In cholesteric liquid crystals (CLC) problems related to the localized optical modes for a non-collinear geometry are studied here in the two wave dynamic diffraction theory approximation. This approximation, which insures the results accuracy order of δ (where δ is the CLC dielectric anisotropy), is applied because for a non-collinear geometry there is no exact analytic solution of the Maxwell equations and a theoretical description of the experimental data becomes more complicated. The dispersion equation for non-collinear localized edge modes (called conical modes (CEM)) is found and analytically solved for the case of thick layers and for this case the lasing threshold and the conditions of the anomalously strong absorption effect are found. It is shown that qualitatively CEMs are very similar to the localized edge modes (EM) in CLCs related to a collinear geometry, i.e., for the case of light propagation along the spiral axis however the CEMs differ by their polarization properties (the CEM eigen polarizations are elliptical ones depending on the degree of CEM deviation from the collinear geometry in contrast to the circular eigen polarizations in the EM case). What is concerned of the CEM quantitative values of the parameters they are “worth” (the photonic effects are not so pronounced) than for the corresponding ones for EM. The CEM lasing threshold is higher than the one for EM, etc. Performed theoretical studies of possible conversion of EMs into CEMs showed that it can be due to the EM reflection at dielectric boundaries at the conditions of a high pumping wave focusing. Known experimental results on the CEM are discussed and optimal conditions for CEM observations are formulated.
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