How Laser Physics Brought Optics to the World of Photonic Crystals

A brief review of authors’ research is presented. An emphasis is made on the photon localization in the helical structure of a chiral liquid crystal (CLC), which was first experimentally registered by the authors. An analysis of the spectral and lasing characteristics of distributed feedback (DF) lasers based on natural CLCs (type 1) and on chiral nematics (type 2) led to a conclusion that the model of photonic crystal is suitable to describe the lasing mechanism in type-2 CLC lasers, but not in type-1 ones. This conclusion is evidenced by the absence of lasing bands at the opposite edges of the selective reflection (SR) band; at the same time, the lasing line is located at its center. It is shown that if the SR band of the CLC overlaps the maximum of the laser dye fluorescence band, the lasing line coincides with the SR band center to an error of ±1 nm. If the layer thickness in the CLC lasers of both types does not exceed 50 мm, when a high-quality planar texture is retained and a low generation threshold is achieved, a significant difference between their optical characteristics takes place. Namely, the SR spectrum for a type-1 CLC laser is approximately described by a Lorentzian profile, whereas the contour of the SR spectrum for a type-2 CLC laser has a profile characteristic of the transmittance through multilayer dielectric mirrors. The origins of the differences between the optical and laser characteristics of the CLC lasers of both types have been analyzed from the viewpoint of two lasing models: DF and photonic-crystal ones.

Renormalization to localization without a small parameter

We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to generality of this model usually called Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.