the cost of signal to noise for the same number of laser shots. Taking twice as many laser shots when dual chopping brings the signal to noise to at least as good as the original single chopping. - -Fibrillation is the intentional randomization of excitation phase during an experiment. Because the interference term depends on the phase of the excitation field relative to the signal, averaging over many shots with random phase will cause the interference term to approach zero. This is a well known strategy for removing unwanted interference terms \cite{SpectorIvanC2015.000, McClainBrianL2004.000}. - -\section{Light Generation} - -\subsection{Automated OPA Tuning} - -\section{Optomechanics} - -\subsection{Automated Neutral Density Wheels} - - diff --git a/instrument/chapter.tex b/instrument/chapter.tex new file mode 100644 index 0000000..6eee6e8 --- /dev/null +++ b/instrument/chapter.tex @@ -0,0 +1,150 @@ +% TODO: BerkTobyS1975.000 people trust computers too much + +\chapter{Instrumental Development} + +\section{Hardware} + +\subsection{Delay Stages} + +% TODO: discuss _all 3_ delay configurations.... implications for sign conventions etc + +\section{Signal Acquisition} + +Old boxcar: 300 ns window, ~10 micosecond delay. Onset of saturation ~2 V. + +\subsection{Digital Signal Processing} + +% TODO: + + + +\section{Artifacts and Noise} + +\subsection{Scatter} + +Scatter is a complex microscopic process whereby light traveling through a material elastically changes its propagation direction. In CMDS we use propagation direction to isolate signal. Scattering samples defeat this isolation step and allow some amount of excitation light to reach the detector. In homodyne-detected 4WM experiments, +\begin{equation} +I_{\mathrm{detected}} = |E_{\mathrm{4WM}} + E_1 + E_2 + E_{2^\prime}|^2 +\end{equation} +Where $E$ is the entire time-dependent complex electromagnetic field. When expanded, the intensity will be composed of diagonal and cross terms: +\begin{equation} +\begin{split} +I_{\mathrm{detected}} = \overline{(E_1+E_2)}E_{2^\prime} + (E_1+E_2)\overline{E_{2^\prime}} + |E_1+E_2|^2 + (E_1+E_2)\overline{E_{\mathrm{4WM}}} \\ + (E_1+E_2)\overline{E_{\mathrm{4WM}}} + \overline{E_{2^\prime}}E_{\mathrm{4WM}} + E_{2^\prime}\overline{E_{\mathrm{4WM}}} + |E_{\mathrm{4WM}}|^2 +\end{split} +\end{equation} +A similar expression in the case of heterodyne-detected 4WM is derived by \textcite{BrixnerTobias2004.000}. The goal of any `scatter rejection' processing procedure is to isolate $|E_{\mathrm{4WM}}|^2$ from the other terms. + +% TODO: verify derivation + +\subsubsection{Abandon the Random Phase Approximation} + +\subsubsection{Interference Patterns in TrEE} + +TrEE is implicitly homodyne-detected. Scatter from excitation fields will interfere on the amplitude level with TrEE signal, causing interference patterns that beat in delay and frequency space. The pattern of beating will depend on which excitation field(s) reach(es) the detector, and the parameterization of delay space chosen. + +First I focus on the interference patterns in 2D delay space where all excitation fields and the detection field are at the same frequency. + +\begin{figure}[p!] \label{fig:scatterinterferenceinTrEEold} + \centering + \includegraphics[scale=0.5]{"instrument/scatter/scatter interference in TrEE old"} + \caption[Simulated interference paterns in old delay parameterization.]{Numerically simulated interference patterns between scatter and TrEE for the old delay parametrization. Each column has scatter from a single excitation field. The top row shows the measured intensities, the bottom row shows the 2D Fourier transform, with the colorbar's dynamic range chosen to show the cross peaks.} +\end{figure} +Here I derive the slopes of constant phase for the old delay space, where $\mathrm{d1}=\tau_{2^\prime1}$ and $\mathrm{d2}=\tau_{21}$. For simplicity, I take $\tau_1$ to be $0$, so that $\tau_{21}\rightarrow\tau_2$ and $\tau_{2^\prime1}\rightarrow\tau_{2^\prime}$. The phase of signal is then +\begin{equation} +\Phi_{\mathrm{sig}} = \mathrm{e}^{-\left((\tau_{2^\prime}-\tau_2)\omega\right)} +\end{equation} +The phase of each excitation field can also be written: +\begin{eqnarray} +\Phi_{1} &=& \mathrm{e}^0 \\ +\Phi_{2} &=& \mathrm{e}^{-\tau_2\gls{omega}} \\ +\Phi_{2^\prime} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} +\end{eqnarray} +The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$ and $\Phi_\mathrm{scatter}$. The cross terms are: +\begin{eqnarray} +\Delta_{1} = \Phi_{\mathrm{sig}} &=& \mathrm{e}^{-\left((\tau_{2^\prime}-\tau_2)\omega\right)} \\ +\Delta_{2} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_2\omega} &=& \mathrm{e}^{-\left((\tau_{2^\prime}-2\tau_2)\omega\right)}\\ +\Delta_{2^\prime} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_{2^\prime}\omega} &=& \mathrm{e}^{-\tau_{2}\omega} +\end{eqnarray} +Figure \ref{fig:scatterinterferenceinTrEEold} presents numerical simulations of scatter interference as a visual aid. See Yurs 2011 \cite{YursLenaA2011.000}. +% TODO: Yurs 2011 Data + +\begin{figure}[p!] \label{fig:scatterinterferenceinTrEEcurrent} + \centering + \includegraphics[width=7in]{"instrument/scatter/scatter interference in TrEE current"} + \caption[Simulated interference paterns in current delay parameterization.]{Numerically simulated interference patterns between scatter and TrEE for the current delay parametrization. Each column has scatter from a single excitation field. The top row shows the measured intensities, the bottom row shows the 2D Fourier transform, with the colorbar's dynamic range chosen to show the cross peaks.} +\end{figure} + +Here I derive the slopes of constant phase for the current delay space, where $\mathrm{d1}=\tau_{22^\prime}$ and $\mathrm{d2}=\tau_{21}$. I take $\tau_2$ to be $0$, so that $\tau_{22^\prime}\rightarrow\tau_{2^\prime}$ and $\tau_{21}\rightarrow\tau_1$. The phase of the signal is then +\begin{equation} +\Phi_{\mathrm{sig}} = \mathrm{e}^{-\left((\tau_{2^\prime}+\tau_1)\omega\right)} +\end{equation} +The phase of each excitation field can also be written: +\begin{eqnarray} +\Phi_{1} &=& \mathrm{e}^{-\tau_1\omega} \\ +\Phi_{2} &=& \mathrm{e}^{0} \\ +\Phi_{2^\prime} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} +\end{eqnarray} +The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$ and $\Phi_\mathrm{scatter}$. The cross terms are: +\begin{eqnarray} +\Delta_{1} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_1\omega} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} \\ +\Delta_{2} = \Phi_{\mathrm{sig}} &=& \mathrm{e}^{-\left((\tau_2+\tau_1)\omega\right)} \\ +\Delta_{2^\prime} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_{2^\prime}\omega} &=& \mathrm{e}^{-\tau_1\omega} +\end{eqnarray} +Figure \ref{fig:scatterinterferenceinTrEEcurrent} presents numerical simulations of scatter interference for the current delay parameterization. + +\subsubsection{Instrumental Removal of Scatter} + +The effects of scatter can be entirely removed from CMDS signal by combining two relatively straight-forward instrumental techniques: \textit{chopping} and \textit{fibrillation}. Conceptually, chopping removes intensity-level offset terms and fibrillation removes amplitude-level interference terms. Both techniques work by modulating signal and scatter terms differently so that they may be separated after light collection. + +\begin{table}[h] \label{tab:phase_shifted_parallel_modulation} + \begin{center} + \begin{tabular}{ r | c | c | c | c } + & A & B & C & D \\ + signal & & & \checkmark & \\ + scatter 1 & & \checkmark & \checkmark & \\ + scatter 2 & & & \checkmark & \checkmark \\ + other & \checkmark & \checkmark & \checkmark & \checkmark + \end{tabular} + \end{center} + \caption[Shot-types in phase shifted parallel modulation.]{Four shot-types in a general phase shifted parallel modulation scheme. The `other' category represents anything that doesn't depend on either chopper, including scatter from other excitation sources, background light, detector voltage offsets, etc.