Spectral Representation for the Effective Macroscopic Response of a Polycrystal: Application to Third-Order Nonlinear Susceptibility

TL;DR

This paper extends spectral theory to uniaxial polycrystals and applies it to calculate their third-order nonlinear optical susceptibility, providing a detailed derivation and acknowledging prior related work.

Contribution

It provides a detailed derivation of spectral representation for uniaxial polycrystals and applies it to nonlinear optical property calculations, aligning with earlier conjectures by Milton.

Findings

Spectral representation applies to uniaxial polycrystals.

Calculated third-order nonlinear susceptibility using spectral theory.

Confirmed the spectral function matches Milton's earlier conjecture.

Abstract

Erratum: In our paper, we show that the spectral representation for isotropic two-component composites also applies to uniaxial polycrystals. We have learned that this result was, in fact, first conjectured by G.W. Milton. While our derivation is more detailed, our result for the spectral function is the same as Milton's. We very much regret not having been aware of this work at the time of writing our paper. Original abstract: We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a nonlinear decoupling approximation as modified by Ma et al., to calculate the third-order nonlinear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.