  Haldane predicted an analog of the Integer Quantum Hall Effect in gyrotropic
photonic crystals, where the net number of electromagnetic edge modes moving
left-to-right is given by a bulk Chern number. His prediction --- topological
effects are bona fide wave and not quantum phenomena --- has been confirmed in
a number of experiments. However, theoretical physicists have tacitly used
three different definitions for the bulk Chern numbers that enter the bulk-edge
correspondence --- on the basis of electromagnetic Bloch functions, electric
Bloch functions and magnetic Bloch functions. We use vector bundle theoretic
arguments to prove that in media such as those considered by Haldane these
three potentially different Chern numbers necessarily agree with one another,
and consequently, any one of them can be used in Haldane's photonic bulk-edge
correspondence.
