Far-field approximation in electromagnetic scattering

The volume integral equation formalism is used to derive and analyze specific criteria of applicability of the far-field approximation in electromagnetic scattering by a finite three-dimensional object. In the case of wavelength-sized and larger objects, this analysis leads to a natural subdivision of the entire external space into a near-field zone, a transition zone, and a far-field zone. It is demonstrated that the general criteria of far-field scattering are consistent with the theory and practice of T-matrix computations.     

Sound radiation from point-excited structures: Comparison of plate and sphere

Acoustic radiation from a structure can be expressed in terms of “modal radiation” and “modal coefficients”. This paper investigates the contributions of these two modal properties to radiation excited by a point force. Sound radiation from two basic structures is considered: a baffled rectangular plate and a closed spherical shell. The plate behaviour is familiar, and governed by the relation between the natural frequency of a mode and its coincidence frequency. For a closed spherical shell, there are either zero or two “critical frequencies”, depending on the radius and thickness. When there are two the shell radiates well both above and below the two frequencies, and poorly in the frequency range between them.     

Dynamic equations for a fully anisotropic elastic plate

A hierarchy of dynamic plate equations is derived for a fully anisotropic elastic plate. Using power series expansions in the thickness coordinate for the displacement components, recursion relations are obtained among the expansion functions. Adopting these in the boundary conditions on the plate surfaces and along the edges, a set of dynamic equations with pertinent edge boundary conditions are derived on implicit form. These can be truncated to any order and are believed to be asymptotically correct. For the special case of an orthotropic plate, explicit plate equations are presented and compared analytically and numerically to other approximate theories given in the literature. These results show that the present theory capture the plate behavior accurately concerning dispersion curves, eigenfrequencies as well as stress and displacement distributions.     

A variable closure differential approximation for anisotropic radiation

Spatially varying closure based on ellipsoidal intensity modeling is used to describe the anisotropic radiation field by means of a modified differential approximation. Singular behavior in region corners is identified and accounted for, and a self-consistent boundary condition suggested for the ratio of lowest order moments of intensity. Completed examples indicate removal of virtually the entire differences between Milne-Eddington and exact results.     

各向异性有耗介质板介电系数和电导率的反演

简述了各向异性介质FDTD方法，并用FDTD方法分析了三维各向异性有耗介质板的瞬态后向散射.根据各向异性介质板后向散射与入射电磁波极化方向有关的特点，利用其后向RCS的谐振特性和后向散射场的时域波形特点反演有耗介质板的横向介电系数和电导率.数值模拟结果表明本反演方法可行，且方便、快捷. 关键词： 各向异性板 FDTD方法 有耗介质 谐振 反演     

One-dimensional anisotropic magnet in the long-wavelength approximation

The nonlinear equation for the wavefunction of spin excitations in the long-wavelength approximation possessing a soliton-like solution is obtained by means of an exact transition from Pauli operators to Fermi operators.     

Far-field properties of a cylindrically polarized vector beam and its beam quality beyond the paraxial approximation

<正>The far-field analytical expressions for the electromagnetic fields of a cylindrically polarized vector beam propagating in free space are obtained based on the vector angular spectrum and the method of stationary phase.The far-field energy flux distributions and the beam quality by the power in the bucket(PIB) in the nonparaxial regime have been investigated.The PIB of the cylindrically polarized beam depends on the ratio of the waist width to wavelength,the order of the Laguerre polynomial,and the angle between the electrical vector and the radial direction.The analyses show that azimuthal polarization compared with radial polarization has better energy focusability in the far field.     

Transient radiation in an anisotropic magnetodielectric plate in a waveguide

We have considered transient radiation of a charged particle in an anisotropic magnetodielectric plate placed into a regular waveguide. It is assumed that the charged particle passes through the plate moving at a constant velocity perpendicularly to the waveguide axis. Wave equations and analytical expressions for transverse electric (TE) and transverse magnetic (TM) fields in different regions of the waveguide have been obtained. Energies of transient radiation of the moving particle have been calculated. The properties of transient radiation and Vavilov–Cherenkov radiation have been analyzed for the case of a rectangular waveguide. Energies of transient radiation have been calculated for the case of a “thin” plate in the waveguide, when the wavelength in the plate is much greater than the length of the plate.     

Two alternative methods for solving ion transport equation with anisotropic approximation

By means of two alternative methods namely, the maximum entropy and Chapman-Enskog, flux limited approach the ion transport equation for slowing-down problem of low-energy light ions in solid has been solved explicitly. Maximum entropy technique yields approximate solutions in the form of locally Maxwellian distribution function, based on moments expansion truncated upon entropy maximization.The behavior of the approximate maximum entropy and the flux limited solutions have the same tendency. Knowing the distribution function obtained by flux limited approach, allows us to calculate directly the path length distributions of backscattered ions, and compared with that found by other theories such as Laplace-transform and double Legendre polynomial approximation. One can see that the flux limited approach is better than the previous method namely, (DPN) Laplace-transform.The results reported in this article provide further evidence of the usefulness of both maximum entropy and flux limited for obtaining the solution of ion transport equation in compact form.     

Far-field superlens for nanolithography

A far-field optical lithography is developed in this paper. By designing the structure of a far-field optical superlens, lithographical resolution can be improved by using a conventional UV light source. The finite different time domain numerical studies indicate that the lithographic resolution at 50~nm line width is achievable with the structure shown in this paper by using 365~nm wavelength light, and the light can be transferred to a far distance in the photoresist.     

