Examples of electric properties of various crystalline materials, insulators and semiconductors, liquid crystals, films, and nanostructures are presented. Among crystals, particular attention is paid to piezoelectrics, pyroelectrics, and ferroelectrics, whose dielectric properties depend strongly on the external electric field and temperature. The electro-optic properties of these materials, as well as the photovoltaic effect and photorefraction, are considered. Liquid crystals, whose optical properties depend strongly on applied electric field, are considered separately. The electric properties of materials are widely used in most diverse fields of science and technology.

Examples of manifestation of magneto-optical Faraday, Cotton–Mouton, and Kerr effects in some crystals and artificial materials are considered. Most attention is paid to the Faraday effect: optical activity manifesting itself in an external magnetic field. Cases of diamagnetic, paramagnetic, and magnetically ordered crystals are considered. The largest values of magneto-optical effects are observed in artificial structures, such as various magnetic films, magnetic photonic crystals, plasmonic crystals, and graphene.

The influence of the imperfection of optical elements of a spectrophotometric system on the polarization transmission spectra of a uniaxial optically active absorbing plate has been analyzed by the example of a La 3 Ta 0.25 Ga 5.25 Si 0.5 O 14 crystal, belonging to the langasite family. A comparison of the calculated and experimental transmission spectra for two samples with different thicknesses and optical-axis orientations shows that the optical-activity parameters of a crystal and the angle of deviation of the optical axis from the normal (when this angle is small) can be estimated.

The influence of the imperfection of a polarizer, an analyzer, and a photoelectron multiplier of a spectrophotometric complex on the intensity of light passed through a plane-parallel plate of a uniaxial transparent or absorbing crystal has been theoretically investigated. Expressions for calculating the birefringence and dichroism at different wavelengths are obtained and analyzed. It is established that the influence of the imperfection of optical elements is stronger for calculating the birefringence value, as compared with the calculation of dichroism.

The possible numbers of optical axes in absorbing triclinic crystals have been considered. Most of these crystals possess four circular optical axes; however, there may be crystals having one isotropic optical axis, two or three circular optical axes, or simultaneously one isotropic and one or two circular optical axes. It is shown that particular cases significantly differ from the general case of crystal with four circular axes. The dependence of the form of the complex permittivity tensor on the number of optical axes is presented. The ellipticities of eigenwaves and the transmitted-light ellipticity in the case of normal incidence of a wave with a right- or left-hand circular polarization are calculated for these crystals.

Рассмотрены возможные варианты количества оптических осей в поглощающих триклинных кристаллах. В большинстве таких кристаллов имеются четыре круговые оптические оси, но возможно существование кристаллов с одной изотропной оптической осью, двумя или тремя круговыми оптическими осями, или одновременно с одной изотропной и одной или двумя круговыми оптическими осями. Показано существенное отличие частных случаев от общего случая кристалла с четырьмя круговыми осями. Представлен вид комплексного тензора диэлектрической проницаемости в зависимости от числа оптических осей. Рассчитаны эллиптичности собственных волн для таких кристаллов, а также эллиптичности прошедшего света при нормальном падении на кристалл волны правой или левой круговой поляризации.

The specific features of polarization of natural waves propagating in crystals near their optical axes have been studied successively in transparent gyrotropic, absorbing, and gyrotropic absorbing crystals of classes 222, 2, 1, m, and mm2. The dependences of the ellipticities of natural waves and the azimuth of polarization of light transmitted through a crystalline plate (the case of normal incidence) on the orientation of the optical-axis plane of the plate axes with respect to the normal to surface are calculated for these crystals. These characteristics are compared for crystals of axial and planal classes with two different orientations of the optical-axis plane with respect to the symmetry elements of crystal.

Analytical expressions have been derived for the components of the complex permittivity tensor as a function of the number of optical axes existing in an absorbing monoclinic crystal. Some specific features of the orientation of these axes are considered. The ellipticities of natural waves are calculated for these crystals, as well as the ellipticities of transmitted light for right- or left- hand circularly polarized waves normally incident on a crystal. A significant difference of particular cases of absorbing monoclinic crystals from the general case of crystal with four circular axes is demonstrated.

