A General Theory of Inhomogeneous Broadening for Nonlinear Susceptibilities: The Second Hyperpolarizability

A general theory of inhomogeneous broadening is rarely applied to nonlinear spectroscopy in lieu of either a simple Lorentzian or a Gaussian model. In this paper, 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.