Two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape

A two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape using the multigrid-moment method is examined. The scattered field is expressed in terms of the integral form by an infinite summation of the surface integral over the cross section of the reference cylinder. The integral form is converted into the matrix equation by using the moment method. The integration in the elements of the matrix equation is evaluated by the lattice-sums technique to obtain a precise solution. The multigrid method is applied to the matrix equation to improve the CPU time. The CPU time and the residual norm are examined numerically for a given number of iterations and cycle indices. Then the effects of shape and material of the periodic structure on the power reflection coefficient of the fundamental Floquet mode are shown. In addition, the results indicate the effect of changing the relative permittivity of the dielectric coated body and the reflection coefficient.     

Electromagnetic scattering from a multilayered sphere located in an arbitrary beam

A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.     

Two-dimensional non-Fourier heat conduction with arbitrary initial and periodic boundary conditions

In this paper, the (2+1)-dimensional hyperbolic heat conduction equation is analytically solved under the influence of arbitrary initial conditions for a rectangular plate with homogeneous boundary conditions of first-kind. The temperature field is obtained as a double Fourier series. The presented solution is valid even for discontinuous but integrable initial conditions. Afterwards, the solution is generalized by means of a transformation to cover problems with inhomogeneous first-kind boundary conditions. Another interesting issue is that the obtained solution can be considered as a solution to the Klein–Gordon equation under the influence of arbitrary initial conditions by means of a simple transformation.     

Light scattering by a multilayered spheroidal particle

The light scattering problem for a confocal multilayered spheroid has been solved by the extended boundary condition method with a corresponding spheroidal basis. The solution preserves the advantages of the approach applied previously to homogeneous and core-mantle spheroids, i.e., the separation of the radiation fields into two parts and a special choice of scalar potentials for each of the parts. The method is known to be useful in a wide range of the particle parameters. It is particularly efficient for strongly prolate and oblate spheroids. Numerical tests are described. Illustrative calculations have shown that the extinction factors converge to average values with a growing number of layers and how the extinction varies with a growth of particle porosity.     

Explicit results for scattering parameters in three-dimensional wave propagation through a doubly periodic system of arbitrary openings

Summary In the present paper, an analytical approach previously formulated for two-dimensional scattering problems is further developed to study three-dimensional problems. A scalar plane wave is assumed to (normally) penetrate into a plane screen having identical openings of arbitrary shape which are periodically distributed. This problem is first described by an integral equation holding over the typical openings' domain. Then, by applying simple approximations (uniformly) valid in the assumed regime of propagation, some auxiliary integral equations are deduced which are independent of the wave frequency. A linear algebraic system is finally set up whose solution provides explicit analytical formulas for the main scattering parameters. By solving numerically this system of equations for assigned obstacle shapes, several graphs are obtained which show comparison between such explicit formulas and the corresponding rigorous numerical solution of the original integral equation.     

Two-dimensional multipoles from arbitrary current densities in polygonal domains

A complex analytic multipole decomposition of the magnetic field produced by an arbitrary, continuous current density in a two-dimensional polygonal domain is obtained by series expanding the Green's function of complex magnetic field. The multipole coefficients are given explicitly as functions of the vertex coordinates of the polygon.     

Micromorphic effects in a modelling of periodic multilayered elastic composites

The paper deals with the problems of modelling of multilayered periodic composites. The proposed models take into account certain micromorphic effects resulting from the periodic structure of the body. The governing equations describing motions and stresses of the nonhomogeneous elastic materials with microperiodic structure in the nonlinear as well as linear cases have been derived. As an example the time-harmonic vibrations of laminated medium consisting of alternating layers of two homogeneous, isotropic, linear-elastic materials have been discussed.     

Debye series for light scattering by a multilayered sphere

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.     

周期分布不规则体对弹性波的二维散射

建立了一种基于均布线载动力格林函数的周期间接边界元方法(PIBEM),进而研究了全空间中周期分布不规则体对弹性波的散射问题。方法利用平面波入射下,各不规则体周围波场频域内仅相差一个相位的特征,仅需针对其中一个不规则体进行离散和求解,即可求得问题的解;相对于选取有限多个不规则体进行近似求解的方法,该方法具有较高精度的同时,最大限度的降低了求解自由度;在对方法正确性验证的基础上,以全空间中空洞和加塞两种模型为例开展了数值计算分析,重点探讨了空洞形状、空洞间距和加塞刚度等参数对减振效应的影响。数值分析结果表明:周期分布空洞与多个空洞的位移幅值具有差异,且频率低时差异更为显著;三种形状空洞中,周期分布圆形空洞减振效果最佳,周期分布三角形空洞减振效果最差;周期分布加塞与周期分布空洞减振原理不同,加塞通过消耗地震波的能量减振,而空洞通过阻隔地震波减振;周期分布软加塞的消能减振效果优于周期分布硬加塞。     

Improved recursive algorithm for light scattering by a multilayered sphere

An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters andrefractive indices.     

Debye series for Gaussian beam scattering by a multilayered sphere

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.     

Generalized pulse equations for through-transmission evaluation of arbitrary multilayered structures

Generalized transit time and pulse amplitude equations have been derived for modeling the ultrasonic through-transmission wave propagation of an arbitrary n-layered structure. The equations can be programmed into an expert system and used to identify and predict the through-transmission pulse signals from the critical interfaces of a multilayered structure. To test the formulas, we measured the through-transmission responses from one- and three-layered configurations in the laboratory and compared the experimental measurements with computer-generated data that were determined using the derived equations. The results verify the validity of the formulas.     

