  We study wave propagation and diffraction in a bidimensional photonic crystal
with finite height, in case where the wavelength is large with respect to the
period of the structure. The device is made of materials with anisotropic
permittivity and permeability tensors. We derive rigorously the homogenized
system, using the concept of two-scale convergence. The effective permittivity
and permeability tensors turn out to be that of a two-dimensional photonic
crystal with infinite height.
