Homogenization of Maxwell\u2019s equations in a layered system beyond the static approximation

Alexander M Merzlikin,Roman S Puzko

doi:10.1038/s41598-020-72727-8

Abstract

The propagation of electromagnetic waves through a disordered layered system is considered in the paradigm of the homogenization of Maxwell’s equations. Although the accuracy of the effective dielectric permittivity and/or magnetic permeability is still unclear outside the static approximation, we show that the effective wave vector can be correctly introduced even in high-frequency cases. It is demonstrated that both the real and imaginary parts of the effective wave vector are self-averaging quantities connected by the Kramers–Kronig relations. We provide a unified approach to describe the propagation and localization of electromagnetic waves in terms of the effective wave vector. We show that the effective wave vector plays the same role in describing composite materials in electrodynamics as the effective dielectric permittivity does in statics.

Highlights

The propagation of electromagnetic waves through a disordered layered system is considered in the paradigm of the homogenization of Maxwell’s equations
The problem of replacing an inhomogeneous composite system with a homogeneous material with effective parameters is called the homogenization problem
We considered the propagation of an electromagnetic wave through a disordered layered system

Summary

Introduction

The propagation of electromagnetic waves through a disordered layered system is considered in the paradigm of the homogenization of Maxwell’s equations. The accuracy of the effective dielectric permittivity and/or magnetic permeability is still unclear outside the static approximation, we show that the effective wave vector can be correctly introduced even in high-frequency cases. We show that the effective wave vector plays the same role in describing composite materials in electrodynamics as the effective dielectric permittivity does in statics. The description of metamaterials as homogeneous by means of their effective parameters (dielectric permittivity and magnetic permeability, chirality coefficients, etc.) remains a relevant problem in electrodynamics. It is assumed that the effective parameters of a homogeneous system provide the same scattered field as that of an inhomogeneous system (see Fig. 1). The effective parameters allow the description of light scattering by a composite system without considering the inhomogeneous structure of the system. The scaling theory of G-convergence[4] and spectral t heory[5,6,7,8] have been developed

Methods

Results

Conclusion