Causality, Non-Locality and Negative Refraction

TL;DR

This paper develops a fundamental theory of negative refraction in electromagnetic materials that incorporates spatial non-locality, showing that both dissipation and non-locality are essential for negative refraction to occur.

Contribution

It presents a first-principles, comprehensive theory of negative refraction that includes non-local effects, providing new fundamental conditions for its existence.

Findings

Both dissipation and spatial non-locality are necessary for negative refraction.

Provides a sufficient condition for negative refraction in weakly non-local materials.

Broad implications for the analysis of wave phenomena in complex media.

Abstract

The importance of spatial non-locality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes non-locality in its full generality. The theory shows that both dissipation and spatial non-locality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial non-locality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.