Group Representation of Relativistic Quantum Crystal Optics

A group representation of radiation propagation in an anisotropic medium is developed. The system of wave equations for electromagnetic potentials, obtained from the Maxwell equations with account for the constitutive equations, has been factorized. It is shown that the linear differential operator of the factorized system is orthogonal in transparent crystals and unitary in gyrotropic ones and is represented through the momentum operator. On the basis of the commutation relations for the components of this operator, the eigenvalue problem has been solved and the expression for the change in the radiant energy in the crystal in the form of spherical waves has been obtained. The dependences of the ray and phase velocities and the polarization vectors of waves on the birefringence anisotropy and gyrotropy as well as on the angular momentum, displacement current, and bound charge determining them have been analyzed. It has been established that in the general case of gyrotropic crystals where the nonreciprocity phenomenon takes place and in magnetoelectrics Maxwell equations are represented in a form similar to the Dirac equations and the electromagnetic radiation is correctly described by means of bispinors and is quantized as fermions.     

Optical Anisotropy of Biaxial Magnetic Crystals

The two–dimensional orthogonal representation of electromagnetic waves in crystals is developed. Simple expressions determining the directions of optical axes and dependence of group and phase velocities and polarization vectors on the direction, in the general case, of triclinic crystals of magnetic dielectrics are obtained. A solution of the Maxwell equations in the form of two isonormal harmonic waves is found to be directly related to the exponential, two–dimensional spinor, and three–dimensional tensor representations.     

Amplitude-Phase Effects in Acousto-Optical Interaction in Gyrotropic Cubic Crystals

The amplitude-phase features of an intermediate regime of light diffraction on ultrasound in gyrotropic cubic crystals have been investigated. It is established that in the gyrotropic medium excited by ultrasound two coupled phase lattices of photoelasticity appear as a result of the rotation of the polarization planes of interacting waves. These lattices determine the polarization and energy characteristics of a diffracted light. For a gyrotropic cubic crystal of bismuth germanate, good agreement between the theoretical and experimental dependences of the efficiency of diffraction on the ultrasonic intensity in the intermediate regime close to the Bragg regime of diffraction is obtained.     

Coherence of a Chain of Chaotic Oscillators in a Nonlinear Gyrotropic Medium

We investigate the generalized Kuhn＇s model, namely, a chain of nonlinear chaotic oscillators describing a nonlinear gyrotropic medium. It is shown that despite the chaotic behavior of separate oscillators the chain preserves some coherency as a whole. The relation between the chain synchronization and the physical properties of a random mean field is established.     

Coherence of a Chain of Chaotic Oscillators in a Nonlinear Gyrotropic Medium

We investigate the generalized Kuhn's model, namely, a chain of nonlinear chaotic oscillators describing a nonlinear gyrotropic medium. It is shown that despite the chaotic behavior of separate oscillators the chain preserves some coherency as a whole. The relation between the chain synchronization and the physical properties of a random mean field is established.     

Polarization-Independent Ultrasonic Modulation of Light in Gyrotropic Cubic Bismuth Germanate Crystals

An intermediate regime of light diffraction by ultrasound propagating along the [001] and [110] axes of a gyrotropic cubic bismuth germanate crystal is investigated. The possibility of polarization-independent light modulation in the intermediate regime of diffraction close to the Bragg regime is shown. The dependences of the diffraction efficiency on the incident light polarization azimuth at different ultrasonic wave intensities are given.     

The Bragg Diffraction of Light at Acoustophotorefractive Holographic Gratings in Gyrotropic Cubic Crystals

We investigate diffraction of light at phase holographic-type gratings recorded by a piezoactive ultrasonic wave in gyrotropic cubic photorefractive crystals. We show that the efficiency of diffraction at a holographic grating can be increased substantially by applying a d.c. field to a crystal under the conditions of a longitudinal electrooptical effect; elliptical polarization of diffracted light is determined by electrically induced anisotropy of a crystal in the piezofield of a photorefractive grating, by the external electric field, detuning of phase synchronism, gyrotropy of the crystal, ultrasound frequency, and the time of recombination of charge carriers.     

Gyrotropic and piezoelectric coefficients and attenuation of elastic waves in BaTiO3

Using Landau theory of phase transition, expressions for gyrotropic coefficients and piezoelectric coefficients are obtained for barium titanate in the tetragonal phase. Both coefficients vanish at the ferroelectric phase transition temperature. The piezoelectric coefficients tallied with the literature values. The attenuation coefficients for elastic waves propagating along the principal directions in tetragonal, orthorhombic and rhombohedral phases are derived based on Landau theory. It is predicted that there will be slight amplification for both longitudinal and transverse modes in the rhombohedral phase at a temperature close to the rhombohedral phase transition temperature.     

Bragg Scattering of Surface Waves by a Photo-Induced Array

A pattern of spots of light projected on to a semiconductor wafer creates an array of scatterers that can diffract millimeter-wavelength surface waves through 90° in agreement with the expression for Bragg reflection.     

Features of acousto-optic interaction in uniaxial gyrotropic crystals

The features of noncollinear acousto-optic interaction in gyrotropic crystals in the intermediate diffraction regime and the regime of Bragg diffraction were investigated. The dependence of the efficiency of diffraction in gyrotropic paratellurite, tellurium, and quartz crystals on the intensity of the ultrasonic wave, acousto-optic interaction length, and incident-light polarization was investigated. It is shown that the gyrotropy of the crystal is responsible for the appearance of a multiple-peak structure of the Bragg maximum. It has been established that in the case of propagation of incident and diffracted waves in the vicinity of the optical axis of the crystal, the diffraction efficiency is independent of the polarization state of the incident light. The results of theoretical calculations are in agreement with the experimental results obtained for uniaxial crystals. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 105–110, January–February, 2000.     

