Effective Second-Harmonic Generation Coefficient and C-eigenvalue of Nonlinear Susceptibility Tensors

TL;DR

This paper introduces a method to compute the effective second-harmonic generation coefficient in uniaxial crystals using symmetry properties, optimization models, and compares it with C-eigenvalues, verified through crystal examples.

Contribution

It presents a novel optimization-based approach to calculate the effective SHG coefficient and relates it to C-eigenvalues, simplifying the computation process.

Findings

Optimization models effectively compute the effective SHG coefficient.

The number of variables is reduced to simplify calculations.

Theoretical results are validated with crystal examples.

Abstract

The effective second-harmonic generation (SHG) coefficient is a crucial data that quantifies the efficiency of transforming fundamental frequency light into its second harmonic. With the help of the symmetry of nonlinear optical susceptibility tensors, we mainly discuss the computability of such a effective SHG coefficient in uniaxial crystals. For one thing, the calculation of effective SHG coefficient is converted into the optimization models with some geometric constraints by means of the peculiarity of fundamental frequency light. Secondly, the number of variables of such maximum models are cutted in half to $2$ to calculate it easier, and a comparison between the effective SHG coefficient and C-eigenvalue of susceptibility tensor is given also. Finally, some examples of typical crystal classes are presented to verify the correctness and broader applicabilities of the theoretical results.