A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization

In English Using Bloch waves to represent the full solution of Maxwell’s equations in
periodic media, we study the limit where the material’s period becomes much
smaller than the wavelength. It is seen that for steady-state fields, only a
few of the Bloch waves contribute to the full solution. Effective material
parameters can be explicitly represented in terms of dyadic products of the
mean values of the non-vanishing Bloch waves, providing a new means of
homogenization. The representation is valid for an arbitrary wave vector in
the first Brillouin zone.