Dispersion formulas for hyperpolarizability averages

Abstract

The frequency-dependence of experimentally-derived or point-wise ab initio calculated hyperpolarizability averages is often expanded up to fourth order in the frequencies using the dispersion formula X || (n) (ω1;...,ω n ) = X || (n) (0)(1 + A ω L 2 + B + ω L 4 + O (ω i 6)) with ω L 2 = Σ i ω i 2, where the coefficient A is independent of the optical process. We derive an extension of this dispersion formula which is open ended in the powers of the frequencies, uses only processindependent coefficients, and involves a minimal number of terms per order. It is shown that the dispersion formula can be cast into a form where dispersion coefficients drop out in a systematic manner for optical processes involving static electric fields. We discuss how the concept of these dispersion formulas can be generalized to other hyperpolarizability components and exemplify this approach at the experimentally important components β⊥ and β K of the first hyperpolarizability.