Topological theory of non-Hermitian photonic systems

Abstract: Recently, topological materials and topological effects have elicited a great interest in the photonics community [1]. While condensed-matter phenomena are traditionally described by Hermitian operators, the same is not true in the context of macroscopic electrodynamics where a dissipative response is the rule, not the exception. In this talk, I will discuss how to determine the topological phases of dissipative (non-Hermitian) photonic structures from first principles using a gauge-independent Green function [2, 3]. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the system Green function over a line parallel to the imaginary-frequency axis. The approach introduces in a natural way the "band-gaps" of non-Hermitian systems as the strips of the complex-frequency plane wherein the system Green function is analytical. I apply the developed theory to nonreciprocal electromagnetic continua and photonic crystals, with lossy and or gainy elements. Furthermore, I discuss the validity of the bulk-edge correspondence in the non-Hermitian case.

[1] L. Lu, J. D. Joannopoulos, M. Soljačić, "Topological photonics", Nat. Photonics, 8, 821, (2014).

[2] M. G. Silveirinha, "Topological theory of non-Hermitian photonic systems", Phys. Rev. B, 99, 125155, 2019.

[3] F. R. Prudêncio, M. G. Silveirinha, First Principles Calculation of Topological Invariants of non-Hermitian Photonic Crystals, arXiv:2003.01539

mathematical physics

Audience: researchers in the topic

( video )

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