Modeling the characteristics of the waves scattering by a group of scatterers

The pattern equations method is extended to solving the diffraction problem on a group of bodies. The problem is reduced to solving an algebraic system of equations with respect to the expansion coefficients of the scattering patterns by using a series expansion of the scattering patterns in angular spherical harmonics. The explicit (asymptotic) solution of the problem is obtained in a case when the scattering bodies are far enough from each other.     

Solving of problems of electromagnetic waves scattering by complex-shaped dielectric bodies via the pattern equations method

An efficient method is proposed for solving the problem of diffraction on complex-shaped dielectric bodies with the use of their replacement by a group of bodies with more simple form (fragments of complex objects). The initial problem is reduced to a system of algebraic equations by expanding the scattering patterns in vector angular spherical harmonics. It is shown that the method offers a high rate of convergence that weakly depends on the distances between the bodies. Examples of modeling the scattering characteristics of complex-shaped bodies are considered.     

The application of a modified method of discrete sources for solving the problem of wave scattering by group of bodies

A new universal and effective algorithm for solving the problems of wave diffraction on complicated structures composed of bodies of revolution is presented. The method is applied to diffraction on a group made of two impedance bodies of revolution. The method permits to get the pattern and the field with high accuracy.     

The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture

The rigorous electromagnetic theory of the diffraction of vector beams by an aperture is proposed and numerically evaluated by the diffraction of vector Gaussian beams by a circular aperture. The results are compared with those, by using the vector Rayleigh–Sommerfeld diffraction integrals and angular-spectrum expression theory, showing a good consistency. The numerical calculation shows that the result calculated by the rigorous theory is much more precise than those calculated by the integral method in diffraction near field, and a highly consistency reaches by the three methods in diffraction far field. A further extension of the theory is discussed.     

Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n_1ef, n_2ef, and n_3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n_1ef, n_2ef, and n_3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n₁, n₂ and n₃ are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n₁, n₂ and n₃ of the holographic gratings generated in the photopolymer material.     

Approximate method of solving the problem of diffraction of a plane electromagnetic wave by a thin chiral layer covering a perfectly conducting plane

One-sided approximate impedance-type boundary conditions for a thin chiral layer placed on a perfectly conducting plane are derived. With these conditions, the problem of incidence of a plane electromagnetic wave on a chiral structure is solved. Approximate formulas for the coefficients of reflection of the fundamental and depolarized components are derived for the case of the perpendicular polarization of the electromagnetic wave (the electric field strength is normal to the plane of incidence). A comparison with an exact solution to the problem of diffraction by this chiral structure is made.     

A diagnostic tool for the study of stochastic properties of density striations excited by powerful electromagnetic waves in the ionospheric plasma

Powerful electromagnetic waves illuminating the ionospheric plasma generate small-scale density irregularities elongated in the direction of the geomagnetic field. Stochastic motion of these irregularities results in fluctuations of HF radio signals backscattered by the illuminated region. Observations of the full wave form of the radio signals make it possible to reconstruct the distribution function of the irregularities over their velocities. An experiment with such a reconstruction is proposed.     

Reply to comment by E. Comay on the longitudinal magnetic field of circularly polarized electromagnetic waves

The argument presented by E. Comay in Ref. 1 is in error precisely at the point where he uses the Cartesian form of Stokes' theorem. His Comment is therefore erroneous and inconsequential.     

Three-dimensional problem of diffraction by an ideally conducting wedge with a radio-absorbing cylinder on the edge

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 9, pp. 1074–1081, September, 1988.     

