  The existence of surface electromagnetic waves in the dielectric-metal
interface is due to the sign change of real parts of permittivity across the
interface. In this work, we demonstrate that the interface constructed by two
semi-infinite photonic crystals with different signs of the imaginary parts of
permittivity also supports surface electromagnetic eigenmodes with real
eigenfrequencies, protected by $ PT $ symmetry of such loss-gain interface.
Using a multiple scattering method and full wave numerical methods, we show
that the dispersion of such interface states exhibit unusual features such as
zig-zag trajectories or closed-loops. To quantify the dispersion, we establish
a non-Hermitian Hamiltonian model that can account for the zig-zag and
closed-loop behaviour for arbitrary Bloch momentums. The properties of the
interface states near the Brillouin zone center can also be explained within
the framework of effective medium theory. It is shown that turning points of
the dispersion are exceptional points (EPs), which are characteristic features
of non-Hermitian systems. When the permittivity of photonic crystal changes,
these EPs can coalesce into higher order EPs or anisotropic EPs. These
interface modes hence exhibit and exemplify many complex phenomena related to
exceptional point physics.
