  Doped semiconductors are intrinsically homogeneous media. However, by
applying an external magnetic field that has a spatially periodic variation,
doped semiconductors can behave extrinsically like conventional photonic
crystals. We show this possibility theoretically by calculating the photonic
band structures of a doped semiconductor under an external, spatially periodic
magnetic field. Homogeneous media, behaving like conventional photonic crystals
under some external, spatially periodic fields, define a new kind of photonic
crystals: extrinsic photonic crystals. The proposed extrinsic photonic crystals
could not only extend the concept of photonic crystals but also lead to the
control of the dispersion and propagation of electromagnetic waves in a unique
way: simply manipulating the externally applied fields.
