Eigenvalue dynamics in the presence of non-uniform gain and loss

TL;DR

This paper provides a general theoretical framework for understanding counter-intuitive effects like loss-induced transmission and reversed pump dependence in non-Hermitian systems with patterned gain and loss, expanding the design possibilities.

Contribution

It introduces universal conditions for these effects in complex symmetric matrices without requiring parity-time symmetry or proximity to exceptional points.

Findings

Loss-induced transmission confirmed in simulations

Reversed pump dependence demonstrated

Loss-induced narrowing of density of states observed

Abstract

Loss-induced transmission in waveguides, and reversed pump dependence in lasers, are two prominent examples of counter-intuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex symmetric matrices when a system parameter is varied, we introduce a general set of theoretical conditions for these two effects. We show that these effects arise in any irreducible system where the gain or loss is added to a subset of the elements of the system, without the need for parity-time symmetry or for the system to be near an exceptional point. These results are confirmed using full-wave numerical simulations. The conditions presented here vastly expand the design space for observing these effects. We also show that a similarly broad class of systems exhibit a loss-induced narrowing of the density of states.