Indifferent electromagnetic modes: Bound states and topology

Abstract

At zero energy the difference in the number of spin-up and spin-down modes of the Dirac equation is determined by the topology of both space and the gauge field in which the system sits. Writing Maxwell's equations in a Dirac-like form, we identify cases where a combination of material parameters plays the role of "energy." At zero energy we thus find electromagnetic modes that are indifferent to local changes in the material parameters, with a dispersion relation depending only on the asymptotic values of the material parameters at infinity. We give several examples and show that this theory has implications for non-Hermitian media, where it can be used to construct permittivity profiles that are either reflectionless or act as coherent perfect absorbers or lasers.