2018-04-05 17:29

2 files changed, 17 insertions, 74 deletions

diff --git a/spectroscopy/auto/chapter.el b/spectroscopy/auto/chapter.el
index f316ae6..b067440 100644
--- a/spectroscopy/auto/chapter.el
+++ b/spectroscopy/auto/chapter.el
@@ -7,7 +7,6 @@
     "spc:fig:trive_off_diagonal"
     "spc:fig:trive_population_transfer"
     "fig:ta_and_tr_setup"
-    "eq:ta_complete"
-    "eq:generic"))
+    "eq:ta_complete"))
  :latex)
 
diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex
index 030edd5..2cf088b 100644
--- a/spectroscopy/chapter.tex
+++ b/spectroscopy/chapter.tex
@@ -145,10 +145,19 @@ WMEL diagrams are drawn using the following rules.  %
 	\item Output is represented as a solid wavy line.

 \end{denumerate}

 

+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

+dissertation.  %

+

 \subsection{Linear vs multidimensional}  % --------------------------------------------------------

 

 This derivation adapted from \textit{Optical Processes in Semiconductors} by Jacques I. Pankove

@@ -170,6 +179,8 @@ To extend reflectivity to a differential measurement
 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: Basic ``advantage of dimensionality'' figure.

+

 \subsection{Homodyne vs heterodyne}  % ------------------------------------------------------------

 

 Two kinds of spectroscopies: 1) heterodyne 2) homodyne.

@@ -182,6 +193,8 @@ This literally means that homodyne signals go as the square of heterodyne signal
 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

@@ -203,6 +216,8 @@ Since time-domain pulses in-fact possess all colors in them they cannot be trust
 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

@@ -318,11 +333,10 @@ expression for $\Delta A$ that only depends on my eight measurables.  %
 \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{Pump CMDS-probe}  % -------------------------------------------------------------------

-

 \clearpage

 \section{Instrumentation}  % ======================================================================

 

+In this section I introduce the key components of the MR-CMDS instrument.  %

 

 \subsection{LASER}  % -----------------------------------------------------------------------------

 

@@ -333,73 +347,3 @@ expression for $\Delta A$ that only depends on my eight measurables.  %
 \subsection{Delay stages}  % ----------------------------------------------------------------------

 

 \subsection{Spectrometers}  % ---------------------------------------------------------------------

-

-\subsection{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.

- 

-\subsubsection{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.

-

-\subsubsection{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.  %

-

-\subsubsection{Time-Bandwidth Product}

-

-For a Gaussian, approximately 0.441

-

-% TODO: find reference

-% TODO: number defined on INTENSITY level!
\ No newline at end of file