The charged domain wall is an ultrathin (typically nanosized) interface between two domains; it carries bound charge owing to a change of normal component of spontaneous polarization on crossing the wall. In contrast to hetero-interfaces between different materials, charged domain walls (CDWs) can be created, displaced, erased, and recreated again in the bulk of a material. Screening of the bound charge with free carriers is often necessary for stability of CDWs, which can result in giant two-dimensional conductivity along the wall. Usually in nominally insulating ferroelectrics, the concentration of free carriers at the walls can approach metallic values. Thus, CDWs can be viewed as ultrathin reconfigurable strongly conductive sheets embedded into the bulk of an insulating material. This feature is highly attractive for future nanoelectronics. The last decade was marked by a surge of research interest in CDWs. It resulted in numerous breakthroughs in controllable and reproducible fabrication of CDWs in different materials, in investigation of CDW properties and charge compensation mechanisms, in discovery of light-induced effects, and, finally, in detection of giant two-dimensional conductivity. The present review is aiming at a concise presentation of the main physical ideas behind CDWs and a brief overview of the most important theoretical and experimental findings in the field.

Whispering-gallery resonators (WGR's), based on total internal reflection, possess high quality factors in a broad spectral range. Thus, nonlinear-optical processes in such cavities are ideally suited for the generation of broadband or tunable electromagnetic radiation. Experimentally and theoretically, we investigate the tunability of optical parametric oscillation in a radially structured WGR made of lithium niobate. With a 1.04\,\,$\mu${}m pump wave, the signal and idler waves are tuned from 1.78 to 2.5\,\,$\mu${}m\char22{}including the point of degeneracy\char22{}by varying the temperature between 20 and 62\,\ifmmode^\circ\else\textdegree\fi{}C. A weak off centering of the radial domain structure extends considerably the tuning capabilities. The oscillation threshold lies in the mW-power range.

We propose a novel geometric approach to the description of the relaxation phenomena in complex condensed-matter systems. It is shown within a fairly general random site hopping model that the stretched exponential decay law, $\exp [-(t/\tau {)}^{\beta }]$, originates from the simple and general geometric features of a random distribution of transport and trapping sites in the 3D space. The value of the variable stretching index $\beta$ is determined by the localization radius of hopping electrons. The possibilities for generalization of the obtained results and interpretation of the relevant experimental data are discussed.

It is shown experimentally and theoretically that photorefractive wave coupling can be used for dramatic ($\lesssim 0.025\mathrm{c}\mathrm{m}/\mathrm{s}$) deceleration of light pulses whose width is larger than (or comparable with) the nonlinear response time. This classical nonlinear scheme exhibits similarities with the technique based on the quantum effect of electromagnetically induced transparency. The main distinctive feature of our scheme is amplification of the delayed output pulse. Advantages of the novel technique and its prospects for manipulation with light photons are discussed.