} +\end{table} + +We use the dual chopping scheme developed by \textcite{FurutaKoichi2012.000} called `phase shifted parallel modulation'. In this scheme, two excitation sources are chopped at 1/4 of the laser repetition rate (two pulses on, two pulses off). Very similar schemes are discussed by \textcite{AugulisRamunas2011.000} and \textcite{HeislerIsmael2014.000} for two-dimensional electronic spectroscopy. The two chop patterns are phase-shifted to make the four-pulse pattern represented in Table \ref{tab:phase_shifted_parallel_modulation}. In principle this chopping scheme can be achieved with a single judiciously placed mechanical chopper - this is one of the advantages of Furuta's scheme. Due to practical considerations we have generally used two choppers, one on each OPA. The key to phase shifted parallel modulation is that signal only appears when both of your chopped beams are passed. It is simple to show how signal can be separated through simple addition and subtraction of the A, B, C, and D phases shown in Table \ref{tab:phase_shifted_parallel_modulation}. First, the components of each phase: +\begin{eqnarray} +A &=& I_\mathrm{other} \\ +B &=& I_\mathrm{1} + I_\mathrm{other} \\ +C &=& I_\mathrm{signal} + I_\mathrm{1} + I_\mathrm{2} + I_\mathrm{other} \\ +D &=& I_\mathrm{2} + I_\mathrm{other} +\end{eqnarray} +Grouping into difference pairs, +\begin{eqnarray} +A-B &=& -I_\mathrm{1} \\ +C-D &=& I_\mathrm{signal} + I_\mathrm{1} +\end{eqnarray} +So: +\begin{equation} \label{eq:dual_chopping} +A-B+C-D = I_\mathrm{signal} +\end{equation} +I have ignored amplitude-level interference terms in this treatment because they cannot be removed via any chopping strategy. Interference between signal and an excitation beam will only appear in `C'-type shots, so it will not be removed in Equation \ref{eq:dual_chopping}. To remove such interference terms, you must \textit{fibrillate} your excitation fields. + +An alternative to dual chopping is single-chopping and `leveling'... this technique was used prior to May 2016 in the Wright Group... `leveling' and single-chopping is also used in some early 2DES work... \cite{BrixnerTobias2004.000}. + +\begin{figure}[p!] \label{fig:ta-chopping-comparison} + \centering + \includegraphics[scale=0.5]{"instrument/scatter/TA chopping comparison"} + \caption[Comparison of single, dual chopping.]{Comparison of single and dual chopping in a MoS\textsubscript{2} transient absorption experiment. Note that this data has not been processed in any way - the colorbar represents changes in intensity seen by the detector. The grey line near 2 eV represents the pump energy. The inset labels are the number of laser shots taken and the chopping strategy used.} +\end{figure} + +Figure \ref{fig:ta-chopping-comparison} shows the effects of dual chopping for some representative MoS\textsubscript{2} TA data. Each subplot is a probe wigner, with the vertical grey line representing the pump energy. Note that the single chopper passes pump scatter, visible as a time-invariant increase in intensity when the probe and monochromator are near the pump energy. Dual chopping efficiently removes pump scatter, but at the cost of signal to noise for the same number of laser shots. Taking twice as many laser shots when dual chopping brings the signal to noise to at least as good as the original single chopping. + +Fibrillation is the intentional randomization of excitation phase during an experiment. Because the interference term depends on the phase of the excitation field relative to the signal, averaging over many shots with random phase will cause the interference term to approach zero. This is a well known strategy for removing unwanted interference terms \cite{SpectorIvanC2015.000, McClainBrianL2004.000}. + +\section{Light Generation} + +\subsection{Automated OPA Tuning} + +\section{Optomechanics} + +\subsection{Automated Neutral Density Wheels} + + diff --git a/introduction.tex b/introduction.tex deleted file mode 100644 index 210b1e6..0000000 --- a/introduction.tex +++ /dev/null @@ -1,13 +0,0 @@ -\chapter{Introduction} - -\section{Coherent Multidimensional Spectroscopy} - -\Gls{CMDS}, \gls{coherent multidimensional spectroscopy} - -\section{Photophysics in Semiconductor Systems} - -\subsection{Solar Energy Generation} - -I like to do \acrlong{TA} - -% TODO: discuss Schottky-Quasar, strategies for overcoming diff --git a/introduction/chapter.tex b/introduction/chapter.tex new file mode 100644 index 0000000..210b1e6 --- /dev/null +++ b/introduction/chapter.tex @@ -0,0 +1,13 @@ +\chapter{Introduction} + +\section{Coherent Multidimensional Spectroscopy} + +\Gls{CMDS}, \gls{coherent multidimensional spectroscopy} + +\section{Photophysics in Semiconductor Systems} + +\subsection{Solar Energy Generation} + +I like to do \acrlong{TA} + +% TODO: discuss Schottky-Quasar, strategies for overcoming diff --git a/materials.tex b/materials.tex deleted file mode 100644 index e868421..0000000 --- a/materials.tex +++ /dev/null @@ -1,4 +0,0 @@ -\chapter{Materials} - -"Kroemer's Lemma of Proven Ignorance": If, in discussing a semiconductor problem, you cannot draw an Energy Band Diagram, this shows that you don't know what you are talking about, If you can draw one, but don't, then your audience won't know what you are talking about. %TODO: cite - diff --git a/materials/chapter.tex b/materials/chapter.tex new file mode 100644 index 0000000..e868421 --- /dev/null +++ b/materials/chapter.tex @@ -0,0 +1,4 @@ +\chapter{Materials} + +"Kroemer's Lemma of Proven Ignorance": If, in discussing a semiconductor problem, you cannot draw an Energy Band Diagram, this shows that you don't know what you are talking about, If you can draw one, but don't, then your audience won't know what you are talking about. %TODO: cite + diff --git a/procedures.tex b/procedures.tex deleted file mode 100644 index 3cb42bf..0000000 --- a/procedures.tex +++ /dev/null @@ -1 +0,0 @@ -\chapter{Procedures} \ No newline at end of file diff --git a/procedures/chapter.tex b/procedures/chapter.tex new file mode 100644 index 0000000..3cb42bf --- /dev/null +++ b/procedures/chapter.tex @@ -0,0 +1 @@ +\chapter{Procedures} \ No newline at end of file diff --git a/public.tex b/public.tex deleted file mode 100644 index 9c859e7..0000000 --- a/public.tex +++ /dev/null @@ -1,120 +0,0 @@ -% http://scifun.chem.wisc.edu/Thesis_Awards/chapter_guidelines.html - -\chapter{Public} - -\section{Chemical systems} % --------------------------------------------------------------------- - -Chemical systems are complex! % -They contain many molecules ($10^{25}$ in a cup of coffee, 1 trillion in each human cell). % -These molecules have multiple interaction modes, both internal (intramolecular) and external -(intermolecular). % -The reactivity of the system taken as a whole can be dominated by very rare but very important -species, \textit{e.g.} catalysts. % - -Despite this complexity, scientists have gotten very good at describing chemical systems through -representations of dynamic equilibrium. % -In such situations, several key parameters emerge: % -\begin{itemize} - \item concentration - \item timescale (rate) - \item lengthscale -\end{itemize} - -\subsection{Concentration} - -\subsection{Timescale} - -% TODO: dynamics in chemical systems: collision time, dephasing, rotation, relaxation, diffusion... - -\subsection{Lengthscale} - -\section{Analytical chemistry} % ----------------------------------------------------------------- - -Traditionally, chemists have seen fit to divide themselves into four specializations: analytical, -inorganic, organic, and physical. % -In recent years, materials chemistry and chemical biology have become specializations in their own -right. % -This dissertation focuses on analytical chemistry. % - -Analytical chemists separate, identify, and quantify chemical systems. % -To do this, we build instruments that exploit physical properties of the chemical components: % -\begin{itemize} - \item separation science (chromatography, electrophoresis) - \item mass spectrometry - \item electrochemistry - \item microscopy - \item spectroscopy -\end{itemize} -Spectroscopy is a family of strategies that exploit the interaction of chemical systems with -light. % - -\section{Spectroscopy} % ------------------------------------------------------------------------- - -Molecules respond to electric fields. % -Static electric fields cause charged molecules (ions) to move, as in electrophoresis and mass -spectrometry. % -Oscillating