2018-03-31 17:56

5 files changed, 155 insertions, 77 deletions

diff --git a/spectroscopy/auto/chapter.el b/spectroscopy/auto/chapter.el
index ae8a477..f316ae6 100644
--- a/spectroscopy/auto/chapter.el
+++ b/spectroscopy/auto/chapter.el
@@ -2,6 +2,10 @@
  "chapter"
  (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"
     "eq:generic"))
diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex
index fe10f60..9062e89 100644
--- a/spectroscopy/chapter.tex
+++ b/spectroscopy/chapter.tex
@@ -10,7 +10,7 @@
 % TODO: https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.7b02693

 % TODO: http://journals.sagepub.com/doi/10.1177/0003702816669730

 

-\chapter{Spectroscopy}

+\chapter{Spectroscopy} \label{cha:spc}

 

 \begin{dquote}

   A hundred years ago, Auguste Comte, … a great philosopher, said that humans will never be able to

@@ -26,48 +26,113 @@
   

 \clearpage

 

-In this chapter I lay out the foundations of spectroscopy.

+In this chapter I lay out the foundations of spectroscopy as relevant to this dissertation.  %

+Spectroscopy is the study of the interaction of light (electromagnetic radiation) and matter

+(molecules, crystals, solids, liquids etc).  %

+

+\section{Light-matter interaction}  % =============================================================

+

+As scientists, light is perhaps the most useful tool we have for interrogating materials.  %

+Light is relatively easy to create and control, and light-matter interaction tells us a lot about

+the microscopic physics of the material under investigation.  %

+Spectroscopists use light-matter interaction as an analytical tool.  %

+For the purposes of this document, light can be treated as a classical electromagnetic wave and

+matter can be treated in the quantum mechanical density matrix formalism.  %

+More complete treatments which also take the quantum-mechanical nature of light into account are

+possible (see: ``quantum optics'', ``quantum electrodynamics''), but beyond the scope of this

+dissertation.  %

+This classical treatment still captures the full richness of the wave-nature of light, including

+interference effects.  \cite{HuygensChristiaan1913a}  %

+It merely ignores the quantitization of the electric field---a valid assumption in the limit of

+many photons.  %

+

+% TODO: language from 'how a photon is created or destroyed'

+

+For simplicity, consider a two state system: ``a'' and ``b''.  %

+These two states might be the inital and final states in a transition.  %

+The wavefunction for this system can be written as a sum of the stationary states (eigenstates)

+with appropriate scaling coefficients:

+\begin{equation}

+  \Psi(r, t) = c_a(t)\psi_a(r) + c_b(t)\psi_b(r)

+\end{equation}

+The time dependence lies in the $c_a$ and $c_b$ coefficients, and the spatial dependence lies in

+the $\psi_a$ and $\psi_b$ eigienstates.  %

 

-\section{Light}

+Now we will expose this two-state system to an electric field:

+\begin{equation}

+  E = E^{\circ}\left[ \me^{i(kz-\omega t)} + \me^{-i(kz-\omega t)} \right]

+\end{equation}

 

-% TODO: add reference to HuygensChristiaan1913.000

+For simplicity, we consider a single transition dipole, $\mu$.  %

 

-% TODO: add reference to MaimanTheodore.000

+The Hamiltonian which controls the coupling of or simple system to the electric field described in

+...:

+\begin{equation}

+  H = H_{\circ} - \mu \dot E

+\end{equation}

 

-\section{Light-Matter Interaction}

+Solving for the time-dependent coefficients, then:

+\begin{eqnarray}

+  c_a(t) &=& \cos{\frac{\Omega t}{2}} \me^{-i\omega_at} \\

+  c_b(5) &=& \sin{\frac{\Omega t}{2}} \me^{-i\omega_bt}

+\end{eqnarray}

+Fast and slow parts...

+Bohr and Rabi freuencies...

 

-Spectroscopic experiments all derive from the interaction of light and matter. Many material

-properties can be deduced by measuring the nature of this interaction.  %

+Where $\Omega$ is the \emph{Rabi frequency}:  %

+\begin{equation}

+  \Omega \equiv \frac{\mu E^\circ}{\hbar}

+\end{equation}

 

-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?

+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{\mu} \right| c_aa + c_bb \right>

+\end{equation}

+The complex wavefunction is called a \emph{ket}, represented $|b>$.  %

+The complex conjugate is called a \emph{bra}, represented $<a|$.  %

+When expanded,

+\begin{equation}

+  \mu(t) = c_a^2\mu_a + c_b^2\mu_b + \left< c_aa \left| \hat{mu} \right| c_bb \right> +

+  \left<c_bb \left| \hat{mu} \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.  %

 

-% TODO: Discuss dephasing induced resonance. Example: florescence

+We commonly represent quantum mechanical systems using density matrices, where diagonal elements

+are populations and off-diagonal elements are coherences.  %

+Each density matrix element has the form $\rho_{kb}$, where $k$ is the ket and $b$ is the bra.  %

+% TODO: 4 member density matrix representing system above

+A more complete discussion of the formalism we use to describe light-matter interaction is

+presented in \autoref{cha:mix}.  %

 

-\subsection{Representations}

+% TODO: homogeneous line-width

+

+Spectroscopic experiments are typically performed on an ensemble of states.  %

+In such circumstances, inhomogeneous broadening becomes relevant.  %

+Inhomogeneous broadening arises from permanent differences between different oscillators in the

+ensemble.  %

+% TODO: why is inhomogeneous broadening important?

