Electromagnetic waves in superlattices consisting of alternating isotropic and anisotropic layers of two materials are studied. A nematic liquid crystal (NLC) is considered as an anisotropic layer. The dispersion equation for electromagnetic waves is obtained and numerically analyzed for the case of unbounded layered medium. With special features of NLC (as compared to ordinary crystals)-strong anisotropy of the dielectric constant-taken into account, the spectrum of electromagnetic waves is shown to rearrange qualitatively as the orientation of the director (optic axis) of the NLC is changed, for instance, by an external electric field. Solutions of Maxwell's equations are obtained for a finite superlattice and their modification upon variation of the orientation of the NLC director is studied. The possibility of the efficient control of the transmission coefficient of electromagnetic waves by varying the orientation of the NLC director is shown.
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