  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.
