Light propagation along the helical axis of cholesteric liquid crystals, whose structure has been distorted by a magnetic or electric field perpendicular to the helix axis, is theoretically investigated. The solutions show several reflection bands whose centers are given by the Bragg condition m λm = 2S n (m is an integer, S is the period of the distorted structure, and n is the average refractive index of the material). The bands with m ≥ 2 consist of three subbands, each characterized by the dependence of the reflection on the polarization of the incident beam. Thus, for example, an incident beam linearly polarized in the direction of the distorting field will be reflected at only two of these subbands. Except for very strong applied fields, the band m = 1 is composed of two subbands only. Outside the reflection bands, the modes of propagation are orthogonal linear polarizations.
S. Shtrikman and M. Tur, "Optical properties of the distorted cholesteric structure," J. Opt. Soc. Am. 64, 1178-1189 (1974)