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.
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