From 9c6afe7dc748bf26e4ab6f6df0c70d57e74b610f Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Sat, 7 Apr 2018 14:56:52 -0500 Subject: 2018-04-07 14:56 --- spectroscopy/chapter.tex | 285 ++++++++++++++++++++--------------------------- 1 file changed, 121 insertions(+), 164 deletions(-) (limited to 'spectroscopy/chapter.tex') diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex index 2cf088b..a70cd69 100644 --- a/spectroscopy/chapter.tex +++ b/spectroscopy/chapter.tex @@ -147,193 +147,150 @@ WMEL diagrams are drawn using the following rules. % Representative WMELs can be found in Figures [xxxxxx]. % -% TODO: representative WMEL? - \section{Types of spectroscopy} % ================================================================ Scientists have come up with many ways of exploiting light-matter interaction for measurement purposes. % This section discusses several of these strategies. % I start broadly, by comparing and contrasting differences across categories of spectroscopies. % -I then go into relevant detail regarding a few experiments that are particularly relevant in this +I then go into detail regarding a few experiments that are particularly relevant to this dissertation. % \subsection{Linear vs multidimensional} % -------------------------------------------------------- -This derivation adapted from \textit{Optical Processes in Semiconductors} by Jacques I. Pankove -\cite{PankoveJacques1975a}. % -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{KumarNardeep2013a}. % -To extend reflectivity to a differential measurement -% TODO: finish derivation - -% TODO: (maybe) include discussion of photon echo famously discovered in 1979 in Groningen - -% TODO: spectral congestion figure +Most familiar spectroscopic experiments are linear. % +That is to say, they have just one frequency axis, and they interrogate just one resonance +condition. % +These are workhorse experiments, like absorbance, reflectance, FTIR, UV-Vis, and common old +ordinary Raman spectroscopy (COORS). % +These experiments are incredibly robust, and are typically performed using easy to use commercial +desktop instruments. % +There are now even handheld Raman spectrometers for use in industrial settings. [CITE] % + +Multidimensional spectroscopy contains a lot more information about the material under +investigation. % +In this work, by ``multidimensional'' I mean higher-order spectroscopy. % +I ignore ``correlation spectroscopy'' [CITE], which tracks linear spectral features against +non-spectral dimensions like lab time, pressure, and temperature. % +So, in the context of this dissertation, multidimensional spectroscopy is synonymous with nonlinear +spectroscopy. % 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? +This means that nonlinear spectroscopy is typically very weak. % +Still, nonlinear signals are fairly easy to isolate and measure using modern instrumentation, as +this dissertation describes. % -TODO: Basic ``advantage of dimensionality'' figure. - -\subsection{Homodyne vs heterodyne} % ------------------------------------------------------------ - -Two kinds of spectroscopies: 1) heterodyne 2) homodyne. -Heterodyne techniques may be self heterodyne or explicitly heterodyned with a local -oscillator. - -In all heterodyne spectroscopies, signal goes as $N$. % -In all homodyne spectroscopies, signal goes as $N^2$. % -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. - -Homodyne dynamics go faster: cite Darien correction - -\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{ChengJixin2001a}. % - -An excellent discussion of pulse distortion phenomena in broadband time-domain experiments was -published by \textcite{SpencerAustinP2015a}. % - -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... % - -See Paul's dissertation - -\subsection{Transient grating} % ----------------------------------------------------------------- - -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 - -% TODO: discuss current delay space physical conventions (see inbox) - -\begin{figure} - \includegraphics[scale=1]{"spectroscopy/wmels/trive_on_diagonal"} - \caption[CAPTION TODO]{ - CAPTION TODO - } - \label{spc:fig:trive_on_diagonal} -\end{figure} - +The most obvious advantage of multidimensional spectroscopy comes directly from the dimensionality +itself. % +Multidimensional spectroscopy can \emph{decongest} spectra with overlapping peaks by isolating +peaks in a multidimensional resonance landscape. % +Figure \ref{spc:fig:decongestion} shows... \begin{figure} - \includegraphics[scale=1]{"spectroscopy/wmels/trive_off_diagonal"} - \caption[CAPTION TODO]{ - CAPTION TODO + \caption[Dimensionality and decongestion.]{ + CAPTION TODO. } - \label{spc:fig:trive_off_diagonal} -\end{figure} - -\begin{figure} - \includegraphics[scale=1]{"spectroscopy/wmels/trive_population_transfer"} - \caption[CAPTION TODO]{ - CAPTION TODO - } - \label{spc:fig:trive_population_transfer} -\end{figure} - -\subsection{Transient absorbance} % -------------------------------------------------------------- - -\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} - \includegraphics[width=\textwidth]{"spectroscopy/TA setup"} - \label{fig:ta_and_tr_setup} - \caption{CAPTION TODO} + \label{spc:fig:decongestion} \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. % +\subsection{Frequency vs time domain} % ---------------------------------------------------------- -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 $I_0$. % +Broadly, there are two ways to collect nonlinear spectroscopic signals: frequency and time +domain. % +Both techniques involve exciting a sample with multiple pulses of light and measuring