Scattering of Gaussian beam by arbitrarily shaped inhomogeneous particles

A hybrid finite element-boundary integral method is applied to characterize the scattering of an arbitrarily incident-focused Gaussian beam by arbitrarily shaped inhomogeneous particles. Specifically, the Davis–Barton fifth-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The finite element method is employed to formulate the fields in the interior region of the inhomogeneous particle, while the boundary integral equation is applied to represent the fields in the exterior region. The interior and exterior fields are coupled by means of the field continuity conditions. To reduce the computational burden, the frontal method and the multilevel fast multipole algorithm are adopted to solve the resultant matrix equation. Numerical results for differential scattering cross sections of several selected inhomogeneous particles are presented and can be served as further study on this subject.     

Scattering of particles in wave beam based on series expansion

Based on the orthogonalities of the vector wave functions, the expressions of scattering fields are developed as the particle in the zero order field and in the first order fields of x, y, and z, respectively. A general relation between the expansion coefficients of scattering field and incident field is presented. Taking the elliptical beam for example, the scattering property of a particle in beam is investigated. After analyzing the effects of the beam waist, irradiating distance, etc. on scattering property, the validity of the proposed algorithm is demonstrated. Results show that the beam waist may improve the particle identification property and the particle has a strong scattering both in the forward direction and in the backward direction. The method proposed is simple and is a new way of researching the scattering from particles in electromagnetic beams.     

Scattering of a narrow wave beam by a randomly rough locally diffuse surface subject to pulse illumination

We consider the scattering of a narrow pulse wave beam by a randomly rough surface with a complex local scattering indicatrix. Analytical expressions are found for the mean received power for a normal distribution of heights and slopes of the surface in two cases: where the direction to the receiver is close to the direction of mirror reflection and where the direction to the receiver is very different from the direction of mirror reflection. It is shown that in these two cases the echo pulse is very different in shape and is controlled by the parameters of the source and receiver, the sounding scheme, and the variance of heights of a rough surface. The received power is strongly dependent on the width of the local scattering indicatrix, and the form of this dependence is determined by the angles of illumination and reception. The analytical expressions for the mean received power are in good agreement with the results of numerical calculations. Institute for Radioelectronics and Laser Engineering of the N. é. Bauman State Technical University of Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.42, No.4, pp. 333–339, April 1999.     

Numerical simulation of Gaussian beam scattering by complex particles of arbitrary shape and structure

An efficient numerical method based on the surface integral equations is introduced to simulate the scattering of Gaussian beam by complex particles that consist of an arbitrarily shaped host particle and multiple internal inclusions of arbitrary shape. In particular, the incident focused Gaussian beam is described by the Davis fifth-order approximate expressions in combination with rotation defined by Euler angles. The established surface integral equations are discretized with the method of moments, where the unknown equivalent electric and magnetic currents induced on the surfaces of the host particle and the internal inclusions are expanded using the Rao–Wilton–Glisson (RWG) basis functions. The resultant matrix equations are solved by using the parallel conjugate gradient method. The proposed numerical method is validated and its capability illustrated in several characteristic examples.     

Scattering of charged particles by atoms

A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J _ij with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J _ij are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J _ij makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H^? ions with energy E = 0.1–100 MeV in targets consisting of atoms with Z = 2–54. It is shown that σ_Σ ∝ E ^?1 and θ_c ∝ E ^?1/2 for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.     

Scattering by small thin dielectric particles

In the analysis of electromagnetic scattering by distributions of small dielectric particles an approximation to the scattered field can be obtained by representing the electrical interaction of the particles in terms of the dipole moments of the individual particles. The calculation of the moments necessitates the solution of certain static scattering problems, and this becomes numerically difficult when the particles are thin. An integral equation formulation of the static scattering problem specialized to the case of thin planar dielectric plates is presented, along with an efficient numerical routine. Dipole moments are obtained over a range of permittivities for plates with several thicknesses and a variety of cross-sectional shapes, and the shape dependence is discussed.     

Scattering of particles by long-range magnetic fields

The seattering of nonrelativistic particles (either quantum mechanical or classical) by a magnetic field B is studied in any dimension ν ≥ 2. B(x) is allowed to decay like |x|^{−3.2 · δ} (δ > 0), as |x| → ∞. Assumptions are made about the field strengths and not about the potentials. A gauge is constructed for which the unmodified wave operators exist and are complete even though the corresponding classical motion need not be asymptotically free. The result also holds for Yang-Mills fields.     