electric fields, also known as light, can interact directly with the molecules -themselves, driving transitions. % -However, these transitions can only be driven with the appropriate frequency of light -(resonance). % -Different frequencies (colors) of light interact with different kinds of transitions, revealing -different features of the molecule of interest. % - -% TODO: different energy ranges / transition types (nuclear, rotational, vibrational, electronic) - -% TODO: how is a photon created or absorbed? - -\subsection{Nonlinear spectroscopy} - -Spectroscopy is fantastic, but sometimes simple experiments don't reveal everything. % -Nonlinear spectroscopy uses multiple electric fields simultaniously, revealing even more -information about the chemical system. % - -% TODO: simple graphic of homogeneous vs inhomogeneous broadening - -% TODO: 2D freq-freq with increasing inhomogeneity (from Dan's theory work) - -\section{Instrumentation} % ---------------------------------------------------------------------- - -To accomplish nonlinear spectroscopy, specialized light sources are needed: % -\begin{itemize} - \item gigantic electric fields - \item ultrafast time resoution - \item tunable frequencies -\end{itemize} - -\subsection{LASER} - -These sources are made using Light Amplified by the Stimulated Emission of Radiation (LASER). % - -% TODO: discussion of the original LASER, basic LASER physics - -% TODO: discuss temporal coherence - -% TODO: discuss pulsed sources - -By keeping a wide range ofr colors in phase simulatniously, we are able to create truly ultrafast -pulses of light. % -The work presented in this dissertation was primarily taken using a 35 fs 1 KHz system. % - -35 fs ($35\times10^{15}$ second) pulses are incredibly short: -\begin{equation} - \frac{\text{pulse duration (35 fs)}}{\text{time between pulses (1 ms)}} \approx - \frac{\text{5.75 months}}{\text{age of universe (13.7 billion years)}} % TODO: cite age -\end{equation} -proportionally, our sample spends 6 months in the ``sun'' for every age of the unverse in the -dark. % - -Because all of the energy within the pulse is compressed to such a short period of time, these -pulses are also incredibly powerful: -\begin{equation} - \frac{\text{energy per pulse (4 mJ)}}{\text{pulse duration (35 fs)}} \approx - \frac{\text{US electricity generation} (5.43\times10^{11} W)}{5} % TODO: cite generation -\end{equation} -this laser outputs electric fields one fifth as powerful as total US electricity generation (2016). - -% TODO: pulses are very thin (draw circle, use thickness of paper) to motivate 'hard to handle' - -\subsection{OPA} - -% https://osf.io/vwhjk/ \ No newline at end of file diff --git a/public/chapter.tex b/public/chapter.tex new file mode 100644 index 0000000..9c859e7 --- /dev/null +++ b/public/chapter.tex @@ -0,0 +1,120 @@ +% http://scifun.chem.wisc.edu/Thesis_Awards/chapter_guidelines.html + +\chapter{Public} + +\section{Chemical systems} % --------------------------------------------------------------------- + +Chemical systems are complex! % +They contain many molecules ($10^{25}$ in a cup of coffee, 1 trillion in each human cell). % +These molecules have multiple interaction modes, both internal (intramolecular) and external +(intermolecular). % +The reactivity of the system taken as a whole can be dominated by very rare but very important +species, \textit{e.g.} catalysts. % + +Despite this complexity, scientists have gotten very good at describing chemical systems through +representations of dynamic equilibrium. % +In such situations, several key parameters emerge: % +\begin{itemize} + \item concentration + \item timescale (rate) + \item lengthscale +\end{itemize} + +\subsection{Concentration} + +\subsection{Timescale} + +% TODO: dynamics in chemical systems: collision time, dephasing, rotation, relaxation, diffusion... + +\subsection{Lengthscale} + +\section{Analytical chemistry} % ----------------------------------------------------------------- + +Traditionally, chemists have seen fit to divide themselves into four specializations: analytical, +inorganic, organic, and physical. % +In recent years, materials chemistry and chemical biology have become specializations in their own +right. % +This dissertation focuses on analytical chemistry. % + +Analytical chemists separate, identify, and quantify chemical systems. % +To do this, we build instruments that exploit physical properties of the chemical components: % +\begin{itemize} + \item separation science (chromatography, electrophoresis) + \item mass spectrometry + \item electrochemistry + \item microscopy + \item spectroscopy +\end{itemize} +Spectroscopy is a family of strategies that exploit the interaction of chemical systems with +light. % + +\section{Spectroscopy} % ------------------------------------------------------------------------- + +Molecules respond to electric fields. % +Static electric fields cause charged molecules (ions) to move, as in electrophoresis and mass +spectrometry. % +Oscillating electric fields, also known as light, can interact directly with the molecules +themselves, driving transitions. % +However, these transitions can only be driven with the appropriate frequency of light +(resonance). % +Different frequencies (colors) of light interact with different kinds of transitions, revealing +different features of the molecule of interest. % + +% TODO: different energy ranges / transition types (nuclear, rotational, vibrational, electronic) + +% TODO: how is a photon created or absorbed? + +\subsection{Nonlinear spectroscopy} + +Spectroscopy is fantastic, but sometimes simple experiments don't reveal everything. % +Nonlinear spectroscopy uses multiple electric fields simultaniously, revealing even more +information about the chemical system. % + +% TODO: simple graphic of homogeneous vs inhomogeneous broadening + +% TODO: 2D freq-freq with increasing inhomogeneity (from Dan's theory work) + +\section{Instrumentation} % ---------------------------------------------------------------------- + +To accomplish nonlinear spectroscopy, specialized light sources are needed: % +\begin{itemize} + \item gigantic electric fields + \item ultrafast time resoution + \item tunable frequencies +\end{itemize} + +\subsection{LASER} + +These sources are made using Light Amplified by the Stimulated Emission of Radiation (LASER). % + +% TODO: discussion of the original LASER, basic LASER physics + +% TODO: discuss temporal coherence + +% TODO: discuss pulsed sources + +By keeping a wide range ofr colors in phase simulatniously, we are able to create truly ultrafast +pulses of light. % +The work presented in this dissertation was primarily taken using a 35 fs 1 KHz system. % + +35 fs ($35\times10^{15}$ second) pulses are incredibly short: +\begin{equation} + \frac{\text{pulse duration (35 fs)}}{\text{time between pulses (1 ms)}} \approx + \frac{\text{5.75 months}}{\text{age of universe (13.7 billion years)}} % TODO: cite age +\end{equation} +proportionally, our sample spends 6 months in the ``sun'' for every age of the unverse in the +dark. % + +Because all of the energy within the pulse is compressed to such a short period of time, these +pulses are also incredibly powerful: +\begin{equation} + \frac{\text{energy per pulse (4 mJ)}}{\text{pulse duration (35 fs)}} \approx + \frac{\text{US electricity generation} (5.43\times10^{11} W)}{5} % TODO: cite generation +\end{equation} +this laser outputs electric fields one fifth as powerful as total US electricity generation (2016). + +% TODO: pulses are very thin (draw circle, use thickness of paper) to motivate 'hard to handle' + +\subsection{OPA} + +% https://osf.io/vwhjk/ \ No newline at end of file diff --git a/readme.tex b/readme.tex deleted file mode 100644 index 3e76fc7..0000000 --- a/readme.tex +++ /dev/null @@ -1,4 +0,0 @@ -\chapter{README} - -This chapter lays out the technical aspects of this dissertation as a software and data product, -including instructions for obtaining the source and regeneration of figures and documents. % \ No newline at end of file diff --git a/software.tex b/software.tex deleted file mode 100644 index e2c9652..0000000 --- a/software.tex +++ /dev/null @@ -1,115 +0,0 @@ -% TODO: add StoddenVictoria2016.000 (Enhancing reproducibility for computational methods) -% TODO: add MillmanKJarrod2011.000 (Python for Scientists and Engineers) -% TODO: add vanderWaltStefan2011.000 (The NumPy Array: A Structure for Efficient Numerical Computation) -% TODO: reference https://www.nsf.gov/pubs/2016/nsf16532/nsf16532.htm (Software Infrastructure for Sustained Innovation (SI2: SSE & SSI)) - -\chapter{Software} - -Cutting-edge science increasingly relies on custom software. In their 2008 survey, \textcite{HannayJoErskine2009.000} demonstrated just how important software is to the modern scientist. -\begin{enumerate}[topsep=-1.5ex, itemsep=0ex, partopsep=0ex, parsep=0ex, label=$\rightarrow$] - \item 84.3\% of surveyed scientists state that developing scientific software is important or very important for their own research. - \item 91.2\% of surveyed scientists state that using scientific software is important or very important for their own research. - \item On average, scientists spend approximately 40\% of their work time using scientific software. - \item On average, scientists spend approximately 30\% of their work time developing scientific software. -\end{enumerate} -Despite the importance of software to science and scientists, most scientists are not familiar with basic software engineering concepts. -% TODO: demonstrate that `most scientists are not familiar with basic software engineering concepts' -This is in part due to the their general lack of formal training in programming and software development. \textcite{HannayJoErskine2009.000} found that over 90\% of scientists learn software development through `informal self study'. Indeed, I myself have never been formally trained in software development. - -Software development in a scientific context poses unique challenges. Many traditional software development paradigms demand an upfront articulation of goals and requirements. This allows the developers to carefully design their software, even before a single line of code is written. In her seminal 2005 case study \textcite{SegalJudith2005.000} describes a collaboration between a team of researchers and a contracted team of software engineers. Ultimately -% TODO: finish the discussion of SegalJudith2005.000 -% TODO: segue to reccomendation of agile development practices: http://agilemanifesto.org/ - -\section{Overview} - -In the Wright Group, \gls{PyCMDS} replaces the old acquisition softwares `ps control', written by Kent Meyer and `Control for Lots of Research in Spectroscopy' written by Schuyler Kain. - -\section{WrightTools} - -WrightTools is a software package at the heart of all work in the Wright Group. - -\section{PyCMDS} - -PyCMDS directly addresses the hardware during experiments. - -\subsection{Overview} - -PyCMDS has, through software improvements alone, dramatically lessened scan times... - -\begin{itemize}[topsep=-1.5ex, itemsep=0ex, partopsep=0ex, parsep=0ex, label=$\rightarrow$] - \item simultaneous motor motion - \item digital signal processing % TODO: reference section when it exists - \item ideal axis positions \ref{sec:ideal_axis_positions} -\end{itemize} - -\subsection{Ideal Axis Positions}\label{sec:ideal_axis_positions} - -Frequency domain multidimensional spectroscopy is a time-intensive process. A typical \gls{pixel} takes between one-half second and three seconds to acquire. Depending on the exact hardware being scanned and signal being detected, this time may be mostly due to hardware motion or signal collection. Due to the \gls{curse of dimensionality}, a typical three-dimensional CMDS experiment contains roughly 100,000 pixels. CMDS hardware is transiently-reliable, so speeding up experiments is a crucial component of unlocking ever larger dimensionalities and higher resolutions. - -One obvious way to decrease the scan-time is to take fewer pixels. Traditionally, multidimensional scans are done with linearly arranged points in each axis---this is the simplest configuration to program into the acquisition software. Because signal features are often sparse or slowly varying (especially so in high-dimensional scans) linear stepping means that \emph{most of the collected pixels} are duplicates or simply noise. A more intelligent choice of axis points can capture the same nonlinear spectrum in a fraction of the total pixel count. - -An ideal distribution of pixels is linearized in \emph{signal}, not coordinate. This means that every signal level (think of a contour in the N-dimensional case) has roughly the same number of pixels defining it. If some generic multidimensional signal goes between 0 and 1, one would want roughly 10\% of the pixels to be between 0.9 and 1.0, 10\% between 0.8 and 0.9 and so on. If the signal is sparse in the space explored (imagine a narrow two-dimensional Lorentzian in the center of a large 2D-Frequency scan) this would place the majority of the pixels near the narrow peak feature(s), with only a few of them defining the large (in axis space) low-signal floor. In contrast linear stepping would allocate the vast majority of the pixels in the low-signal 0.0 to 0.1 region, with only a few being used to capture the narrow peak feature. Of course, linearizing pixels in signal requires prior expectations about the shape of the multidimensional signal---linear stepping is still an appropriate choice for low-resolution ``survey'' scans. - -CMDS scans often posses correlated features in the multidimensional space. In order to capture such features as cheaply as possible, one would want to define regions of increased pixel density along the correlated (diagonal) lineshape. As a concession to reasonable simplicity, our acquisition software (PyCMDS) assumes that all scans constitute a regular array with-respect-to the scanned axes. We can acquire arbitrary points along each axis, but not for the multidimensional scan. This means that we cannot achieve strictly ideal pixel distributions for arbitrary datasets. Still, we can do much better than linear spacing. % TODO: refer to PyCMDS/WrightTools 'regularity' requirement when that section exists - -Almost all CMDS lineshapes (in frequency and delay) can be described using just a few lineshape functions: - -\begin{itemize}[topsep=-1.5ex, itemsep=0ex, partopsep=0ex, parsep=0ex, label=$\rightarrow$] - \item exponential - \item Gaussian - \item Lorentzian - \item bimolecular -\end{itemize} - -Exponential and bimolecular dynamics fall out of simple first and second-order kinetics (I will ignore higher-order kinetics here). Gaussians come from our Gaussian pulse envelopes or from normally-distributed inhomogeneous broadening. The measured line-shapes are actually convolutions of the above. I will ignore the convolution except for a few illustrative special cases. More exotic lineshapes are possible in CMDS---quantum beating and breathing modes, for example---I will also ignore these. Derivations of the ideal pixel positions for each of these lineshapes appear below. %TODO: cite Wright Group quantum beating paper, Kambempati breathing paper - -\subsection{Exponential} - -Simple exponential decays are typically used to describe population and coherence-level dynamics in CMDS. For some generic exponential signal $S$ with time constant $\tau$, - -\begin{equation} \label{eq:simple_exponential_decay} -S(t) = \me^{-\frac{t}{\tau}}. -\end{equation} - -We can write the conjugate equation to \ref{eq:simple_exponential_decay}, asking ``what $t$ do I need to get a certain signal level?'': - -\begin{eqnarray} -\log{(S)} &=& -\frac{t}{\tau} \\ -t &=& -\tau\log{(S)}. -\end{eqnarray} - -So to step linearly in $t$, my step size has to go as $-\tau\log{(S)}$. - -We want to go linearly in signal, meaning that we want to divide $S$ into even sections. If $S$ goes from 0 to 1 and we choose to acquire $N$ points, - -\begin{eqnarray} -t_n &=& -\tau\log{\left(\frac{n}{N}\right)}. -\end{eqnarray} - -Note that $t_n$ starts at long times and approaches zero delay. So the first $t_1$ is the smallest signal and $t_N$ is the largest. - -Now we can start to consider realistic cases, like where $\tau$ is not quite known and where some other longer dynamics persist (manifested as a static offset). Since these values are not separable in a general system, I'll keep $S$ normalized between 0 and 