Permittivity and permeability for Floquet-Bloch space harmonics in infinite 1D magneto-dielectric periodic structures

Abstract

For an infinite 1D periodic structure with unit cells consisting of two planar slabs of magneto-dielectric materials, the electric field - as well as magnetic field, electric flux density, magnetic flux density, polarization, and magnetization - can be expressed as infinite series of Floquet-Bloch space harmonics. We discuss how space harmonic permittivity and permeability can be expressed in seemingly different though equivalent forms, and we investigate these parameters of the zeroeth order space harmonic for a particular 1D periodic structure that is based on a previously reported 3D periodic structure with unit cells containing a magneto-dielectric sphere.