Diffraction Optics of Complex-Structured Periodic Media

§This book presents recent theoretical and experimental results on localized optical modes and low-threshold lasing in spiral photonic media. Efficient applications of these modes for low-threshold lasing at the frequencies of localized modes are a central topic of the book, which emphasizes the analytical approach to the problem. The book focuses on one of the most extensively studied media in this field, cholesteric liquid crystals. The chosen model, in the absence of dielectric interfaces, overcomes the problem of polarization mixing at surfaces, layers and defect structures. It allows one to reduce the corresponding equations to the equations for light of diffracting polarization only. The problem concentrates on the edge and defect optical modes. The possibility to reduce the lasing threshold due to an anomalously strong absorption effect is theoretically investigated for distributed feedback lasing. It is shown that a minimum of the threshold-pumping wave intensity can be reached for the pumping wave propagating at a certain angle to the helical axes. Analytic expressions for transmission and reflection coefficients are presented. Additionally, experimental observations of theoretically revealed phenomena in spiral photonic media are discussed. The main results obtained for spiral media are qualitatively valid for photonic crystals of any nature and therefore may be applied as a guide when investigating other photonic crystals where the corresponding theory is more complicated and demands a numerical approach. For the convenience of the reader, an introduction is given to conventional linear and nonlinear optics of structured periodic media. This book will be valuable to researchers, postgraduate, and graduate students active in theoretical and experimental physics in the field of interaction of radiation with condensed matter.§