Finite-element time-domain modelling of plane wave scattering by a periodic structure using an exact boundary condition

A two-dimensional singly-periodic structure, at plane wave oblique incidence, is modelled using the finite-element time-domain method. Over the non-periodic boundaries of the computational domain, an exact Floquet modal absorbing boundary condition is developed, in detail, for the finite element method in the time domain. The proposed formulation is validated by comparing its results with that of the finite-element frequency-domain method and with independently obtained published results. Very accurate numerical results, over a wide frequency range and incident angle range, are obtained for both transverse electric and transverse magnetic polarised plane wave illuminations     

Refraction and diffraction by a metal-dielectric multilayered structure

An optical refraction prism consisting of metal and dielectric, subwavelength, periodic multilayered thin films has been proposed. The multilayered structure of metal and dielectric thin films has a cylindrical dispersion surface for TM polarized light. The light behaviors are very different from those of conventional glass prisms and photonic crystal superprisms. Refraction and diffraction of the light wave for the metal-dielectric multilayered prism has been investigated by numerical simulations and graphical representation based on the dispersion surface. A prism with 0.2 microm period had an angular dispersion of 0.20 degrees /nm for approximately 0.8 microm wavelength light. The finite thick metal-dielectric multilayered structure acted as a slab waveguide.     

Calculating x-ray diffraction from multilayer lateral crystal structures with arbitrary shapes and composition profiles

A theory of x-ray diffraction in the vertical direction from a lateral crystal having an arbitrary shape and arbitrary depth-composition profile has been developed within the framework of the kinematic approximation. The results of a numerical simulation of diffraction patterns from such crystals in high-resolution triple-axis diffractometry scheme are presented.     

Analysis of scattering from arbitrary configuration of elliptical obstacles using T-matrix representation

A new method of analysis of an arbitrary configuration of elliptical cylinders is presented. The treatment of such a problem is based on a combination of the cylindrical and elliptical coordinates systems. This approach is applied to the formulation of the scattered field at the surface of equivalent cylinder surrounding dielectric or metal elliptical object. To analyse the arbitrary set of elliptical cylinders, the iterative scattering procedure is used. A good agreement of the proposed method with the commercial FD simulator is achieved.     

Inelastic scattering by particles of arbitrary shape

The shape effect of inelastic scattering by small particles is investigated using geometrical optics. The particles considered are described by surfaces composed of triangles. In order to determine the accuracy of this model, the results for an approximated sphere with different degrees of discretization are compared with the result for a smooth sphere. The triangulation method is then used for describing a superellipsoid. This enables us to consider inelastic scattering for a variety of particles by changing only a few parameters.     

Two-dimensional scattering from an impenetrable cylindrical obstacle in an acoustic quarterspace

The problem of sound scattering by an infinitely long hard or soft circular cylindrical obstacle suspended near a rigid corner is investigated. The separation of variables technique, the appropriate wave field expansions and the method of images along with the translational addition theorem for cylindrical wave functions are used to derive a closed-form analytical solution in form of infinite series. The analytical results are illustrated with a numerical example in which the cylindrical obstacle is positioned near the rigid boundary of a water-filled acoustic quarter-space. The backscattering form function amplitude and spatial distribution of the total acoustic pressure are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and proximity of the cylinder to the rigid boundary are examined. Limiting case involving an infinite cylinder in an acoustic halfspace is considered and fair agreement with a well-known solution is established.     

水下复合边缘扁平结构散射声场特性研究

通过采用边界积分方法并结合水声无源材料自由场测试等工程实际,对几种典型复合边缘结构形式的水下扁平结构的散射声场分布规律开展了进一步地研究与分析。在此基础上,尝试在不改变主体扁平矩板结构声学性能的前提下,提出通过附加边缘结构设计即物理解决途径上对自由场测试中存在的边缘效应进行抑制或去除,为提高测试精度（尤其是低频段测试精度）创造条件,也为边缘效应抑制机理和技术的研究与开发奠定基础。数值仿真与理论分析结果表明：1.复合附加边缘矩板结构的散射声场频域分布特性与多数附加边缘类型扁平矩板结构散射声场分布的总体规律基本一致,在趋势上是相似的,而边缘重数的增加加剧了前向散射与镜向散射声场间的差异性和不同程度地增大了声场的波动程度;2.附加边缘声学结构设计（如共振吸声结构或软表面声学处理、增加有效边缘重数等）对抑制结构边缘效应负面影响是有效的和可行的,且具有较好的可控性。     

Reconstruction of periodic structures from optical scattering measurements using adjoint equations

A new numerical approach to efficiently reconstruct the profile of a grating from measurements of reflection coefficients is demonstrated. The problem is posed in the mathematical framework of an inverse scattering problem and solved using gradient-based algorithms. The gradient is computed efficiently using adjoint equations, which amounts to an extra scattering computation per iteration. For symmetric profiles it is shown that only knowledge of the scattered field is sufficient to compute the gradient. As a result, complex profiles can be reconstructed rapidly, and the method can be potentially used in metrology applications in semiconductors. The technique is demonstrated for the case of TE polarization.