Рассмотрены особенности проявления оптической активности и поглощения в кристаллах ромбической сингонии класса 222. Проанализировано влияние каждого из эффектов на величины эллиптичностей собственных волн. Подробно рассмотрены зависимости азимута, эллиптичности и интенсивности прошедшего света вблизи и вдали от направления оптических осей. Показано, в каких случаях можно пользоваться приближенными соотношениями, полученными без учета многократных отражений и неортогональности собственных волн в кристалле. Проанализированы отличия смоделированных коноскопических картин двуосных поглощающих оптически активных кристаллов по сравнению с картинами кристаллов, не обладающих оптической активностью или поглощением.

Peculiarities of the manifestation of optical activity and absorption in crystals of the orthorhombic system of the 222 class are considered. The influence of each effect on the ellipticities of eigenwaves is analyzed. The dependences of the azimuth, ellipticity, and intensity of transmitted light in directions slightly and significantly deviating from the optical axes are considered in detail. Cases are indicated where the approximate relations obtained disregarding multiple reflections and nonorthogonality of eigenwaves in crystal hold true. The differences of the simulated conoscopic patterns of the biaxial absorbing optically active crystals from the patterns of inactive or nonabsorbing crystals are analyzed.

The exact dispersion equations describing the resonant excitation of a polariton-plasmon at the crystal-metal interface, which were previously analytically studied within the approximate impedance approach, have been numerically analyzed. The results of an exact numerical analysis and an approximate analytical consideration almost coincide in the long-wave limit (IR region). Conversion arises simultaneously with the resonance: the incident pump wave is completely converted into a polariton of the other polarization branch, which is localized at the crystal boundary, while the amplitude of the reflected bulk wave of the same branch is zero. When passing from the IR range to the visible region, the decrease in the wavelength leads to an increasing difference in the conditions for the existence of resonance and conversion reflections and the height of the resonance peak becomes distinctly smaller than the value predicted by the approximate theory. The parameters of the resonant and conversion reflections have been calculated for optically uniaxial saltpe- ter and calomel crystals with an aluminum coating for the wavelength range of 0.4–5.0 μm.

Examples of total internal reflection manifestation have been considered on the basis of a solution to boundary problems of crystal optics using the Berreman matrix method and applying the Mathematica-5 system. It is shown how optical activity manifests itself in the total internal reflection and how this effect can be used to monitor the quality and homogeneity of film coatings.

The optical properties of a biaxial absorbing KGd(WO 4 ) 2 :Nd 3+ crystal have been investigated. The main refractive indices were measured in the visible spectral range and the absorption and transmission spectra of samples of these crystals were studied. The changes in the refractive indices were in the region of the absorption bands with the use of the Kramers-Kronig relation. Conoscopic pictures of this crystal in the regions of transparency and absorption bands were calculated and are presented.

Investigation of the optical properties of natural violet diamonds from the Yakutian kimberlites is performed. A red shift of the absorption edge is revealed in the absorption spectra of these crystals. This shift is indicative of the presence of a high concentration of nitrogen in the diamonds studied. Along with the strong band at 0.550 μm, weaker bands at 0.390, 0.456 and 0.496 μm are revealed. It is shown that violet diamond crystals have birefringence and dichroism of about 10 −5 and 10 −6 , respectively. When a light beam propagates perpendicularly to colored lamellas, the dichroism is much larger and the birefringence is smaller than in the case where the beam direction is parallel to lamellas.

Specific features of manifestation of optical activity in cubic, uniaxial, and biaxial crystals are described. The effect of optical activity on characteristics of transmitted light is considered as a function of the wavelength of incident light, temperature, and the orientation the optical axis. The results of the investigation of crystals of different symmetry classes are reported.

The intensity of light transmitted through a system consisting of a polarizer, a sample, and an anlyzer is calculated with due regard for multiple reflections at the sample boundaries. The intensities of the transmitted light calculated with and without allowance for multiple reflections are compared in the presence and the absence of absorption. It is shown that multiple reflections considerably change the transmitted-light characteristics. The computational errors are evaluated for sample birefringence and dichroism with due regard for multiple reflection.