Recently there has been developed a homogenization theory of photonic crystals, based on the averaging of
the Maxwell Equations within the unitary cell. 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.
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