用Laplace变换法求解端点系有集中质量的弹性杆的振动问题

用Laplace变换法求解了一端为齐次边界条件,另一端系有集中质量的弹性杆的纵振动问题,推广了相关文献的结果。     

Thermally induced effects on the diffraction pattern of a dye doped nematic film

We investigate the effects produced on the diffraction pattern of a dyed nematic thin film under the action of an optical field and a low frequency AC electric field. For a homeotropically aligned mixture of the nematic E7 doped with a dichroic dye, a sequence of dynamical regimes of the far field diffraction pattern is observed. For specific values of the beam's power, frequency and amplitude of the AC field, a uniform steady rotational motion (SR) of the pattern sets in with a measured angular velocity ν_exp =2.58 Hz. To account for this and other observed features of the diffraction pattern an analytical model is proposed. This allows us to describe quantitatively the reorientation of the film, to calculate some specific structural features of the diffraction pattern, as well as its angular velocity. We find that the predicted angular velocity ν_theor=5.7 Hz, is in quite good agreement with the measured value.     

基于粗测位置和方位的三视场快速星图识别方法

为了在已知粗略方位角和地理位置时实现三视场天文定位定向设备的快速测量,给出了一种三视场定位定向设备的快速局部星图识别方法。分析了三视场定位定向设备使用全天球识别数据库执行三角形识别时识别效率低的原因;指出了应先进行视场内识别,后进行视场间识别以提高效率,并给出星图识别时角距误差门限的选取范围;给出了一种基于粗略位置和方位快速生成局部识别数据库的方法,它可以减少识别信息的冗余,实现高效的星图识别。仿真实验和野外实验结果表明：使用此局部识别方法正确识别率可达99.19%,识别速度为24.3 ms,基本满足三视场天文定位定向设备快速高效测量的要求。验证了局部星图识别方法的效率,以及采用先视场内识别后进行视场间识别方式的正确性。     

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations. Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.     

Propagation of a short electromagnetic pulse in a linear medium with frequency and spatial dispersion: Direct integration of the Maxwell equations by the finite difference method

The specific features of the propagation of a short (on the order of ten oscillations) electromagnetic pulse in an isotropic linear medium with frequency and spatial dispersion, which were established via integration of a system of Maxwell equations by the finite-difference time-domain method using an auxiliary differential equation, are discussed. The variation of the direction of the electric field-strength vector oscillations that occurs in an optically active medium upon propagation of a linearly polarized ultrashort pulse incident on it is shown to be significantly different from the rotation of the polarization plane (proportional to the propagation coordinate) in the case of the incidence of a long pulse.     

再论用Laplace变换法求解端点系有集中质量的弹性杆的振动问题

将作者在《大学物理》2004年第12期上的一篇文章的解法推广到弹性杆的强迫纵振动问题,并求解了两端系有集中质量的弹性杆的自由纵振动问题．     

Numerical solution of a stationary nonisothermal two-phase filtration problem by the steadying method

The structure of solutions of a stationary nonisothermal problem of the two-phase filtration of immiscible fluids is studied numerically. The character of the convergence of nonstationary solutions to stationary ones is investigated. It is shown that at different parameter values the solution may have an interval, where s(x) ≡ 0 or s(x) ≡ 1. The temperature effect on the structure of the solutions of the equation for water saturation is investigated. The work was partially supported by the SB RAS (Integration Project No. 117).     

复杂含核粒子对贝塞尔波束散射特性的影响

基于面积分方程的矩量法及其快速算法研究了复杂含核粒子对任意入射贝塞尔波束的散射特性.将零阶贝塞尔束的矢量解和坐标系旋转理论相结合,推导出任意入射贝塞尔波束电磁场分量的数学表达式.根据等效原理,建立了求解具有任意形状和复杂内部结构含核粒子散射问题的面积分方程.对贝塞尔波束任意入射下一些复杂含核粒子的散射进行了数值模拟,结果表明:贝塞尔波束入射时的微分散射截面要小于平面波入射时的微分散射截面,且随着半锥角的减小而增大;当波束中心的位置远离粒子中心时,微分散射截面会减小;微分散射截面对波束的入射角非常敏感.这为激光对微粒的探测、诊断以及操纵技术提供有益帮助.