Mean field theory of metallo-dielectric photonic crystals with magnetic components: the long-wavelength limit

摘要

Recently there has been developed a homogenization theory of photonic crystals, based on the averaging of the Maxwell Equations within the unitary cell [P. Halevi and F. Perez-Rodriguez, Proc. SPIE 6320, 63200T (2006)]. It leads to the bianisotropic response with the electric displacement D and the magnetic induction B vectors both depending linearly on the electric E and magnetic H fields. Despite the generality of this theory, the case of naturally magnetic ingredients has not been considered. For this reason, in this work we extend the aforementioned theory in this sense. In this way the ingredients of the unitary cell are characterized by a permeability, in addition to a generalized complex conductivity. These parameters are assumed to be given for every position in the unitary cell of the photonic crystal. We conclude that in the presence of naturally magnetic ingredients the medium response is still bianisotropic, but now the material dyadics depend on both the permeability and complex conductivity. Numerical results are given for the case of a one-dimensional photonic crystal with ferrite layers.