Influence of the sign of the refractive index in the reflectivity of a metamaterial surface with localized roughness

TL;DR

This paper investigates how the sign of the refractive index in metamaterials affects their surface reflectivity with localized roughness, revealing differences from conventional materials especially in non-specular directions.

Contribution

It generalizes scattering methods to include materials with negative or positive refractive indices and analyzes their impact on rough surface reflectivity.

Findings

Reflectivity of rough surfaces depends on the sign of the refractive index.

Change of sign affects reflectivity even at low roughness levels.

Differences are prominent in directions away from the specular reflection.

Abstract

To study the scattering properties of metamaterials, we generalize two scattering methods developed for conventional (non-magnetic) isotropic materials to the case of materials with arbitrary values (positive or negative) of magnetic permeability and electric permittivity. The generalized methods are used to study the changes in the reflectivity of a metamaterial surface with localized roughness when the relative refractive index changes sign. Our results show that, unlike the case of a plane surface whose reflectivity is unaffected by the change of sign of the relative refractive index, in rough surfaces the change of sign is manifested in the reflectivity, even for very low roughness, particularly in observation directions away from the specular direction.