From 58a5425154d4d7eec55463e5e2a89b7ade067781 Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Sun, 15 Apr 2018 17:04:18 -0500
Subject: 2018-04-15 17:04

---
 spectroscopy/chapter.tex | 152 +++++++++++++++++++++++------------------------
 1 file changed, 75 insertions(+), 77 deletions(-)

(limited to 'spectroscopy/chapter.tex')

diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex
index 819fe94..805bce8 100644
--- a/spectroscopy/chapter.tex
+++ b/spectroscopy/chapter.tex
@@ -38,7 +38,7 @@ many photons.  %
 
 The basics of light matter interaction have been covered in many texts.  %
 For a beginners introduction I recommend ``How a Photon is Created or Absorbed'' by
-\textref{HendersonGiles1994a}.  %
+\textcite{HendersonGiles1994a}.  %
 Here I present a very minimal overview.  %
 
 Consider a two state system: ``a'' and ``b''.  %
@@ -61,8 +61,8 @@ For simplicity, we consider a single transition dipole, $\mu$.  %
 The Hamiltonian which controls the coupling of or simple system to the electric field described in
 \autoref{spc:eqn:E} can be written.  %
 \begin{eqnarray}
-  H &=& H_{0} - \mu \cdot E \\
-  &=& H_{0} - \mu \cdot \frac{E^0}{2}\left[ \me^{i(kz-\omega t)} + \me^{-i(kz-\omega t)} \right]
+  H &=& H_{0} + \mu \cdot E \\
+  &=& H_{0} + \mu \cdot \frac{E^0}{2}\left[ \me^{i(kz-\omega t)} + \me^{-i(kz-\omega t)} \right]
 \end{eqnarray}
 
 Solving for the time-dependent coefficients, then:
@@ -79,15 +79,11 @@ Where $\omega_a$ and $\omega_b$ are the fast (and familiar) Bohr frequencies and
 In Dirac notation \cite{DiracPaulAdrienMaurice1939a}, an observable (such as $\mu(t)$) can be
 written simply:  %
 \begin{equation}
-  \mu(t) = \left< c_aa + c_bb \left| \hat{H} \right| c_aa + c_bb \right>
+  \mu(t) = |c_a(t)|^2 \langle \phi_a | \mu | \phi_a \rangle + |c_b(t)|^2 \langle \phi_b | \mu | \phi_b \rangle +  c_a(t) c_b^*(t) \langle \phi_b | \mu | \phi_a \rangle  +
+  c_b(t) c_a^*(t) \langle \phi_a | \mu | \phi_b \rangle 
 \end{equation}
 The complex wavefunction is called a \emph{ket}, represented $\left|b\right>$.  %
 The complex conjugate is called a \emph{bra}, represented $\left<a\right|$.  %
-When expanded,
-\begin{equation}
-  \mu(t) = c_a^2\mu_a + c_b^2\mu_b + \left< c_aa \left| \hat{H} \right| c_bb \right> +
-  \left<c_bb \left| \hat{H} \right| c_aa \right>
-\end{equation}
 The first two terms are populations and the final two terms are coherences.  %
 The coherent terms will evolve with the rapid Bohr oscillations, coupling the dipole observable
 with the time-dependent electric field.  %
@@ -146,18 +142,19 @@ These are workhorse experiments, like absorbance, reflectance, FTIR, UV-Vis, and
 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]  %
+There are now even handheld Raman spectrometers for use in industrial settings. \cite{nanoram}  %
 
