Scattering matrix of the boundary of a nonlocal metamaterial providing insights into non-Maxwellian boundary conditions due to spatial dispersion

TL;DR

This paper introduces a model to analyze the scattering matrix at the boundary between local and nonlocal metamaterials, revealing non-Maxwellian boundary conditions caused by spatial dispersion.

Contribution

The paper provides a simple mathematical model to calculate the scattering matrix at interfaces involving nonlocal metamaterials, offering new insights into non-Maxwellian boundary conditions.

Findings

Calculated scattering matrix for vacuum-photonic crystal interface

Identified non-Maxwellian boundary conditions due to spatial dispersion

Validated model with numerical tests

Abstract

We present a simple model of the interface between a local homogeneous medium and a potentially nonlocal metamaterial/photonic crystal. This model allows us to calculate the scattering matrix elements of the interface for a plane wave of light normally incident upon the interface from either direction. The resulting scattering matrix provides insight into the non-Maxwellian boundary conditions present at the interface between a homogeneous medium and a metamaterial/photonic crystal with strong spatial dispersion. We present the model mathematically. As an example, the model is used to calculate the scattering matrix of the interface between vacuum and a simple photonic crystal. Several tests of the calculated scattering matrix elements are presented. Finally, we used the results of the scattering model to postulate possible forms for the non-Maxwellian boundary conditions.