Mean Field Theory for Lossy Nonlinear Composites

TL;DR

This paper develops a mean-field theoretical framework for analyzing lossy nonlinear composites with complex dielectric functions, using spectral representations and self-consistent equations to predict effective responses.

Contribution

It introduces a novel mean-field approach for lossy nonlinear composites, extending spectral representation methods to complex, field-dependent dielectric properties.

Findings

Derived self-consistent equations for effective dielectric response.

Applied the theory to Maxwell-Garnett and effective medium microstructures.

Validated the approach through illustrative microstructure models.

Abstract

The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop self-consistent equations for the effective response. We examine two types of microstructure, namely, the Maxwell-Garnett approximation and the effective medium approximation to illustrate the theory.