Anomalous transient amplification of waves in non-normal photonic media

TL;DR

This paper reveals that optical systems with unbalanced loss and gain, described by non-normal operators, can transiently amplify signals despite overall losses, opening new avenues for photonic and quantum optical device design.

Contribution

It introduces a mathematical framework for analyzing and designing non-normal optical media that can transiently amplify signals, despite overall dissipation.

Findings

Lossy systems can transiently amplify signals by several orders of magnitude.

A mathematical framework for non-normal wave dynamics is developed.

Design principles for non-normal power amplifiers are proposed.

Abstract

Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally been the mitigation of optical losses. Recent work has shown that a new class of optical materials that consist of a precisely balanced distribution of loss and gain can be exploited to engineer novel functionalities for propagating and filtering electromagnetic radiation. Here we show a generic property of optical systems that feature an unbalanced distribution of loss and gain, described by non-normal operators, namely that an overall lossy optical system can transiently amplify certain input signals by several orders of magnitude. We present a mathematical framework to analyze the dynamics of wave propagation in media with an arbitrary distribution of loss and gain and construct the initial conditions to engineer such non-normal power amplifiers. Our results point to a new design space for engineered optical systems employed in photonics and quantum optics.