The Electromagnetic Green's Function for Layered Topological Insulators

The dyadic Green's function of the inhomogeneous vector Helmholtz equation describes the field pattern of a single frequency point source. It appears in the mathematical description of many areas of electromagnetism and optics including both classical and quantum, linear and nonlinear optics, dispersion forces (such as the Casimir and Casimir-Polder forces) and in the dynamics of trapped atoms and molecules. Here, we compute the Green's function for a layered topological insulator. Via the magnetoelectric effect, topological insulators are able to mix the electric, E, and magnetic induction, B, fields and, hence, one finds that the TE and TM polarizations mix on reflection from/transmission through an interface. This leads to novel field patterns close to the surface of a topological insulator.