% http://scifun.chem.wisc.edu/Thesis_Awards/chapter_guidelines.html

\chapter{Public}

\section{Chemical systems}  % ---------------------------------------------------------------------

Chemical systems are complex!  %
They contain many molecules ($10^{25}$ in a cup of coffee, 1 trillion in each human cell).  %
These molecules have multiple interaction modes, both internal (intramolecular) and external
(intermolecular).  %
The reactivity of the system taken as a whole can be dominated by very rare but very important
species, \textit{e.g.} catalysts.  %

Despite this complexity, scientists have gotten very good at describing chemical systems through
representations of dynamic equilibrium.  %
In such situations, several key parameters emerge:  %
\begin{itemize}
  \item concentration
  \item timescale (rate)
  \item lengthscale
\end{itemize}

\subsection{Concentration}

\subsection{Timescale}

% TODO: dynamics in chemical systems: collision time, dephasing, rotation, relaxation, diffusion...

\subsection{Lengthscale}

\section{Analytical chemistry}  % -----------------------------------------------------------------

Traditionally, chemists have seen fit to divide themselves into four specializations: analytical,
inorganic, organic, and physical.  %
In recent years, materials chemistry and chemical biology have become specializations in their own
right.  %
This dissertation focuses on analytical chemistry.  %

Analytical chemists separate, identify, and quantify chemical systems.  %
To do this, we build instruments that exploit physical properties of the chemical components:  %
\begin{itemize}
  \item separation science (chromatography, electrophoresis)
  \item mass spectrometry
  \item electrochemistry
  \item microscopy
  \item spectroscopy
\end{itemize}
Spectroscopy is a family of strategies that exploit the interaction of chemical systems with
light.  %

\section{Spectroscopy}  % -------------------------------------------------------------------------

Molecules respond to electric fields.  %
Static electric fields cause charged molecules (ions) to move, as in electrophoresis and mass
spectrometry.  %
Oscillating electric fields, also known as light, can interact directly with the molecules
themselves, driving transitions.  %
However, these transitions can only be driven with the appropriate frequency of light
(resonance).  %
Different frequencies (colors) of light interact with different kinds of transitions, revealing
different features of the molecule of interest.  %

% TODO: different energy ranges / transition types (nuclear, rotational, vibrational, electronic)

% TODO: how is a photon created or absorbed?

\subsection{Nonlinear spectroscopy}

Spectroscopy is fantastic, but sometimes simple experiments don't reveal everything.  %
Nonlinear spectroscopy uses multiple electric fields simultaniously, revealing even more
information about the chemical system.  %

% TODO: simple graphic of homogeneous vs inhomogeneous broadening

% TODO: 2D freq-freq with increasing inhomogeneity (from Dan's theory work)

\section{Instrumentation}  % ----------------------------------------------------------------------

To accomplish nonlinear spectroscopy, specialized light sources are needed:  %
\begin{itemize}
  \item gigantic electric fields
  \item ultrafast time resoution
  \item tunable frequencies
\end{itemize}

\subsection{LASER}

These sources are made using Light Amplified by the Stimulated Emission of Radiation (LASER).  %

% TODO: discussion of the original LASER, basic LASER physics

% TODO: discuss temporal coherence

% TODO: discuss pulsed sources

By keeping a wide range ofr colors in phase simulatniously, we are able to create truly ultrafast
pulses of light.  %
The work presented in this dissertation was primarily taken using a 35 fs 1 KHz system.  %

35 fs ($35\times10^{15}$ second) pulses are incredibly short:
\begin{equation}
  \frac{\text{pulse duration (35 fs)}}{\text{time between pulses (1 ms)}} \approx
  \frac{\text{5.75 months}}{\text{age of universe (13.7 billion years)}}  % TODO: cite age
\end{equation}
proportionally, our sample spends 6 months in the ``sun'' for every age of the unverse in the
dark.  %

Because all of the energy within the pulse is compressed to such a short period of time, these
pulses are also incredibly powerful:
\begin{equation}
  \frac{\text{energy per pulse (4 mJ)}}{\text{pulse duration (35 fs)}} \approx
  \frac{\text{US electricity generation} (5.43\times10^{11} W)}{5}  % TODO: cite generation
\end{equation}
this laser outputs electric fields one fifth as powerful as total US electricity generation (2016).

% TODO: pulses are very thin (draw circle, use thickness of paper) to motivate 'hard to handle'

\subsection{OPA}

% https://osf.io/vwhjk/