Propagation of a twisted anisotropic Gaussian Schell-model beam beyond the paraxial approximation

With the help of a tensor method, an analytical nonparaxial propagation formula for a twisted anisotropic Gaussian Schell-model (GSM) beam in free space is derived based on the generalized Raleigh-Sommerfeld diffraction integral. The far-field nonparaxial propagation expression for a twisted anisotropic GSM beam is also derived. The paraxial approximation is dealt with as a special case of our general result. Our numerical results show that the nonparaxial propagation properties of a twisted anisotropic GSM beam are closely related to the initial beam parameters (i.e., twist factor, transverse spot width matrix, coherence width matrix and wavelength) and the propagation distance. Our formulae provide a convenient and powerful way for studying the paraxial and nonparaxial propagation of an isotropic or anisotropic GSM beam with or without twist phase in free space.     

各向异性介质的平行平板干涉

提出了各向异性介质平行平板干涉中的相位差计算方法.证明了e光干涉产生的条纹为严格的椭圆曲线,椭圆长短轴的比值等于o光主折射率与e光主折射率之比,而与晶体厚度、干涉级等参数无关.拍摄了实验干涉图,并用最小二乘法对干涉条纹进行椭圆曲线拟合,结果与理论完全一致.本文提出的方法可用于晶体主折射率比值的精确简便测量.     

Fast and accurate radiance calculations using truncation approximation for anisotropic scattering phase functions

The phase function for solar light scattering by large particles such as cloud droplets is strongly anisotropic due to very strong peaking in the forward direction. This creates numerical difficulties when attempting to calculate accurate reflected and transmitted radiances, which are important for remote sensing of atmospheric and surface properties. A popular approach uses the delta function to approximate the forward-scattering peak in a fraction of energy and a limited number of polynomial terms or a geometrically truncated function for the remaining fraction (so-called truncation approximations). This article compares and discusses several methods for fast and accurate calculations using truncation approximations. When using a single truncation approximation for all scattering orders, large biases appear in directions near the solar and anti-solar points. As shown here, high accuracy can be obtained using different truncation approximations depending on the order of scattering. Of particular importance is the use of phase functions close to the exact phase functions for the first few orders of scattering. Applying the method in combination with the Monte Carlo (MC) method, in which the truncation fraction for a scattering order depends on the scattering angle at the previous scattering event, obtains accurate radiance calculations under almost all geometrical and optical conditions, including in directions near the solar point. Because the method also reduces computational noise due to the MC sampling of radiance, it is useful for fast and accurate radiance calculations for cloudy atmospheres.     

Theory of the photon-drag effect inp-type germanium with a parabolic and anisotropic band-structure approximation

This paper shows that many features of the photon-drag voltage generated by illumination ofp-germanium with 10.6 μm radiation can be understood on the basis of a parabolic but anisotropic band-structure model. The group velocities of the heavy and light holes participating in the optical transitions are obtained by an analysis of the conservation laws. Since the nonequilibrium hole densities in both bands depend directly on the momentum relaxation times in the determinant equations of continuity, these times are the parameters with the strongest influence on the numerical results. The photon-drag voltage consists of components longitudinal and transverse with respect to the axis of illumination. For the longitudinal components, good agreement between our theoretical results and experimental data from the literature is achieved if the crystal is illuminated along a [100] or [111] direction. Though a transition probability independent of light polarisation has been assumed, the transverse effect (illumination along [111]) can be computed for special measuring conditions. The calculated effects of anisotropy are higher than known from experiments possibly due to the approximations used for the valence bands and the transition probability. An erratum to this article is available at .     

各向异性固体板中的非线性超声导波

将超声导波的非线性视为线性波动响应的一个二阶微扰,采用二阶微扰近似和导波的模式展开分析方法,从理论上研究了各向异性固体板中超声导波的二次谐波发生效应,给出了超声导波二次谐波声场的一般形式解。板材的各向异性可从多个方面对二次谐波发生效应产生影响,尤其是板材各向异性引起的导波模式相速度的改变,可显著地影响到构成导波二次谐波声场的二倍频导波模式随传播距离的积累增长程度。根据理论分析和数值计算结果可知,在不同传播方向上超声导波的非线性效应存在较显著的差异,伴随基频导波模式的传播所发生的二次谐波对固体板材的各向异性表现出更为敏感的性质,这一结果可为准确定征板材的弹性各向异性提供一种理论依据。     

Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material

The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean-squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance function, or equivalently, projecting the tensor of elastic stiffness onto the appropriate symmetry. This has implications for how to best select anisotropic constants to acoustically model complex materials.     

Approximate study of the free vibrations of a cantilever anisotropic plate carrying a concentrated mass

This study is concerned with the vibration analysis of a cantilevered rectangular anisotropic plate when a concentrated mass is rigidly attached to its center point. Based on the classical theory of anisotropic plates, the Ritz method is employed to perform the analysis. The deflection of the plate is approximated by a set of beam functions in each principal coordinate direction. The influence of the mass magnitude on the natural frequencies and modal shapes of vibration is studied for a boron-epoxy plate and also in the case of a generic anisotropic material. The classical Ritz method with beam functions as the spatial approximation proved to be a suitable procedure to solve a problem of this analytical complexity.     

Far-field emission of a semiconductor nanowire laser

The polarization properties and angular distribution of intensity of the far fields from a nanowire laser are investigated. The far-field emission depends strongly on the mode type (HE11, TE01, TM01) and the radius of the nanowire. The emission is weakly directional, and a large part of it can be emitted in the backward direction. Our results can be applied for experimental determination of a lasing mode by its far fields as well as for optimization of laser emission.