Localized optical modes and low threshold lasing in photonic spiral media

The recent original theoretical investigations on the localized opical modes and low threshold lasing in spiral photonic media are presented. Main attention is paid to the analytical approach to the problem. One of the most studied media of this kind are the cholesteric liquid crystals. It is why the localized opical modes and lasing in photonic spiral media are studied for the certainty at the example of chiral liquid crystals (CLCs). The chosen here model (absence of dielectric interfaces in the studied structures) allows one to get rid off the polarization mixing at the surfaces of the CLC layer and the defect structure (DMS) and to reduce the corresponding equations to the equations for the light of diffracting in the CLC polarization only. The dispersion equations determining connection of the EM and DM frequencies with the CLC layer parameters and other parameters of the DMS are obtained. Analytic expressions for the transmission and reflection coefficients of the DMS are presented and analyzed. As specific cases are considered DMS with an active (i.e. transforming the light intensity or polarization) defect layer and CLC layers with locally anisotropic absorption. It is shown that the active layer (excluding an amplifying one) reduces the DM lifetime (and increase the lasing threshold) in comparison with the case of DM at an isotropic defect layer. The case of CLC layers with an anisotropic local absorption is, in particular, analyzed and it is shown that due to the Borrmann effect the EM life-times for the EM frequncies at the opposite stop-bans edges may be signifinately different and concequently the lasing threshold for the EM frequencies at the both stop-band edges are different. The options of experimental observations of the theoretically revealed phenomena in spiral photonic media are briefly discussed.