 

 Many strategies have been introduced for diagrammatically representing the interaction of multiple

 electric fields in an experiment.  %

+Spectroscopists have used diagrams to represent nonlinear optical phenomena since 1965.

+\cite{WardJF1965a}  %

+Several competing strategies have been defined over the years.  %

+In 1978, \textcite{YeeTK1978a} defined the ``circle diagram'' convention.  %

+Since then, the more popular  ``closed-time path-loop'' \cite{MarxChristophA2008a,

+  RoslyakOleksiy2009a} and ``double-sided Feynman'' diagrams \cite{MukamelShaul1995a} (also known

+as Mukamel diagrams) were introduced.  %

+\textcite{BiggsJasonD2012a} have written a paper which does an excellent job defining and comparing

+these two strategies.  %

+In their seminal 1985 work, \emph{A Unified View of Raman, Resonance Raman, and Fluorescence

+  Spectroscopy}, \textcite{LeeDuckhwan1985a} defined the conventions for a ``wave-mixing energy

+level'' (WMEL) diagram.  %

+Today, double-sided Feynman diagrams are probably most popular, but WMELs will be used in this

+document due to author preference.  %

 

-\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{LeeDuckhwan1985a}.  %

 \gls{WMEL} diagrams are drawn using the following rules.  %

-\begin{enumerate}

+\begin{denumerate}

 	\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

@@ -77,15 +142,13 @@ spectroscopy for Wright group members.  %
 	\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}

+\end{denumerate}

 

-% TODO: Discuss Mukamel diagrams from a historical perspective

+% TODO: representative WMEL?

 

-\section{Linear Spectroscopy}

+\section{Types of spectroscopy}  % ================================================================

 

-\subsection{Reflectivity}

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

 

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

 \cite{PankoveJacques1975a}.  %

@@ -99,30 +162,14 @@ Further derivation adapted from \cite{KumarNardeep2013a}.  %
 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}

+% TODO: spectral congestion figure

 

-\subsection{Six Wave}

-

-\gls{multiple population-period transient spectroscopy} (\Gls{MUPPETS})

-

-\section{Strategies for CMDS}

+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?

 

-\subsection{Homodyne vs. Heterodyne Detection}

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

 

 Two kinds of spectroscopies: 1) \gls{heterodyne} 2) \gls{homodyne}.

 Heterodyne techniques may be \gls{self heterodyne} or explicitly heterodyned with a local

@@ -134,9 +181,7 @@ 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.

 

-\Gls{transient absorption}, \gls{TA}

-

-\subsection{Frequency vs. Time Domain}

+\subsection{Frequency vs time domain}  % ----------------------------------------------------------

 

 Time domain techniques become more and more difficult when large frequency bandwidths are

 needed.  %

@@ -157,7 +202,7 @@ Since time-domain pulses in-fact possess all colors in them they cannot be trust
 perturbative fluence.  %

 See that paper that Natalia presented...  %

 

-\subsection{Triply Electronically Enhanced Spectroscopy}

+\subsection{Transient grating}  % -----------------------------------------------------------------

 

 Triply Electronically Enhanced (TrEE) spectroscopy has become the workhorse homodyne-detected 4WM

 experiment in the Wright Group.  %

@@ -166,7 +211,34 @@ experiment in the Wright Group.  %
 

 % TODO: Discussion of old and current delay space

 

-\subsection{Transient Absorbance Spectroscopy} 

+% 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}

+

+\subsection{Transient absorbance}  % --------------------------------------------------------------

 

 \Gls{transient absorption} (\gls{TA})

 

@@ -247,13 +319,23 @@ 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{Cross Polarized TrEE}

+\subsection{Pump CMDS-probe}  % -------------------------------------------------------------------

+

+\clearpage

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

+

 

-\subsection{Pump-TrEE-Probe}

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

 

-\Gls{pump TrEE probe} (\gls{PTP}).

+% TODO: add reference to MaimanTheodore.000 (ruby laser)

 

-\section{Instrumental Response Function}

+\subsection{Optical parametric amplifiers}  % -----------------------------------------------------

+

+\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

@@ -261,7 +343,7 @@ attempt.  %
 

 It is particularly useful to define bandwidth.

  

-\subsection{Time Domain}

+\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.  %

@@ -310,23 +392,15 @@ Finally, since we measure $\sigma_P$ and wish to extract $\sigma$:
 

 Again, all of these widths are on the \textit{intensity} level.

 

-\subsection{Frequency Domain}

+\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.  %

 

-\subsection{Time-Bandwidth Product}

+\subsubsection{Time-Bandwidth Product}

 

 For a Gaussian, approximately 0.441

 

 % TODO: find reference

-% TODO: number defined on INTENSITY level!

-

-

-

-

-

-

-

-

+% TODO: number defined on INTENSITY level!
\ No newline at end of file
diff --git a/spectroscopy/wmels/trive_off_diagonal.png b/spectroscopy/wmels/trive_off_diagonal.png
new file mode 100644
index 0000000..f27cd21
--- /dev/null
+++ b/spectroscopy/wmels/trive_off_diagonal.png
diff --git a/spectroscopy/wmels/trive_on_diagonal.png b/spectroscopy/wmels/trive_on_diagonal.png
new file mode 100644
index 0000000..27df1a6
--- /dev/null
+++ b/spectroscopy/wmels/trive_on_diagonal.png
diff --git a/spectroscopy/wmels/trive_population_transfer.png b/spectroscopy/wmels/trive_population_transfer.png
new file mode 100644
index 0000000..bea8668
--- /dev/null
+++ b/spectroscopy/wmels/trive_population_transfer.png