Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals

Abstract

We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit non-trivial point gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be either made of lossy isotropic media which is reciprocal, or lossy magneto-optical media which is non-reciprocal. We discuss the effects of reciprocity on the properties of the point gap topology. We also show that such a non-trivial point gap topology leads to non-Hermitian skin effect when the photonic crystal is truncated. In contrast to most previous studies on point gap topology which used tight-binding models, our work indicates that such non-Hermitian topology can studied in photonic crystals, which represent a more realistic system that has technological significance.

Photonic corner skin modes

“…It is observed that the bulk band clusters become tighter than that in PBC. The reason is that the nonreciprocal bulk band combined with the gain/loss makes the system support first-order NHSE, so that the bulk spectrum is sensitive to the boundary condition [68]. We also see that there are complex chiral edge states across the line band gap.…”

“…Indeed, topological defects as one way to localize light has attracted much attention for the possibility to enhance light-matter interactions [61][62][63][64]. NHSE as a new way to localize light has also been studied in photonic crystals most recently [65][66][67][68][69][70]. However the second-order version of NHSE featured in this work as photonic corner skin modes is still not investigated until now.…”