Optical properties of anisotropic periodic helical structures

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Abstract
An optical model is considered describing a wide class of optically anisotropic media such as chiral smectic liquid crystals and, in the limiting cases, cholesteric liquid crystals and anisotropic homogeneous media. It describes a structure having a periodicity along a given axis generated by a uniform rotation of the dielectric tensor. Maxwell's equations for this model, studied so far only in particular cases, are here solved for the general case where the direction of the propagating waves and the orientation of the dielectric tensor make an arbitrary angle with respect to the rotation axis. The resolving procedure involves the evaluation of the eigenmodes of the electromagnetic wave, i.e. the Bloch waves intrinsic to the specific periodic structure, which reduce to the ordinary and extraordinary waves in the limiting case of anisotropic homogeneous structures. The dispersion relation for the eigenmodes is deduced, allowing the study of the optical properties of this structure on a general basis. The Bragg reflection bands are found to be constituted alternatively by singlets and triplets. In general the even order bands are triplets whose lateral peaks correspond to the Bragg instabilities of each eigenmode, while the central peak is common to both eigenmodes and gives total reflection with a mode exchange. The odd order bands are singlets whose characteristics are very similar to the central peak of the triplets. The polarization properties of the eigenmodes are studied in the particular case of locally uniaxial media, where the Bloch waves show an abrupt polarization change for a particular value of the angle between the optical axis and the rotation axis