Generalized Theory of Nonlinear Susceptibilities and Linear Electrooptic Coefficients Based on a Three-Dimensional Anharmonic Oscillator Model

Abstract

First-order nonlinear susceptibilities are treated theoreticaly, and a conventional one-dimensional anharmonic oscillator (AHO) model based on the shell model is extended to the three-dimensional model. The potential on this model includes anharmonic terms of the form Akimqikqilqim+Bklmqikqilqem+Cklmqikqelqem+Dklmqekqelqem, where qiα, qeα are the α-th components of qi, qe, which are the ionic and electronic configurational coordinates, respectively. Aklm, Bklm, Cklm and Dklm are anharmonic potential coefficients, which are considered to be components of third-rank tensors. Various nonlinear optical effects in crystals with arbitrary crystal structures can be treated by this extended theory. As an example, despersion formulas of first-order nonlinear susceptibilities in wurtzite-type crystals are derived for sum-frequency generation, electro-optic effect and second harmonic generation.