Dimensional Crossover in the Effective Second Harmonic Generation of Films of Random Dielectrics

TL;DR

This paper develops a theoretical model for the effective second harmonic generation in films of random dielectrics, validated by numerical simulations, highlighting the role of film thickness and effective-medium approximation.

Contribution

It introduces a new theoretical expression for the nonlinear response of random dielectric films that incorporates film thickness and is validated by numerical simulations.

Findings

The theoretical model accurately predicts the nonlinear response.

Numerical simulations agree well with the theoretical results.

Effective-medium approximation is effective for estimating nonlinear response.

Abstract

The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective second harmonic generation susceptibility, incorporating the thickness of the film, is obtained by combining a modified effective-medium approximation with the general expression for the effective second harmonic generation susceptibility in a composite. The validity of the thoretical results is tested against results obtained by numerical simulations on random resistor networks. Numerical results are found to be well described by our theory. The result implies that the effective-medium approximation provides a convenient way for the estimation of the nonlinear response in films of random dielectrics.