1. - -\begin{eqnarray} -S &=& (1-c)\me^{-\frac{t}{\tau_{\mathrm{actual}}}} + c \\ -S_n &=& (1-c)\me^{-\frac{-\tau_{\mathrm{step}}\log{\left(\frac{n}{N}\right)}}{\tau_{\mathrm{actual}}}} + c \\ -S_n &=& (1-c)\me^{-\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}} \log{\left(\frac{N}{n}\right)}} + c \\ -S_n &=& (1-c)\left(\frac{N}{n}\right)^{-\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}}} + c \\ -S_n &=& (1-c)\left(\frac{n}{N}\right)^{\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}}} + c -\end{eqnarray} - -\begin{figure}[p!] \label{fig:exponential_steps} - \centering - \includegraphics[scale=0.5]{"software/PyCMDS/ideal axis positions/exponential"} - \caption[TODO]{TODO} -\end{figure} - -\subsubsection{Gaussian} - -\subsubsection{Lorentzian} - -\subsubsection{Bimolecular} - -\section{WrightSim} - -WrightSim does simulations. diff --git a/software/chapter.tex b/software/chapter.tex new file mode 100644 index 0000000..e2c9652 --- /dev/null +++ b/software/chapter.tex @@ -0,0 +1,115 @@ +% TODO: add StoddenVictoria2016.000 (Enhancing reproducibility for computational methods) +% TODO: add MillmanKJarrod2011.000 (Python for Scientists and Engineers) +% TODO: add vanderWaltStefan2011.000 (The NumPy Array: A Structure for Efficient Numerical Computation) +% TODO: reference https://www.nsf.gov/pubs/2016/nsf16532/nsf16532.htm (Software Infrastructure for Sustained Innovation (SI2: SSE & SSI)) + +\chapter{Software} + +Cutting-edge science increasingly relies on custom software. In their 2008 survey, \textcite{HannayJoErskine2009.000} demonstrated just how important software is to the modern scientist. +\begin{enumerate}[topsep=-1.5ex, itemsep=0ex, partopsep=0ex, parsep=0ex, label=$\rightarrow$] + \item 84.3\% of surveyed scientists state that developing scientific software is important or very important for their own research. + \item 91.2\% of surveyed scientists state that using scientific software is important or very important for their own research. + \item On average, scientists spend approximately 40\% of their work time using scientific software. + \item On average, scientists spend approximately 30\% of their work time developing scientific software. +\end{enumerate} +Despite the importance of software to science and scientists, most scientists are not familiar with basic software engineering concepts. +% TODO: demonstrate that `most scientists are not familiar with basic software engineering concepts' +This is in part due to the their general lack of formal training in programming and software development. \textcite{HannayJoErskine2009.000} found that over 90\% of scientists learn software development through `informal self study'. Indeed, I myself have never been formally trained in software development. + +Software development in a scientific context poses unique challenges. Many traditional software development paradigms demand an upfront articulation of goals and requirements. This allows the developers to carefully design their software, even before a single line of code is written. In her seminal 2005 case study \textcite{SegalJudith2005.000} describes a collaboration between a team of researchers and a contracted team of software engineers. Ultimately +% TODO: finish the discussion of SegalJudith2005.000 +% TODO: segue to reccomendation of agile development practices: http://agilemanifesto.org/ + +\section{Overview} + +In the Wright Group, \gls{PyCMDS} replaces the old acquisition softwares `ps control', written by Kent Meyer and `Control for Lots of Research in Spectroscopy' written by Schuyler Kain. + +\section{WrightTools} + +WrightTools is a software package at the heart of all work in the Wright Group. + +\section{PyCMDS} + +PyCMDS directly addresses the hardware during experiments. + +\subsection{Overview} + +PyCMDS has, through software improvements alone, dramatically lessened scan times... + +\begin{itemize}[topsep=-1.5ex, itemsep=0ex, partopsep=0ex, parsep=0ex, label=$\rightarrow$] + \item simultaneous motor motion + \item digital signal processing % TODO: reference section when it exists + \item ideal axis positions \ref{sec:ideal_axis_positions} +\end{itemize} + +\subsection{Ideal Axis Positions}\label{sec:ideal_axis_positions} + +Frequency domain multidimensional spectroscopy is a time-intensive process. A typical \gls{pixel} takes between one-half second and three seconds to acquire. Depending on the exact hardware being scanned and signal being detected, this time may be mostly due to hardware motion or signal collection. Due to the \gls{curse of dimensionality}, a typical three-dimensional CMDS experiment contains roughly 100,000 pixels. CMDS hardware is transiently-reliable, so speeding up experiments is a crucial component of unlocking ever larger dimensionalities and higher resolutions. + +One obvious way to decrease the scan-time is to take fewer pixels. Traditionally, multidimensional scans are done with linearly arranged points in each axis---this is the simplest configuration to program into the acquisition software. Because signal features are often sparse or slowly varying (especially so in high-dimensional scans) linear stepping means that \emph{most of the collected pixels} are duplicates or simply noise. A more intelligent choice of axis points can capture the same nonlinear spectrum in a fraction of the total pixel count. + +An ideal distribution of pixels is linearized in \emph{signal}, not coordinate. This means that every signal level (think of a contour in the N-dimensional case) has roughly the same number of pixels defining it. If some generic multidimensional signal goes between 0 and 1, one would want roughly 10\% of the pixels to be between 0.9 and 1.0, 10\% between 0.8 and 0.9 and so on. If the signal is sparse in the space explored (imagine a narrow two-dimensional Lorentzian in the center of a large 2D-Frequency scan) this would place the majority of the pixels near the narrow peak feature(s), with only a few of them defining the large (in axis space) low-signal floor. In contrast linear stepping would allocate the vast majority of the pixels in the low-signal 0.0 to 0.1 region, with only a few being used to capture the narrow peak feature. Of course, linearizing pixels in signal requires prior expectations about the shape of the multidimensional signal---linear stepping is still an appropriate choice for low-resolution ``survey'' scans. + +CMDS scans often posses correlated features in the multidimensional space. In order to capture such features as cheaply as possible, one would want to define regions of increased pixel density along the correlated (diagonal) lineshape. As a concession to reasonable simplicity, our acquisition software (PyCMDS) assumes that all scans constitute a regular array with-respect-to the scanned axes. We can acquire arbitrary points along each axis, but not for the multidimensional scan. This means that we cannot achieve strictly ideal pixel distributions for arbitrary datasets. Still, we can do much better than linear spacing. % TODO: refer to PyCMDS/WrightTools 'regularity' requirement when that section exists + +Almost all CMDS lineshapes (in frequency and delay) can be described using just a few lineshape functions: + +\begin{itemize}[topsep=-1.5ex, itemsep=0ex, partopsep=0ex, parsep=0ex, label=$\rightarrow$] + \item exponential + \item Gaussian + \item Lorentzian + \item bimolecular +\end{itemize} + +Exponential and bimolecular dynamics fall out of simple first and second-order kinetics (I will ignore higher-order kinetics here). Gaussians come from our Gaussian pulse envelopes or from normally-distributed inhomogeneous broadening. The measured line-shapes are actually convolutions of the above. I will ignore the convolution except for a few illustrative special cases. More exotic lineshapes are possible in CMDS---quantum beating and breathing modes, for example---I will also ignore these. Derivations of the ideal pixel positions for each of these lineshapes appear below. %TODO: cite Wright Group quantum beating paper, Kambempati breathing paper + +\subsection{Exponential} + +Simple exponential decays are typically used to describe population and coherence-level dynamics in CMDS. For some generic exponential signal $S$ with time