A general theory of inhomogeneous broadening for nonlinear susceptibilities: the second hyperpolarizability

TL;DR

This paper develops a comprehensive theoretical framework for modeling inhomogeneous broadening in nonlinear susceptibilities, improving spectral feature fitting and transition moment estimation in spectroscopy.

Contribution

It generalizes third-order nonlinear susceptibility expressions to include Gaussian and stretched Gaussian distributions, enhancing spectral analysis accuracy.

Findings

Better fit to subtle spectral features

More accurate determination of transition moments

Improved modeling of inhomogeneous broadening

Abstract

A general theory of inhomogeneous broadening is rarely applied to nonlinear spectroscopy in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important third-order nonlinear susceptibility expressions obtained with sum-over state quantum calculations to include Gaussian and stretched Gaussian distributions of Lorentzians. This theory gives a better fit to subtle spectral features - such as the shoulder of the electroabsorption peak, and is a more accurate tool for determining transition moments from spectroscopy experiments.