  We propose a method of measuring topological invariants of a photonic crystal
through phase spectroscopy. We show how the Chern numbers can be deduced from
the winding numbers of the reflection coefficient phase. An explicit proof of
existence of edge states in system with nonzero reflection phase winding number
is given. The method is illustrated for one- and two-dimensional photonic
crystals of nontrivial topology.

Mesoscale and Nanoscale Physics;Optics;Quantum Physics