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We studied the propagation of an electromagnetic (EM) wave in a piezoelectric superlattice. Because of the piezoelectric effect, a transverse polarization can be induced by a longitudinal wave which couples strongly to the EM wave in some particular frequency regions, resulting in the creation of a new type of polariton that does not exist in ionic crystals. The forbidden band associated with the polariton is not due to the Bragg reflection, but rather to the coupling.
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Zhu et al. (2003) studied this question.
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