Optical edge modes in photonic liquid crystals

An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the n's mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material. Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical values of the relevant parameters.