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

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.

arXiv comment5 pages, 3 figures

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Cited by in corpus (8)

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• Finite-size effects in non-Hermitian topological systems
• Limits to the Optical Response of Graphene and 2D Materials
• Statistical PT-symmetric lasing in an optical fiber network
• Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer
• Effects of non-uniform distributions of gain and loss in photonic crystals
• Loss revives bistable state near the exceptional point in a non-Hermitian microwave photonic meta-molecule
• Emergence of exceptional points and their spectroscopic signature in Dirac semimetal-dirty Superconductor heterojunction