  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.
