Operator effective medium approximation for inhomogeneous and curvilinear media

Abstract

Effective medium theory is an integral part of the area of metamaterials providing insights into the physics behind their interaction with light. In this paper, we develop the operator effective medium approximation for spherical and cylindrical multilayer systems. Equating evolution operators (wave propagators) for the actual multilayer and homogenized medium, we establish the effective material parameters, which differ for planar and curvilinear cases. We supplement the criterion for applicability of the effective medium approximation with the assertion that the radii of curvilinear layers must be about or greater than the radiation wavelength. The operator effective medium approximation provides a clear way to approach nonlocal corrections, as well as characterize structures with balanced loss and gain. We envisage that the operator effective medium approximation will be useful for the characterization of metamaterials and other nanophotonic systems of complex shapes.