  Here, building on our previous work [Phys. Rev. B, 92, 125153, (2015)], it is
shown that the propagation of unidirectional gapless edge states at an
interface of two topologically distinct electromagnetic continua with a
well-behaved asymptotic electromagnetic response is rigorously predicted by the
bulk-edge correspondence principle. We work out detailed examples demonstrating
that when the spatial-cut off of the nonreciprocal part of the material
response is considered self-consistently in the solution of the relevant
electromagnetic problem, the number of unidirectional gapless edge modes is
identical to the difference of the Chern numbers of the bulk materials.
Furthermore, it is shown how the role of the spatial cut-off can be imitated in
realistic systems using a tiny air gap with a specific thickness. This theory
provides a practical roadmap for the application of topological concepts to
photonic platforms formed by nonreciprocal electromagnetic continua.
