Homogenization of Maxwell's equations in layered system beyond static approximation

TL;DR

This paper introduces an effective wave vector concept for describing electromagnetic wave propagation and localization in layered disordered systems, extending beyond static approximations and providing a unified analytical framework.

Contribution

It proposes a new homogenization approach using an effective wave vector that remains valid beyond static limits and relates to the system's frequency-dependent properties.

Findings

Effective wave vector is self-averaging at any frequency.

Real and imaginary parts of the effective wave vector are well-defined.

The approach generalizes the Jones-Herbert-Thouless formula.

Abstract

The propagation of electromagnetic waves through disordered layered system is considered in the paradigm of Maxwell's equations homogenization. In spite of the impossibility to describe the system in terms of effective dielectric permittivity and/or magnetic permeability the unified way to describe the propagation and Anderson localization of electromagnetic waves is proposed in terms of the introduced effective wave vector (effective refractive index). It is demonstrated that both real and imaginary parts of the effective wave vector (contrary to effective dielectric permittivity and/or magnetic permeability) are the self-averaging quantities at any frequency. The introduced effective wave vector is analytical function of frequency; corresponding Kramers-Kronig relation generalizes the Jones-Herbert-Thouless formula.