A general theory of inhomogeneous broadening for nonlinear susceptibilities: polarizability and hyperpolarizability

TL;DR

This paper develops a comprehensive theory for inhomogeneous broadening in nonlinear susceptibilities, extending traditional models to include Gaussian and stretched Gaussian distributions, improving the analysis of spectral features in nonlinear optical spectroscopy.

Contribution

It introduces a generalized framework for inhomogeneous broadening in nonlinear susceptibilities, enhancing the accuracy of spectral analysis beyond simple Lorentzian or Gaussian models.

Findings

Better fit to subtle spectral features in experiments

Importance of choosing the correct broadening model for limited wavelength ranges

Enhanced understanding of resonance shoulder regions

Abstract

While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important linear and second-order nonlinear susceptibility expressions obtained with sum-over state quantum calculations to include Gaussian and stretched Gaussian distributions of Lorentzians. We show that using the correct model to analyze experiments that probe a limited wavelength range can be critical and that this theory is better able to fit the subtle spectral features - such as the shoulder region of a resonance - when both models produce qualitatively similar responses.