constant $\tau$, + +\begin{equation} \label{eq:simple_exponential_decay} +S(t) = \me^{-\frac{t}{\tau}}. +\end{equation} + +We can write the conjugate equation to \ref{eq:simple_exponential_decay}, asking ``what $t$ do I need to get a certain signal level?'': + +\begin{eqnarray} +\log{(S)} &=& -\frac{t}{\tau} \\ +t &=& -\tau\log{(S)}. +\end{eqnarray} + +So to step linearly in $t$, my step size has to go as $-\tau\log{(S)}$. + +We want to go linearly in signal, meaning that we want to divide $S$ into even sections. If $S$ goes from 0 to 1 and we choose to acquire $N$ points, + +\begin{eqnarray} +t_n &=& -\tau\log{\left(\frac{n}{N}\right)}. +\end{eqnarray} + +Note that $t_n$ starts at long times and approaches zero delay. So the first $t_1$ is the smallest signal and $t_N$ is the largest. + +Now we can start to consider realistic cases, like where $\tau$ is not quite known and where some other longer dynamics persist (manifested as a static offset). Since these values are not separable in a general system, I'll keep $S$ normalized between 0 and 1. + +\begin{eqnarray} +S &=& (1-c)\me^{-\frac{t}{\tau_{\mathrm{actual}}}} + c \\ +S_n &=& (1-c)\me^{-\frac{-\tau_{\mathrm{step}}\log{\left(\frac{n}{N}\right)}}{\tau_{\mathrm{actual}}}} + c \\ +S_n &=& (1-c)\me^{-\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}} \log{\left(\frac{N}{n}\right)}} + c \\ +S_n &=& (1-c)\left(\frac{N}{n}\right)^{-\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}}} + c \\ +S_n &=& (1-c)\left(\frac{n}{N}\right)^{\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}}} + c +\end{eqnarray} + +\begin{figure}[p!] \label{fig:exponential_steps} + \centering + \includegraphics[scale=0.5]{"software/PyCMDS/ideal axis positions/exponential"} + \caption[TODO]{TODO} +\end{figure} + +\subsubsection{Gaussian} + +\subsubsection{Lorentzian} + +\subsubsection{Bimolecular} + +\section{WrightSim} + +WrightSim does simulations. diff --git a/spectroscopy.tex b/spectroscopy.tex deleted file mode 100644 index 4e3546e..0000000 --- a/spectroscopy.tex +++ /dev/null @@ -1,267 +0,0 @@ -% TODO: discuss and cite CerulloGiulio2003.000 -% TODO: discuss and cite BrownEmilyJ1999.000 -% TODO: cite and discuss Sheik-Bahae 1990 (first z-scan) - -\chapter{Spectroscopy} - -In this chapter I lay out the foundations of spectroscopy. - -\section{Light} - -% TODO: add reference to HuygensChristiaan1913.000 - -% TODO: add reference to MaimanTheodore.000 - -\section{Light-Matter Interaction} - -Spectroscopic experiments all derive from the interaction of light and matter. Many material properties can be deduced by measuring the nature of this interaction. - -Nonlinear spectroscopy relies upon higher-order terms in the light-matter interaction. In a generic system, each term is roughly ten times smaller than the last. % TODO: cite? - -% TODO: Discuss dephasing induced resonance. Example: florescence - -\subsection{Representations} - -Many strategies have been introduced for diagrammatically representing the interaction of multiple electric fields in an experiment. - -\subsubsection{Circle Diagrams} - -% TODO: add reference to YeeTK1978.000 - -% TODO: Discuss circle diagrams from a historical perspective - -\subsubsection{Double-sided Feynman Diagrams} - -% TODO: Discuss double-sided Feynman diagrams from a historical perspective - -\subsubsection{WMEL Diagrams} - -So-called wave mixing energy level (\gls{WMEL}) diagrams are the most familiar way of representing spectroscopy for Wright group members. \gls{WMEL} diagrams were first proposed by Lee and Albrecht in an appendix to their seminal work \emph{A Unified View of Raman, Resonance Raman, and Fluorescence Spectroscopy} \cite{LeeDuckhwan1985.000}. \gls{WMEL} diagrams are drawn using the following rules. -\begin{enumerate} - \item The energy ladder is represented with horizontal lines - solid for real states and dashed for virtual states. - \item Individual electric field interactions are represented as vertical arrows. The arrows span the distance between the initial and final state in the energy ladder. - \item The time ordering of the interactions is represented by the ordering of arrows, from left to right. - \item Ket-side interactions are represented with solid arrows. - \item Bra-side interactions are represented with dashed arrows. - \item Output is represented as a solid wavy line. -\end{enumerate} - -\subsubsection{Mukamel Diagrams} - -% TODO: Discuss Mukamel diagrams from a historical perspective - -\section{Linear Spectroscopy} - -\subsection{Reflectivity} - -This derivation adapted from \textit{Optical Processes in Semiconductors} by Jacques I. Pankove \cite{PankoveJacques1975.000}. For normal incidence, the reflection coefficient is -\begin{equation} -R = \frac{(n-1)^2+k^2}{(n+1)^2+k^2} -\end{equation} -% TODO: finish derivation - -Further derivation adapted from \cite{KumarNardeep2013.000}. To extend reflectivity to a differential measurement -% TODO: finish derivation - -\section{Coherent Multidimensional Spectroscopy} - -% TODO: (maybe) include discussion of photon echo famously discovered in 1979 in Groningen - -\gls{multiresonant coherent multidimensional spectroscopy} - - -\subsection{Three Wave} - -\subsection{Four Wave} - -Fluorescence - -Raman - -\subsection{Five Wave} - -\subsection{Six Wave} - -\gls{multiple population-period transient spectroscopy} (\Gls{MUPPETS}) - -\section{Strategies for CMDS} - -\subsection{Homodyne vs. Heterodyne Detection} - -Two kinds of spectroscopies: 1) \gls{heterodyne} 2) \gls{homodyne}. Heterodyne techniques may be \gls{self heterodyne} or explicitly heterodyned with a local oscillator. - -In all heterodyne spectroscopies, signal goes as $\gls{N}$. In all homodyne spectroscopies, signal goes as $\gls{N}^2$. This literally means that homodyne signals go as the square of heterodyne signals, which is what we mean when we say that homodyne signals are intensity level and heterodyne signals are amplitude level. - -\Gls{transient absorption}, \gls{TA} - -\subsection{Frequency vs. Time Domain} - -Time domain techniques become more and more difficult when large frequency bandwidths are needed. With very short, broad pulses: - -\begin{itemize} - \item Non-resonant signal becomes brighter relative to resonant signal - \item Pulse distortions become important. -\end{itemize} - -This epi-CARS paper might have some useful discussion of non-resonant vs resonant for shorter and shorter pulses \cite{ChengJixin2001.000}. - -An excellent discussion of pulse distortion phenomena in broadband time-domain experiments was published by \textcite{SpencerAustinP2015.000}. - -Another idea in defense of frequency domain is for the case of power studies. Since time-domain pulses in-fact possess all colors in them they cannot be trusted as much at perturbative fluence. - -\subsection{Triply Electronically Enhanced Spectroscopy} - -Triply Electronically Enhanced (TrEE) spectroscopy has become the workhorse homodyne-detected 4WM experiment in the Wright Group. - -% TODO: On and off-diagonal TrEE pathways - -% TODO: Discussion of old and current delay space - -\subsection{Transient Absorbance Spectroscopy} - -\Gls{transient absorption} (\gls{TA}) - -\subsubsection{Quantitative TA} - -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 - \includegraphics[width=\textwidth]{"spectroscopy/TA setup"} - \label{fig:ta_and_tr_setup} - \caption{CAPTION TODO} -\end{figure} - -\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 opaque (pyrite) or non-reflective (quantum dot) samples \dots - -Typically one attempts to calculate the change in absorbance $\Delta A$ \dots - -\begin{eqnarray} -\Delta A &=& A_{\mathrm{on}} - A_{\mathrm{off}} \\ -&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}} + I_{\Delta\mathrm{R}}}{I_0}\right) + \log\left(\frac{I_\mathrm{T}+I_\mathrm{R}}{I_0}\right) \\ -&=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}})-\log_{10}(I_0)\right)+\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R})-\log_{10}(I_0)\right) \\ -&=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}})-\log_{10}(I_\mathrm{T}+I_\mathrm{R})\right) \\ -&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}}}{I_\mathrm{T}+I_\mathrm{R}}\right) \label{eq:ta_complete} -\end{eqnarray} - -\autoref{eq:ta_complete} simplifies beautifully