Spatially Dispersive Inhomogeneous Electromagnetic Media with Periodic Structure

Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the Floquet modes. A complete set of approximate solutions is calculated which are valid when the inhomogeneity is small. This is applied to inhomogeneous wire media. A new feature arises when considering spatially dispersive media, that is the existence of coupled modes.