Finite Scale Homogenization of Periodic Bianisotropic Structures
This chapter explains how a composite material with a periodic microstructure can be modeled with effective material parameters in the low-frequency limit. In particular, we treat the problem of how to compute the material parameters when the scale of the microstructure is finite compared to the applied wavelength. For lossless anisotropic media, a self-adjoint eigenvalue problem can be formulated to compute the relevant material parameters, whereas a singular value decomposition of Maxwell’s equations can be used to treat the general lossy bianisotropic case. The fundamental idea is the number of degrees of freedom: homogenization is possible precisely when the electromagnetic field can only be excited (or observed) corresponding to the degrees of freedom possible in a homogeneous material. When the scale difference is not large, this requires spatial dispersion in the homogenized model.