Magnetodielectric and Metalomagnetic 1D Photonic Crystals Homogenization:ε-μLocal Behavior

Abstract

A theory for calculating the effective optic response of photonic crystals with metallic and magnetic inclusions is reported, for the case when the wavelength of the electromagnetic fields is much larger than the lattice constant. The theory is valid for any type of Bravais lattice and arbitrary form of inclusions in the unitary cell. An equations system is obtained for macroscopic magnetic field and magnetic induction components expanding microscopic electromagnetic fields in Bloch waves. Permittivity and permeability effective tensors are obtained comparing the equations system with an anisotropic nonlocal homogenous medium. In comparison with other homogenization theories, this work uses only two tensors: nonlocal permeability and permittivity. The proposal showed here is based on the use of permeability equations, which are exact and very simple. We present the explicit form of these tensors in the case of binary 1D photonic crystals.