# 3: Third-Order Nonlinear Spectroscopies

- Page ID
- 298956

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

Third-order nonlinear spectroscopies are the most widely used class of nonlinear methods, including the common pump-probe experiment. This section will discuss a number of these methods. The approach here is meant to be practical, with the emphasis on trying to connect the particular signals with their microscopic origin. This approach can be used for describing any experiment in terms of the wave-vector, frequency and time-ordering of the input fields, and the frequency and wavevector of the signal.

- 3.1: Selecting signals by wavevector
- The question is how to select particular contributions to the signal. It won’t be possible to uniquely select particular diagrams. However, you can use the properties of the incident and detected fields to help with selectivity.

- 3.2: Photon Echo
- The photon echo experiment is most commonly used to distinguish static and dynamic linebroadening, and time-scales for energy gap fluctuations.

- 3.3: Transient Grating
- The transient grating is a third-order technique used for characterizing numerous relaxation processes, but is uniquely suited for looking at optical excitations with well-defined spatial period.

- 3.4: Pump-Probe
- The pump-probe or transient absorption experiment is perhaps the most widely used third-order nonlinear experiment. It can be used to follow many types of time-dependent relaxation processes and chemical dynamics, and is most commonly used to follow population relaxation, chemical kinetics, or wavepacket dynamics and quantum beats.