Depth of origin of sputtered particles under the oblique incidence of a primary ion beam

A physical model and mathematical calculations of the maximum partial depths of origin of sputtered particles versus mass, energy, and the angle of incidence of ions bombarding a one-component amorphous target are presented. Calculations reveal that the maximum depth of origin of secondary particles depends on the primary-ion incidence angle, which attains the highest value at angles of 30°–60° relative to the normal to the sample surface. When the primary beam and the target material have identical parameters, the maximum depths of origin of light secondary particles exceed those of heavy ones. Secondary particles exhibit the isotope effect. For light elements (Li, Be, and B), a heavier isotope has a larger maximum depth of origin than a lighter one. In the case of heavy elements (e.g., Mo), a lighter isotope has a greater maximum depth of origin than a heavier one.     

Scattering and absorption by spherical multilayer particles

We present a recursion formalism for the scattering coefficients of multilayered spherical particles which is more treatable for computer programs than the matrixformalism of Bhandari [1]. We computed explicitely the extinction and scattering cross section spectra of different metal coated spheres. Comparison with experimental results is done for gold-silver heterosystems. The spectra are in very good agreement with the experimental data.     

Scattering of a Bessel beam by a sphere

The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.     

Scattering of gaussian beam by a ferrite cylinder

The scattering of a Gaussian beam by a ferrite cylinder is analyzed using two methods. The spatial pictures in the amplitude of the total Gaussian beam near the cylinder resulting from the two methods are both clarified and compared. The scattering by a ferrite cylinder coating a dielectric sleeve is also presented.     

Scattering of an unpolarized Bessel beam by spheres

The scattering process of an unpolarized Bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x-and y-polarized Bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized Bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the Bessel beam.     

基于涡旋光照明的暗场数字全息显微方法研究

提出了一种基于涡旋光照明的暗场数字全息显微方法. 从理论上阐述了涡旋光环形照明原理和暗场数字全息显微原理, 分析了涡旋光的准无衍射特性对成像的影响; 搭建了相应的数字全息显微成像系统, 采用690 nm的聚苯乙烯小球作为实验样品; 最后通过对小球明暗场下数字全息显微再现像的分析对比, 证明该方法可以有效地提高数字全息系统的分辨率, 同时增强了再现像的对比度. 关键词： 全息 暗场数字全息显微 涡旋光 分辨率     

超短激光照射下颗粒的散射效应

对两个纳米颗粒受超短激光照射时表面吸收光强的分布情况进行了研究。基于米散射理论和蒙特卡罗方法建立程序来模拟和追踪光子的运动轨迹,米散射理论主要用于确定光子的散射方向,运用兰贝特定律和解析解对模拟结果进行验证。通过对比材料为金和黑体时双颗粒的光强分布发现,颗粒的散射和激光照射宽度的增加会使颗粒相邻处的光强增大,颗粒底部的光强主要取决于颗粒的反照率大小以及散射光强的分布情况。     

Scattering of particles by deformed non-rotating black holes

We study the excitation of axial quasi-normal modes of deformed non-rotating black holes by test particles and we compare the associated gravitational wave signal with that expected in general relativity from a Schwarzschild black hole. Deviations from standard predictions are quantified by an effective deformation parameter, which takes into account deviations from both the Schwarzschild metric and the Einstein equations. We show that, at least in the case of non-rotating black holes, it is possible to test the metric around the compact object, in the sense that the measurement of the gravitational wave spectrum can constrain possible deviations from the Schwarzschild solution.     

超短激光照射下颗粒的散射效应

对两个纳米颗粒受超短激光照射时表面吸收光强的分布情况进行了研究。基于米散射理论和蒙特卡罗方法建立程序来模拟和追踪光子的运动轨迹,米散射理论主要用于确定光子的散射方向,运用兰贝特定律和解析解对模拟结果进行验证。通过对比材料为金和黑体时双颗粒的光强分布发现,颗粒的散射和激光照射宽度的增加会使颗粒相邻处的光强增大,颗粒底部的光强主要取决于颗粒的反照率大小以及散射光强的分布情况。     

Holographic contouring by displacing the object and the illumination beam

A contouring technique based on a double exposure hologram is described. Between the two exposures both the illumination source and the object are displaced. The contour fringes originate from the moiré pattern due to the superposition of the fringe patterns resulting from the two displacements. Experimental results are given.