Waves in front of the Venetian littoral

Summary The second-generation HISWA model, specifically developed for shallow water areas, was used to estimate the wave conditions in front of the Venetian littoral. The model is based on the wave action equation, and it includes conservative interactions with bottom and currents, generation by wind and dissipation by bottom friction and breaking. A detailed sensitivity analysis has been carried out on the main processes that affect the output of the model. The performance of the model has then been checked by comparison with laboratory and field data. Finally, the HISWA model has been applied to several severe storms which have occurred in the Northern Adriatic and also to extreme wave conditions in the same area, thus allowing the corresponding wave conditions at the coast to be estimated. The results suggest that wave evolution towards the coast is greatly influenced by bottom friction in intermediate water depth and by breaking in shallow water. These processes could lead to saturation conditions during extreme wave events.     

Bäcklund Transformations,Solitary Waves,Conoid Waves and Bessel Waves of the (2+1)-Dimensional Euler equation

Some simple special Bäcklund transformation theorems are proposed and utilized to obtain exact solutions for the (2+1)-dimensional Euler equation. It is found that the (2+1)-dimensional Euler equation possesses abundant soliton or solitary wave structures, conoid periodic wave structures and the quasi-periodic Bessel wave structures on account of the arbitrary functions in its solutions. Moreover, all solutions of the arbitrary two dimensional nonlinear Poisson equation can be used to construct exact solutions of the (2+1)-dimensional Euler equation.     

Specific features of waves in magnetic crystals

On the basis of the asymmetric velocity tensor introduced we develop an orthogonal representation of wave propagation in anisotropic magnetic dielectrics. Simple expressions are obtained for the direct dependence of polarization vectors, refractive indices, and phase and group velocities of isonormal waves in a magnetic dielectric on the vectors of principal velocities. We show that the presence of magnetic properties is manifested in the optical range in the fact that the velocities of wave propagation in uniaxial crystals are determined by three main refractive indices, and therefore, both waves except for specific directions become extraordinary, whereas in biaxial crystals (also because of a large number of parameters) the cones of internal and external refraction become elliptic. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 5, pp. 597–600, September–October, 1999     

Subgroups of Hypercubic Group and Many Electron States in Crystals

The point subgroups of index 2 of hypercubic group and their irreducible representations are obtained. The elements of the hypercubic group are represented as rotation about two axis. Possible physical meaning of hypercubic group for electron states is investigated. The reduction relations for the representations of orthogonal group O ₄ on hypercubic group are obtained. These relations are used for additional classification of electron states in crystals.     

粘性物质中正激波稳定性分析

用线性稳定性理论,分析粘性物质中的正激波稳定性问题.粘性物质中任意强度的一维激波,其稳定性问题可归结为处理复数范围内的特征值问题,该特征值问题由两个一阶常微分方程及一个二阶常微分方程构成.这些常微分方程的系数依赖于流动的基本流场的物理量及其梯度.所获得的特征值问题由一个四阶精度的有限差分离散求解.分析考虑物质粘性的金属铝中的正激波稳定性,可以看出,正激波运动是稳定的,并且激波速度对波前和波后的小扰动量的衰减有相反的作用,而物质粘性有致稳的作用.     

Parametric Instabilities of Two Kind of Millimeter Waves and Multiplication of Frequency in GaAs Semiconductors

This paper deals, at first, with the non-linear parametric effects on both space charge and electromagnetic waves in GaAs semiconductors. If an external electric field is applied, at the critical field value, the mobility changes its sign and becomes negative, as a result, non-linear instabilities of the interactions are obtained. At the optimal value of electric field, E _opt, all non-linear processes are very effectives. The second point is the multiplication of the wave frequency, which is also effective thanks to the non-linearity. This process is used for carring waves into millimeter range instead of generation process, which in this range is non-effective. The Multiplication effect is based on the using space charge waves.     

铁-铍介质界面上激波折射现象的数值研究

用数值方法研究铁-铍介质界面上的激波折射现象.运用激波极曲线理论分析不同强度的激波从正规折射过渡到非正规折射的临界角变化.运用一个具有二阶精度和波传播性质的激波捕捉法,数值求解激波折射运动的流体力学方程组.对正规折射,数值结果与激波极曲线理论一致;对非正规折射,不同强度的激波大都存在前驱的折射激波,并且入射激波的强度不同、入射角度不同,激波折射的图像也不同.     

The Group Property of Darboux Transformations from R2 to U(N)

It is proved that the basic Darboux transformations of harmonic maps from R² to U(N) generate an Abelian transformation group on the moduli space of harmonic maps.     

Increase of the Number of Detectable Gravitational Waves Signals Due to Gravitational Lensing

This article deals with the gravitational lensing (GL) of gravitational waves (GW). We compute the increase in the number of detected GW events due to GL. First, we check that geometrical optics is valid for the GW frequency range on which Earth-based detectors are sensitive, and that this is also partially true for what concerns the future space-based interferometer LISA. To infer this result, both the diffraction parameter and a cut-off frequency are computed. Then, the variation in the number of GW signals is estimated in the general case, and applied to some lens models: point mass lens and singular isothermal sphere (SIS profile). An estimation of the magnification factor has also been done for the softened isothermal sphere and for the King profile. The results appear to be strongly model-dependent, but in all cases the increase in the number of detected GW signals is negligible. The use of time delays among images is also investigated.