Total internal reflection and evanescent gain

TL;DR

This paper investigates the conditions under which evanescent gain occurs during total internal reflection when the low-index medium is active, revealing fundamental causality constraints and stability issues.

Contribution

It introduces a causality-based framework to determine when evanescent gain can exist and analyzes the stability challenges in active media with total internal reflection.

Findings

Evanescent gain depends on the analytic properties of the permittivity.

Weak gain media can lead to absolute instabilities.

Evanescent gain can be achieved in certain stable configurations.

Abstract

Total internal reflection occurs for large angles of incidence, when light is incident from a high-refractive-index medium onto a low-index medium. We consider the situation where the low-index medium is active. By invoking causality in its most fundamental form, we argue that evanescent gain may or may not appear, depending on the analytic and global properties of the permittivity function. For conventional, weak gain media, we show that there is an absolute instability associated with infinite transversal dimensions. This instability can be ignored or eliminated in certain cases, for which evanescent gain prevails.