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

We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit nontrivial point-gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be made of either lossy isotropic media which is reciprocal or lossy magneto-optical media which is nonreciprocal. We discuss the effects of reciprocity on the properties of the point-gap topology. We also show that such a nontrivial point-gap topology leads to the 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.