if reflectivity is negligible \dots - -Now I define a variable for each experimental measurable: -\begin{center} - \begin{tabular}{c | l} - $V_\mathrm{T}$ & voltage recorded from transmitted beam, without pump \\ - $V_\mathrm{R}$ & voltage recorded from reflected beam, without pump \\ - $V_{\Delta\mathrm{T}}$ & change in voltage recorded from transmitted beam due to pump \\ - $V_{\Delta\mathrm{R}}$ & change in voltage recorded from reflected beam due to pump - \end{tabular} -\end{center} - -We will need to calibrate using a sample with a known transmisivity and reflectivity constant: -\begin{center} - \begin{tabular}{c | l} - $V_{\mathrm{T},\,\mathrm{ref}}$ & voltage recorded from transmitted beam, without pump \\ - $V_{\mathrm{R},\,\mathrm{ref}}$ & voltage recorded from reflected beam, without pump \\ - $\mathcal{T}_\mathrm{ref}$ & transmissivity \\ - $\mathcal{R}_\mathrm{ref}$ & reflectivity - \end{tabular} -\end{center} - -Define two new proportionality constants... -\begin{eqnarray} -C_\mathrm{T} &\equiv& \frac{\mathcal{T}}{V_\mathrm{T}} \\ -C_\mathrm{R} &\equiv& \frac{\mathcal{R}}{V_\mathrm{R}} -\end{eqnarray} -These are explicitly calibrated (as a function of probe color) prior to the experiment using the calibration sample. - -Given the eight experimental measurables ($V_\mathrm{T}$, $V_\mathrm{R}$, $V_{\Delta\mathrm{T}}$, $V_{\Delta\mathrm{R}}$, $V_{\mathrm{T},\,\mathrm{ref}}$, $V_{\mathrm{R},\,\mathrm{ref}}$, $\mathcal{T}_\mathrm{ref}$, $\mathcal{R}_\mathrm{ref}$) I can express all of the intensities in \autoref{eq:ta_complete} in terms of $I_0$. - -\begin{eqnarray} -C_\mathrm{T} &=& \frac{\mathcal{T}_\mathrm{ref}}{V_{\mathrm{T},\,\mathrm{ref}}} \\ -C_\mathrm{R} &=& \frac{\mathcal{R}_\mathrm{ref}}{V_{\mathrm{R},\,\mathrm{ref}}} \\ -I_\mathrm{T} &=& I_0 C_\mathrm{T} V_\mathrm{T} \\ -I_\mathrm{R} &=& I_0 C_\mathrm{R} V_\mathrm{R} \\ -I_{\Delta\mathrm{T}} &=& I_0 C_\mathrm{T} V_{\Delta\mathrm{T}} \\ -I_{\Delta\mathrm{R}} &=& I_0 C_\mathrm{R} V_{\Delta\mathrm{R}} -\end{eqnarray} - -Wonderfully, the $I_0$ cancels when plugged back in to \autoref{eq:ta_complete}, leaving a final expression for $\Delta A$ that only depends on my eight measurables. - -\begin{equation} -\Delta A = - \log_{10} \left(\frac{C_\mathrm{T}(V_\mathrm{T} + V_{\Delta\mathrm{T}}) + C_\mathrm{R}(V_\mathrm{R} + V_{\Delta\mathrm{R}})}{C_\mathrm{T} V_\mathrm{T} + C_\mathrm{R} V_\mathrm{R}}\right) -\end{equation} - -\subsection{Cross Polarized TrEE} - -\subsection{Pump-TrEE-Probe} - -\Gls{pump TrEE probe} (\gls{PTP}). - -\section{Instrumental Response Function} - -The instrumental response function (IRF) is a classic concept in analytical science. Defining IRF becomes complex with instruments as complex as these, but it is still useful to attempt. - -It is particularly useful to define bandwidth. - -\subsection{Time Domain} - -I will use four wave mixing to extract the time-domain pulse-width. I use a driven signal \textit{e.g.} near infrared carbon tetrachloride response. I'll homodyne-detect the output. In my experiment I'm moving pulse 1 against pulses 2 and 3 (which are coincident). - - - -The driven polarization, $P$, goes as the product of my input pulse \textit{intensities}: - -\begin{equation} -P(T) = I_1(t-T) \times I_2(t) \times I_3(t) -\end{equation} - -In our experiment we are convolving $I_1$ with $I_2 \times I_3$. Each pulse has an \textit{intensity-level} width, $\sigma_1$, $\sigma_2$, and $\sigma_3$. $I_2 \times I_3$ is itself a Gaussian, and - -\begin{eqnarray} -\sigma_{I_2I_3} &=& \dots \\ -&=& \sqrt{\frac{\sigma_2^2\sigma_3^2}{\sigma_2^2 + \sigma_3^2}}. -\end{eqnarray} - -The width of the polarization (across $T$) is therefore - -\begin{eqnarray} -\sigma_P &=& \sqrt{\sigma_1^2 + \sigma_{I_2I_3}^2} \\ -&=& \dots \\ -&=& \sqrt{\frac{\sigma_1^2 + \sigma_2^2\sigma_3^2}{\sigma_1^2 + \sigma_2^2}}. \label{eq:generic} -\end{eqnarray} - -% TODO: determine effect of intensity-level measurement here - -I assume that all of the pulses have the same width. $I_1$, $I_2$, and $I_3$ are identical Gaussian functions with FWHM $\sigma$. In this case, \autoref{eq:generic} simplifies to - -\begin{eqnarray} -\sigma_P &=& \sqrt{\frac{\sigma^2 + \sigma^2\sigma^2}{\sigma^2 + \sigma^2}} \\ -&=& \dots \\ -&=& \sigma \sqrt{\frac{3}{2}} -\end{eqnarray} - -Finally, since we measure $\sigma_P$ and wish to extract $\sigma$: - -\begin{equation} -\sigma = \sigma_P \sqrt{\frac{2}{3}} -\end{equation} - -Again, all of these widths are on the \textit{intensity} level. - -\subsection{Frequency Domain} - -We can directly measure $\sigma$ (the width on the intensity-level) in the frequency domain using a spectrometer. A tune test contains this information. - -\subsection{Time-Bandwidth Product} - -For a Gaussian, approximately 0.441 - -% TODO: find reference -% TODO: number defined on INTENSITY level! - - - - - - - - diff --git a/spectroscopy/auto/chapter.el b/spectroscopy/auto/chapter.el new file mode 100644 index 0000000..ae8a477 --- /dev/null +++ b/spectroscopy/auto/chapter.el @@ -0,0 +1,9 @@ +(TeX-add-style-hook + "chapter" + (lambda () + (LaTeX-add-labels + "fig:ta_and_tr_setup" + "eq:ta_complete" + "eq:generic")) + :latex) + diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex new file mode 100644 index 0000000..27d763b --- /dev/null +++ b/spectroscopy/chapter.tex @@ -0,0 +1,311 @@ +% TODO: discuss and cite CerulloGiulio2003.000 +% TODO: discuss and cite BrownEmilyJ1999.000 +% TODO: cite and discuss Sheik-Bahae 1990 (first z-scan) + +\chapter{Spectroscopy} + +In this chapter I lay out the foundations of spectroscopy. + +\section{Light} + +% TODO: add reference to HuygensChristiaan1913.000 + +% TODO: add reference to MaimanTheodore.000 + +\section{Light-Matter Interaction} + +Spectroscopic experiments all derive from the interaction of light and matter. Many material +properties can be deduced by measuring the nature of this interaction. % + +Nonlinear spectroscopy relies upon higher-order terms in the light-matter interaction. In a generic +system, each term is roughly ten times smaller than the last. % TODO: cite? + +% TODO: Discuss dephasing induced resonance. Example: florescence + +\subsection{Representations} + +Many strategies have been introduced for diagrammatically representing the interaction of multiple +electric fields in an experiment. % + +\subsubsection{Circle Diagrams} + +% TODO: add reference to YeeTK1978.000 + +% TODO: Discuss circle diagrams from a historical perspective + +\subsubsection{Double-sided Feynman Diagrams} + +% TODO: Discuss double-sided Feynman diagrams from a historical perspective + +\subsubsection{WMEL Diagrams} + +So-called wave mixing energy level (\gls{WMEL}) diagrams are the most familiar way of representing +spectroscopy for Wright group members. % +\gls{WMEL} diagrams were first proposed by Lee and Albrecht in an appendix to their seminal work +\emph{A Unified View of Raman, Resonance Raman, and Fluorescence Spectroscopy} +\cite{LeeDuckhwan1985.000}. % +\gls{WMEL} diagrams are drawn using the following rules. % +\begin{enumerate} + \item The energy ladder is represented with horizontal lines - solid for real states and dashed + for virtual states. + \item Individual electric field interactions are represented as vertical arrows. The arrows span + the distance between the initial and final state in the energy ladder. + \item The time ordering of the interactions is represented by the ordering of arrows, from left + to right. + \item Ket-side interactions are represented with solid arrows. + \item Bra-side interactions are represented with dashed arrows. + \item Output is represented as a solid wavy line. +\end{enumerate} + +\subsubsection{Mukamel Diagrams} + +% TODO: Discuss Mukamel diagrams from a historical perspective + +\section{Linear Spectroscopy} + +\subsection{Reflectivity} + +This derivation adapted from \textit{Optical Processes in Semiconductors} by Jacques I. Pankove +\cite{PankoveJacques1975.000}. % +For normal incidence, the reflection coefficient is +\begin{equation} +R = \frac{(n-1)^2+k^2}{(n+1)^2+k^2} +\end{equation} +% TODO: finish derivation + +Further derivation adapted from \cite{KumarNardeep2013.000}. % +To extend reflectivity to a differential measurement +% TODO: finish derivation + +\section{Coherent