 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.  %
+I ignore ``correlation spectroscopy'' (otherwise known as covariance spectroscopy), 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?
+system, a rule of thumb states that each term is roughly ten times smaller than the last.  %
 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.  %
@@ -261,67 +258,68 @@ 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]
-
-\section{Instrumentation}  % ======================================================================
-
-In this section I introduce the key components of the MR-CMDS instrument.  %
-This also serves to introduce the reader to the particular components used in my research.  %
-
-\subsection{LASER}  % -----------------------------------------------------------------------------
-
-Light Amplified by Stimulated Emission of Radiation (LASER) light sources are absolutely crucial
-components of the modern MR-CMDS instrument.  %
-The first laser was built in 1960 by \textcite{MaimanTheodore1960a}, and pulsed lasers were
-invented soon after.  %
-Today, ultrafast light sources are relatively cheap and reliable.  %
-Our SpectraPhysics ``Tsunami'' oscillator uses passive Kerr-lens mode-locking to generate $\sim$35
-fs seed pulses at $\sim$80 MHz (one pulse every 12.5 nanoseconds). \cite{Tsunami}  %
-This seed is split and fed into two 1 KHz amplifiers, a picosecond ``Spitfire Ace''
-\cite{SpitfireAce} and a femtosecond ``Spitfire Pro'' \cite{SpitfirePro}.  %
-These amplifiers each output several watts of ultrafast pulses at 1 KHz (one pulse per
-millisecond).  %
-
-\subsection{Optical parametric amplifiers}  % -----------------------------------------------------
-
-Optical Parametric Amplifiers (OPAs) are arguably the most crucial component of modern MR-CMDS, as
-they provide the frequency tunable light sources that we require. \cite{CerulloGiulio2003a}  %
-OPAs provide tunability through three-wave sum and difference frequency generation processes.  %
-``Fundamental'' tunability is achieved by splitting the 800 nm photons into two lower energy
-photons, with a splitting ratio determined by motorized optics.  %
-These split photons are called ``signal'' and ``idler'', with signal being the higher energy and
-idler the lower energy photon.  %
-
-% TODO: paragraph about phase matching conditions and polarization
-
-Signal and idler are then either used directly, or amplified through sum or difference frequency
-processes to provide broadband tuneability.  %
-All available optical processes for the TOPAS-C OPAs \cite{TOPAS-C} used on the femtosecond table
-are shown in \autoref{spc:fig:ranges}.  %
-Amazingly, these OPAs offer tunability from the mid-infrared to the ultraviolet.  %
-Currently we do not have proper automated filters to make it possible to continuously scan between
-regions, but such things are possible.  %
-
-On the picosecond table we have three separate kinds of OPAs, including one TOPAS-800
-\cite{TOPAS-800} and two OPA-800 models that have been modified with precision micro control
-\cite{PMC} servo motors to provide automated tunability.  %
-
-\subsection{Delay stages}  % ----------------------------------------------------------------------
-
-Delay stages are simple, one-motor devices which are used to control the relative arrival time of
-pulses at the sample.  %
-The Wright Group currently owns four models of delay stage: 1. Newport MFA-CC [CITE], 2. Aerotech
-... [CITE], 3. Thorlabs LTS300 [CITE].  %
-The fourth ``model'' are actually homemade stages that are driven using PMC motors.  %
-
-\subsection{Spectrometers}  % ---------------------------------------------------------------------
-
-Spectrometers...
-
-\begin{figure}
-  \includegraphics[width=\linewidth]{spectroscopy/ranges}
-  \caption{
-    CAPTION TODO
-  }
-  \label{spc:fig:ranges}
-\end{figure}
\ No newline at end of file
+This fact is often forgotten, and papers have been corrected for forgetting this factor of
+two. \cite{KoivistoinenJuha2017a}  %
+
+% \section{Instrumentation}  % ======================================================================
+
+% In this section I introduce the key components of the MR-CMDS instrument.  %
+% This also serves to introduce the reader to the particular components used in my research.  %
+
+% \subsection{LASER}  % -----------------------------------------------------------------------------
+
+% Light Amplified by Stimulated Emission of Radiation (LASER) light sources are absolutely crucial
+% components of the modern MR-CMDS instrument.  %
+% The first laser was built in 1960 by \textcite{MaimanTheodore1960a}, and pulsed lasers were
+% invented soon after.  %
+% Today, ultrafast light sources are relatively cheap and reliable.  %
+% Our SpectraPhysics ``Tsunami'' oscillator uses passive Kerr-lens mode-locking to generate $\sim$35
+% fs seed pulses at $\sim$80 MHz (one pulse every 12.5 nanoseconds). \cite{Tsunami}  %
+% This seed is split and fed into two 1 KHz amplifiers, a picosecond ``Spitfire Ace''
+% \cite{SpitfireAce} and a femtosecond ``Spitfire Pro'' \cite{SpitfirePro}.  %
+% These amplifiers each output several watts of ultrafast pulses at 1 KHz (one pulse per
+% millisecond).  %
+
+% \subsection{Optical parametric amplifiers}  % -----------------------------------------------------
+
+% Optical Parametric Amplifiers (OPAs) are arguably the most crucial component of modern MR-CMDS, as
+% they provide the frequency tunable light sources that we require. \cite{CerulloGiulio2003a}  %
+% OPAs provide tunability through three-wave sum and difference frequency generation processes.  %
+% ``Fundamental'' tunability is achieved by splitting the 800 nm photons into two lower energy
+% photons, with a splitting ratio determined by motorized optics.  %
+% These split photons are called ``signal'' and ``idler'', with signal being the higher energy and
+% idler the lower energy photon.  %
+
+% % TODO: paragraph about phase matching conditions and polarization
+
+% Signal and idler are then either used directly, or amplified through sum or difference frequency
+% processes to provide broadband tuneability.  %
+% All available optical processes for the TOPAS-C OPAs \cite{TOPAS-C} used on the femtosecond table
+% are shown in \autoref{spc:fig:ranges}.  %
+% Amazingly, these OPAs offer tunability from the mid-infrared to the ultraviolet.  %
+% Currently we do not have proper automated filters to make it possible to continuously scan between
+% regions, but such things are possible.  %
+
+% On the picosecond table we have three separate kinds of OPAs, including one TOPAS-800
+% \cite{TOPAS-800} and two OPA-800 models that have been modified with precision micro control
+% \cite{PMC} servo motors to provide automated tunability.  %
+
+% \subsection{Delay stages}  % ----------------------------------------------------------------------
+
+% Delay stages are simple, one-motor devices which are used to control the relative arrival time of
+% pulses at the sample.  %
+% The Wright Group currently owns four models of delay stage: 1. Newport MFA-CC [CITE], 2. Aerotech
+% ... [CITE], 3. Thorlabs LTS300 [CITE].  %
+% The fourth ``model'' are actually homemade stages that are driven using PMC motors.  %
+
+% \subsection{Spectrometers}  % ---------------------------------------------------------------------
+
+% Spectrometers...
+
+% \begin{figure}
+%   \includegraphics[width=\linewidth]{spectroscopy/ranges}
+%   \caption{
+%     CAPTION TODO
+%   }
+%   \label{spc:fig:ranges}
+% \end{figure}
\ No newline at end of file
-- 
cgit v1.2.3

