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

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 featuressuch as the shoulder of the electroabsorption peak, and is a

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

“…Since real systems are inhomogeneously broadened, Lorentzian broadening must be augmented with statistical averaging of the excited state energies. Studies of broadening suggest that it is important to use appropriate models when analyzing the dispersion of both linear and nonlinear responses. , …”

“…Studies of broadening suggest that it is important to use appropriate models when analyzing the dispersion of both linear and nonlinear responses. 43,44 Discussion Table 1 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 hyperpolarizability. The molecular structures in Figure 1 appear beside the data points and are labeled 1,2,3,4,TM-2, TMC-2, and TMC-3 in correspondence to the labels in the table.…”

“…50 It is plausible that such issues along with experimental uncertainties could have led to an unphysically high value of the intrinsic nonlinearoptical response. Perhaps inhomogenous broadening needs to be included in the theory, 43,44 or perhaps 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.…”

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

“…A similar comparison for the quadratic electroabsorption spectrum of this molecule can be found in the literature. [23], [22] Figure 7 compares SiPc experimental linear absorption data with the Lorentzian (L) theory, and the IB theory for two values of β. A least squares fit gives β = 0.9.…”

“…The approach for evaluating the fundamental transformations from the homogeneous formulation to the inhomogeneous formulation for the quadratic dependencies (cubic dependencies are studied in Ref. [22]) on the transition frequency, ω lg is shown below.…”