  Topological crystalline insulators are a class of materials with a bulk
energy gap and edge or surface modes, which are protected by crystalline
symmetry, at their boundaries. They have been realized in electronic systems:
in particular, in SnTe. In this work, we propose a mechanism to realize
photonic boundary states topologically protected by crystalline symmetry. We
map this one-dimensional system to a two-dimensional lattice model with
opposite magnetic fields, as well as opposite Chern numbers in its even and odd
mirror parity subspaces, thus corresponding to a topological mirror insulator.
Furthermore, we test how sensitive and robust edge modes depend on their mirror
parity by performing time dependent evolution simulation of edge modes in a
photonic setting with realistic experimental parameters.
