2018-04-07 14:56

8 files changed, 279 insertions, 188 deletions

diff --git a/PbSe/chapter.tex b/PbSe/chapter.tex
index c2cb2dc..466a7d9 100644
--- a/PbSe/chapter.tex
+++ b/PbSe/chapter.tex
@@ -1,3 +1,3 @@
-\chapter{PbSe}
+\chapter{PbSe} \label{cha:pbx}
 
 Relevant content from PbSe publications goes here.
\ No newline at end of file
diff --git a/dissertation.tex b/dissertation.tex
index d8bf32a..875a366 100644
--- a/dissertation.tex
+++ b/dissertation.tex
@@ -90,6 +90,8 @@ This dissertation is approved by the following members of the Final Oral Committ
 %\include{hardware/chapter}

 % TODO: consider inserting WrightTools documentation as PDF

 \include{irf/chapter}

+\include{quantitative_ta/chapter}

+\include{tg/chapter}

 %\include{errata/chapter}

 %\include{colophon/chapter}

 \end{appendix}

diff --git a/introduction/chapter.tex b/introduction/chapter.tex
index 109f692..007b95d 100644
--- a/introduction/chapter.tex
+++ b/introduction/chapter.tex
@@ -1,6 +1,18 @@
 \cleardoublepage

 \chapter{Introduction} \label{cha:int}

 

+\begin{dquote}

+  Experience has shown that the experimental implementation of three laser FWM is a formidable task

+  which is far from complete.  %

+  Characterization and improvement of existing apparatus must be a integral part of future research

+  if FWM is to become a viable spectroscopic technique.  %

+  To this end, it would be helpful to stimulate an atmosphere within the scientific community in

+  which the method of measurement is considered to be as important as the result of the

+  measurement.  %

+  

+  \dsignature{Roger Carlson \cite{CarlsonRogerJohn1988a}}

+\end{dquote}

+  

 % TODO: cool quote, if I can think of one...

 

 \clearpage

@@ -165,17 +177,24 @@ These chapters do not directly address improvements to the MR-CMDS methodology,
 as case studies in the potential of MR-CMDS and the utility of the improvements described in

 \autoref{prt:development}.  %

 

-Chapter [...] describes a series of experiments performed on PbSe quantum dots.

-PbSe quantum dots are useful because [...]  %

-We learned [...]  %

+[PARAGRAPH ABOUT PbSe QUANTUM DOTS]

 

-Chapter [...] describes an experiment performed on MoS2.

-MoS2 is useful because [...]  %

-We learned [...]  %

+%Chapter \ref{cha:pbx} describes a series of experiments performed on PbSe quantum dots.  %

+%Quantum dots are an excellent [STARTING SAMPLE... BEGINNING]

+%PbSe quantum dots are useful because [...]  %

+%We learned [...]  %

 

-Chapter [...] describes an experiment performed on PEDOT:PSS.

-useful because...

-we learned...

+[PARAGRAPH ABOUT MOS2]

+

+%Chapter [...] describes an experiment performed on MoS2.

+%MoS2 is useful because [...]  %

+%We learned [...]  %

+

+[PARAGRAPH ABOUT PEDOT:PSS]

+

+%Chapter [...] describes an experiment performed on PEDOT:PSS.

+%useful because...

+%we learned...

 

 % BJT: consider getting rid of the following paragraph

 % if it remains, it needs to address a more 'broader impacts approach' rather than simply

diff --git a/quantitative_ta/chapter.tex b/quantitative_ta/chapter.tex
new file mode 100644
index 0000000..c8b594d
--- /dev/null
+++ b/quantitative_ta/chapter.tex
@@ -0,0 +1,78 @@
+\chapter{Quantitative transient absorbance} \label{cha:qta}
+
+\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}
+\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}
\ No newline at end of file
diff --git a/spectroscopy/auto/chapter.el b/spectroscopy/auto/chapter.el
index b067440..f8550da 100644
--- a/spectroscopy/auto/chapter.el
+++ b/spectroscopy/auto/chapter.el
@@ -3,10 +3,6 @@
  (lambda ()
    (LaTeX-add-labels
     "cha:spc"
-    "spc:fig:trive_on_diagonal"
-    "spc:fig:trive_off_diagonal"
-    "spc:fig:trive_population_transfer"
-    "fig:ta_and_tr_setup"
-    "eq:ta_complete"))
+    "spc:fig:decongestion"))
  :latex)
 
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.  %

diff --git a/tg/chapter.tex b/tg/chapter.tex
new file mode 100644
index 0000000..7d7ac4d
--- /dev/null
+++ b/tg/chapter.tex
@@ -0,0 +1,36 @@
+\chapter{Transient grating} \label{cha:trg}
+
+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}
+
+
+\begin{figure}
+  \includegraphics[scale=1]{"spectroscopy/wmels/trive_off_diagonal"}
+  \caption[CAPTION TODO]{
+    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}
+
diff --git a/todo.org b/todo.org
index d32af20..fef9ecc 100644
--- a/todo.org
+++ b/todo.org
@@ -1,22 +1,25 @@
 * DONE draft challenges section                                    :software:
   CLOSED: [2018-04-05 Thu 09:12]
+* DONE quote from RC                                           :introduction:
+  CLOSED: [2018-04-07 Sat 11:20]
+* TODO dichotomies                                             :spectroscopy:
+* TODO describe spectroscopic instrument                       :spectroscopy:
+* TODO incorporate "most software is not peer reviewed"            :software:
+** see Joppa reference 6
+* TODO incorporate idea "most people over-trust software"          :software:
+* TODO incorporate StoddenVictoria2016a                            :software:
+* TODO incorporate all references                                  :software:
 * TODO citations                                                   :abstract:
 * TODO "quadrants of complexity" idea                           :acquisition:
 ** TODO figure
 ** TODO arguments
 * TODO tables                                                    :processing:
-* TODO summarize PbSe chapter                                  :introduction:
-* TODO summarize MX2 chapter                                   :introduction:
-* TODO summarize PEDOT:PSS chapter                             :introduction:
 * TODO distribution section                                      :processing:
 * TODO development section                                       :processing:
-* TODO incorporate "most software is not peer reviewed"            :software:
-** see Joppa reference 6
-* TODO incorporate idea "most people over-trust software"          :software:
-* TODO incorporate StoddenVictoria2016a                            :software:
-* TODO incorporate all references                                  :software:
-* TODO quote from RC                                           :introduction:
 * TODO insert content                                                  :PbSe:
+* TODO summarize PbSe chapter                                  :introduction:
+* TODO summarize MX2 chapter                                   :introduction:
+* TODO summarize PEDOT:PSS chapter                             :introduction:
 * TODO insert content from SI                                  :mixed_domain:
 * IDEA 2D delay example from ps system                               :active:
 * IDEA consider refactoring or expanding OOP section               :software: