Abstract

Electromagnetic wave propagation in a periodically bent nematic liquid crystal (PBNLC) is studied. For an incident wave polarized perpendicularly to the plane of incidence, which is parallel to the plane containing the optical axis of the PBNLC, only the ordinary wave will be excited, whereas, for an incident wave polarized in the plane of incidence, an extraordinary wave will be excited. By expressing the electromagnetic fields in terms of antipotentials, the extraordinary wave equation is shown to have the form of Ince’s equation [ W. Magus and S. Winkler, Hill’s Equation, Interscience, New York, 1966; Hill’s EquationDover, New York, 1979], for which we present the first reported general solution. The normalized solution and characteristic equation of Ince’s equation are also discussed. The extraordinary wave is shown to have the form of a Bloch wave. The equivalence of the field and antipotential descriptions is shown for the case of normal incidence. The cases of propagating and totally reflected waves are discussed. The Poynting vector depends not only on the angle of incidence but also on the azimuthal angle of the incident wave (π/2 or 3π/2). This dependence in a PBNLC is different from that in a layered inhomogeneous isotopic medium, for, in the latter, a ray propagating obliquely is the mirror image of another ray incident at the same angle but on the other side of the normal, whereas in a PBNLC these rays would not have this special symmetry. However, the critical angle for total reflection to occur depends only on the angle of incidence and is independent of the azimuthal angle of the incident wave.

© 1983 Optical Society of America

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