Abstract. The tensor solution for the electromagnetic wave being in quadrature with the surface of the cholesteric liquid crystal under the influence of the external electric field along axis of swing of crystal, has been found. Description of the reflection, transmission of the electromagnetic wave in multilayer structures composed from cholesteric liquid crystals have been shown. Futher the dependence of the reflection spectrum on the polarization of the incident beam and magnitude of the external electric field are determined.
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