Multidimensional Spectroscopy} + +% TODO: (maybe) include discussion of photon echo famously discovered in 1979 in Groningen + +\gls{multiresonant coherent multidimensional spectroscopy} + + +\subsection{Three Wave} + +\subsection{Four Wave} + +Fluorescence + +Raman + +\subsection{Five Wave} + +\subsection{Six Wave} + +\gls{multiple population-period transient spectroscopy} (\Gls{MUPPETS}) + +\section{Strategies for CMDS} + +\subsection{Homodyne vs. Heterodyne Detection} + +Two kinds of spectroscopies: 1) \gls{heterodyne} 2) \gls{homodyne}. +Heterodyne techniques may be \gls{self heterodyne} or explicitly heterodyned with a local +oscillator. + +In all heterodyne spectroscopies, signal goes as $\gls{N}$. % +In all homodyne spectroscopies, signal goes as $\gls{N}^2$. % +This literally means that homodyne signals go as the square of heterodyne signals, which is what we +mean when we say that homodyne signals are intensity level and heterodyne signals are amplitude +level. + +\Gls{transient absorption}, \gls{TA} + +\subsection{Frequency vs. Time Domain} + +Time domain techniques become more and more difficult when large frequency bandwidths are +needed. % +With very short, broad pulses: % +\begin{itemize} + \item Non-resonant signal becomes brighter relative to resonant signal + \item Pulse distortions become important. +\end{itemize} + +This epi-CARS paper might have some useful discussion of non-resonant vs resonant for shorter and +shorter pulses \cite{ChengJixin2001.000}. % + +An excellent discussion of pulse distortion phenomena in broadband time-domain experiments was +published by \textcite{SpencerAustinP2015.000}. % + +Another idea in defense of frequency domain is for the case of power studies. % +Since time-domain pulses in-fact possess all colors in them they cannot be trusted as much at +perturbative fluence. % +See that paper that Natalia presented... % + +\subsection{Triply Electronically Enhanced Spectroscopy} + +Triply Electronically Enhanced (TrEE) spectroscopy has become the workhorse homodyne-detected 4WM +experiment in the Wright Group. % + +% TODO: On and off-diagonal TrEE pathways + +% TODO: Discussion of old and current delay space + +\subsection{Transient Absorbance Spectroscopy} + +\Gls{transient absorption} (\gls{TA}) + +\subsubsection{Quantitative TA} + +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 + \includegraphics[width=\textwidth]{"spectroscopy/TA setup"} + \label{fig:ta_and_tr_setup} + \caption{CAPTION TODO} +\end{figure} + +\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 +opaque (pyrite) or non-reflective (quantum dot) samples \dots % + +Typically one attempts to calculate the change in absorbance $\Delta A$ \dots % + +\begin{eqnarray} +\Delta A &=& A_{\mathrm{on}} - A_{\mathrm{off}} \\ +&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}} + I_{\Delta\mathrm{R}}}{I_0}\right) + \log\left(\frac{I_\mathrm{T}+I_\mathrm{R}}{I_0}\right) \\ +&=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}})-\log_{10}(I_0)\right)+\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R})-\log_{10}(I_0)\right) \\ +&=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}})-\log_{10}(I_\mathrm{T}+I_\mathrm{R})\right) \\ +&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}}}{I_\mathrm{T}+I_\mathrm{R}}\right) \label{eq:ta_complete} +\end{eqnarray} + +\autoref{eq:ta_complete} simplifies beautifully if reflectivity is negligible \dots + +Now I define a variable for each experimental measurable: +\begin{center} + \begin{tabular}{c | l} + $V_\mathrm{T}$ & voltage recorded from transmitted beam, without pump \\ + $V_\mathrm{R}$ & voltage recorded from reflected beam, without pump \\ + $V_{\Delta\mathrm{T}}$ & change in voltage recorded from transmitted beam due to pump \\ + $V_{\Delta\mathrm{R}}$ & change in voltage recorded from reflected beam due to pump + \end{tabular} +\end{center} + +We will need to calibrate using a sample with a known transmisivity and reflectivity constant: +\begin{center} + \begin{tabular}{c | l} + $V_{\mathrm{T},\,\mathrm{ref}}$ & voltage recorded from transmitted beam, without pump \\ + $V_{\mathrm{R},\,\mathrm{ref}}$ & voltage recorded from reflected beam, without pump \\ + $\mathcal{T}_\mathrm{ref}$ & transmissivity \\ + $\mathcal{R}_\mathrm{ref}$ & reflectivity + \end{tabular} +\end{center} + +Define two new proportionality constants... +\begin{eqnarray} +C_\mathrm{T} &\equiv& \frac{\mathcal{T}}{V_\mathrm{T}} \\ +C_\mathrm{R} &\equiv& \frac{\mathcal{R}}{V_\mathrm{R}} +\end{eqnarray} +These are explicitly calibrated (as a function of probe color) prior to the experiment using the +calibration sample. % + +Given the eight experimental measurables ($V_\mathrm{T}$, $V_\mathrm{R}$, $V_{\Delta\mathrm{T}}$, +$V_{\Delta\mathrm{R}}$, $V_{\mathrm{T},\,\mathrm{ref}}$, $V_{\mathrm{R},\,\mathrm{ref}}$, +$\mathcal{T}_\mathrm{ref}$, $\mathcal{R}_\mathrm{ref}$) I can express all of the intensities in +\autoref{eq:ta_complete} in terms of $I_0$. % + +\begin{eqnarray} +C_\mathrm{T} &=& \frac{\mathcal{T}_\mathrm{ref}}{V_{\mathrm{T},\,\mathrm{ref}}} \\ +C_\mathrm{R} &=& \frac{\mathcal{R}_\mathrm{ref}}{V_{\mathrm{R},\,\mathrm{ref}}} \\ +I_\mathrm{T} &=& I_0 C_\mathrm{T} V_\mathrm{T} \\ +I_\mathrm{R} &=& I_0 C_\mathrm{R} V_\mathrm{R} \\ +I_{\Delta\mathrm{T}} &=& I_0 C_\mathrm{T} V_{\Delta\mathrm{T}} \\ +I_{\Delta\mathrm{R}} &=& I_0 C_\mathrm{R} V_{\Delta\mathrm{R}} +\end{eqnarray} + +Wonderfully, the $I_0$ cancels when plugged back in to \autoref{eq:ta_complete}, leaving a final +expression for $\Delta A$ that only depends on my eight measurables. % + +\begin{equation} +\Delta A = - \log_{10} \left(\frac{C_\mathrm{T}(V_\mathrm{T} + V_{\Delta\mathrm{T}}) + C_\mathrm{R}(V_\mathrm{R} + V_{\Delta\mathrm{R}})}{C_\mathrm{T} V_\mathrm{T} + C_\mathrm{R} V_\mathrm{R}}\right) +\end{equation} + +\subsection{Cross Polarized TrEE} + +\subsection{Pump-TrEE-Probe} + +\Gls{pump TrEE probe} (\gls{PTP}). + +\section{Instrumental Response Function} + +The instrumental response function (IRF) is a classic concept in analytical science. % +Defining IRF becomes complex with instruments as complex as these, but it is still useful to +attempt. % + +It is particularly useful to define bandwidth. + +\subsection{Time Domain} + +I will use four wave mixing to extract the time-domain pulse-width. % +I use a driven signal \textit{e.g.} near infrared carbon tetrachloride response. % +I'll homodyne-detect the output. % +In my experiment I'm moving pulse 1 against pulses 2 and 3 (which are coincident). % + +The driven polarization, $P$, goes as the product of my input pulse \textit{intensities}: + +\begin{equation} +P(T) = I_1(t-T) \times I_2(t) \times I_3(t) +\end{equation} + +In our experiment we are convolving $I_1$ with $I_2 \times I_3$. % +Each pulse has an \textit{intensity-level} width, $\sigma_1$, $\sigma_2$, and $\sigma_3$. $I_2 +\times I_3$ is itself a Gaussian, and +\begin{eqnarray} +\sigma_{I_2I_3} &=& \dots \\ +&=& \sqrt{\frac{\sigma_2^2\sigma_3^2}{\sigma_2^2 + \sigma_3^2}}. +\end{eqnarray} + +The width of the polarization (across $T$) is therefore + +\begin{eqnarray} +\sigma_P &=& \sqrt{\sigma_1^2 + \sigma_{I_2I_3}^2} \\ +&=& \dots \\ +&=& \sqrt{\frac{\sigma_1^2 + \sigma_2^2\sigma_3^2}{\sigma_1^2 + \sigma_2^2}}. \label{eq:generic} +\end{eqnarray} + +% TODO: determine effect of intensity-level measurement here + +I assume that all of the pulses have the same width. % +$I_1$, $I_2$, and $I_3$ are identical Gaussian functions with FWHM $\sigma$. In this case, +\autoref{eq:generic} simplifies to + +\begin{eqnarray} +\sigma_P &=& \sqrt{\frac{\sigma^2 + \sigma^2\sigma^2}{\sigma^2 + \sigma^2}} \\ +&=& \dots \\ +&=& \sigma \sqrt{\frac{3}{2}} +\end{eqnarray} + +Finally, since we measure $\sigma_P$ and wish to extract $\sigma$: + +\begin{equation} +\sigma = \sigma_P \sqrt{\frac{2}{3}} +\end{equation} + +Again, all of these widths are on the \textit{intensity} level. + +\subsection{Frequency Domain} + +We can directly measure $\sigma$ (the width on the intensity-level) in the frequency domain using a +spectrometer. % +A tune test contains this information. % + +\subsection{Time-Bandwidth Product} + +For a Gaussian, approximately 0.441 + +% TODO: find reference +% TODO: number defined on INTENSITY level! + + + + + + + + -- cgit v1.2.3