the output +signal. % +The techniques differ in how they resolve the multiple frequency axes of interest. % + +Frequency domain is probably the more intuitive strategy: frequency axes are resolved directly by +iteratively tuning the frequency of excitation pulses against each-other. % +This relies on pulsed light sources with tunable frequencies. % + +Time domain experiments use an interferometric technique to resolve frequency axes. % +Broadband excitation pulses which contain all of the necessary frequencies are used to excite the +sample. % +The delay (time) between pulses is scanned, and the resonances along that axis are resolved through +Fourier transform of the resulting interferogram. % +In modern experiments, pulse shapers are used to control the delay between pulses in a very +precise, fast, and reproducible way. % +The time domain strategy is by-far the most popular technique in multidimensional spectroscopy +because these technologies allow for rapid, robust data collection. % + +This dissertation focuses on frequency domain strategies, so some discussion of the advantages of +frequency domain when compared to time domain are warranted. % + +One of the biggest instrumental limitations of multidimensional spectroscopy is bandwidth. % +It is easy to get absorbance spectra over the entire visible spectrum, and even into the +ultraviolet and near infrared. % +Multidimensional spectroscopy is limited by the bandwidth of our (tunable) light sources. % +For frequency domain techniques, this limitation is incidental: sources with greater tunability +will be easy to incorporate into these instruments, and creating such sources is only a matter of +more optomechanical engineering. % +Time domain techniques, on the other hand, have a more fundamental issue with bandwidth. % +Time domain requires that all of the desired frequencies be present within the single excitation +pulse, and pulses with very large frequency bandwidth (very short in time) become very hard to use +and control. % +With short, broad pulses: +\begin{ditemize} + \item Non-resonant signal becomes brighter relative to resonant signal. [CITE] + \item Pulse distortions become important. [CITE JONAS] +\end{ditemize} +%This epi-CARS paper might have some useful discussion of non-resonant vs resonant for shorter and +%shorter pulses \cite{ChengJixin2001a}. % +%An excellent discussion of pulse distortion phenomena in broadband time-domain experiments was +%published by \textcite{SpencerAustinP2015a}. % +%See Paul's dissertation + +Time domain experiments require a phase-locked, independently controlled local oscillator in order +to collect the interferogram at the heart of such techniques. % +This local oscillator enhances the information-gathering power of time domain because it allows the +experiment to explicitly collect nonlinear spectra with full phase information. % +At the same time, the local oscillator requirement limits the flexability of the time-domain +because it essentially requires that the output frequency must be the same as one of the inputs. % +Novel, often fully coherent, experiments cannot be accomplished under this limitation. % + +%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... % -\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. % +\subsection{Homodyne vs heterodyne} % ------------------------------------------------------------ -\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} +Within frequency domain multidimensional spectroscopy, one is free to use or forgo a local +oscillator. % +That is to say, frequency domain spectroscopy can be collected in a heterodyne or homodyne +technique. % +As discussed in the previous section, use of a local oscillator means that more useful phase +information can be extracted from the spectrum. % +At the same time, generation of a phase locked, controllable local oscillator can be cumbersome, +limiting the flexibility of possible experiments. % + +Note that heterodyne techniques may be self heterodyned (as in transient absorption) or +``explicitly'' heterodyned with a local oscillator. % + +Besides the aforementioned phase information, probably the biggest difference between heterodyne +and homodyne-detected experiments is their scaling with oscillator number density, $N$. % +In all heterodyne spectroscopies, signal goes linearly, as $N$. % +If the number of oscillators is doubled, the signal doubles. % +In all homodyne spectroscopies, signal goes as $N^2$. % +If the number of oscillators is doubled, the signal goes up by four times. % +This is what we mean when we say that homodyne signals are ``intensity level'' and heterodyne +signals are ``amplitude level''. % + +Recently we have been taking to representing homodyne-detected multidimensional experiments on the +``amplitude level'' by plotting the square root of the collected signal. % +Many of the figures in this dissertation are plotted in this way. % +In my opinion, this strategy makes interpretation of spectra easier. % +Certainly it eases comparison with other experiments, like absorbance and COORS, which go as +$N$. % + +One easy-to-miss consequence of homodyne collected experiments is the behavior of signals in delay +space. % +Since signal goes as $N^2$, signal decays much faster in homodyne-collected experiments. % +If signal decays as a single exponential, the extracted decay is twice as fast for homodyne vs +heterodyne-detected data. % +[CITE DARIEN CORRECTION] -\clearpage \section{Instrumentation} % ====================================================================== In this section I introduce the key components of the MR-CMDS instrument. % -- cgit v1.2.3