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

Abstract

Abstract-While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinearoptical 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.

Intrinsic Hyperpolarizabilities as a Figure of Merit for Electro-optic Molecules

“…Studies of broadening suggest that it is important to use appropriate models when analyzing the dispersion of both the linear and nonlinear response. [43,44] III. DISCUSSION Table I summarizes our analysis of experimental results found in the literature [45,46] and Figure 1 shows a plot of the intrinsic off-resonant hyperpolarizability as a function of the measured off-resonant hyperpolarizabil-ity.…”

“…[50] It is plausible that such issues along with experimental uncertainties could have lead to an un-physically high value of the intrinsic nonlinear-optical response. Perhaps inhomogenous broadening needs to be included in the theory; [43,44] or, the conventions of expressing β are are not consistent. Alternatively, the theory may need to be revisited for the possibility that the fundamental limits may be underestimated.…”