LAUSR

Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re-examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where electromagnetic material parameters play the roles of `mass' and `energy' in an equivalent Dirac equation. The modes trapped between a gyrotropic medium and a mirror are then the counterpart of those at a `domain wall', where the mass of the Dirac particle changes sign. Extending this analogy, we relate the integral of the Berry curvature (the Chern number) to the number of interface states. In contrast to the common approach we show that the Chern number can be computed without knowledge of how the material parameters depend on frequency.