Modal expansions in dispersive material systems with application to quantum optics and topological photonics
Mário G. Silveirinha
Abstract
The objective of this chapter is to highlight that for lossless material platforms formed by arbitrary inhomogeneous bianisotropic and possibly nonreciprocal materials, the natural modes of oscillation form, indeed, a complete set of expansion functions. Based on our recent work, it is proven that the Maxwell equations in dispersive systems can always be reduced to a generalized dynamical problem whose time evolution is described by a Hermitian operator. The effects of material dispersion are taken into account by introducing additional variables that may model the internal degrees of freedom of the material. With such a result, we construct formal expansions of the electromagnetic field in terms of the normal modes, and in particular it is highlighted that the modal expansion coefficients are not unique. The developed theory is used to obtain a modal expansion of the system Green function.