Negative refraction, negative phase velocity, and counterposition

TL;DR

This paper investigates the complex wave behaviors in materials supporting negative refraction and phase velocity, revealing that these phenomena depend on polarization, incidence angle, and can coexist in simple materials.

Contribution

It provides a theoretical and numerical analysis showing that negative refraction, phase velocity, and counterposition can occur independently and coexist in various materials, challenging traditional assumptions.

Findings

Negative refraction can occur with positive phase velocity.

Counterposition can occur with both positive and negative refraction.

Negative phase velocity can coexist with positive refraction in isotropic dielectrics.

Abstract

The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wavevectors may need to be considered. This is especially significant for materials which support negative refraction, negative phase velocity, and counterposition. By means of a numerical example based on a commonly studied bianisotropic material, our theoretical investigation revealed that: (i) negative (positive) refraction can arise even though the phase velocity is positive (negative); (ii) counterposition can arise in instances of positive and negative refraction; (iii) the phase velocity and time-averaged Poynting vectors can be mutually orthogonal; and (iv) whether or not negative refraction occurs can depend upon the state of polarization and angle of incidence. A further numerical example revealed that negative phase velocity and positive refraction can co-exist even in a simple isotropic dielectric material.