Scattering from a penetrable sphere at short wavelengths

A scalar plane wave incident on a penetrable sphere is considered in the short wavelength limit. A new representation of the scattering amplitude is introduced which is particularly appropriate in this limit, and which requires only the evaluation of certain integrals. Some of these may be evaluated asymptotically by the method of steepest descent and lead to the geometrical optics field contribution. Included in this is the bow field. The remainder of the integrals are evaluated by the method of residues and lead to the diffracted field contribution. This “diffracted ray” field is known from recent investigations in diffraction theory. An essential part of the analysis is the introduction of the parameter p, the number of internal refractions that a ray which hits the sphere undergoes. The results obtained are all in agreement with that which would be expected on the basis of geometrical diffraction theory.     

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 Mathieu beams by a rigid sphere

Based on the recent results on the scattering of Bessel beams by a sphere and using the Whittaker integral, the scattering by a rigid sphere centred on a Mathieu beam is derived. The scattering field is expressed as a partial wave series involving the scattering angles relative to the beam axis and Mathieu beam parameters. Some numerical calculations are performed and it is shown that the illumination of a rigid sphere by a Mathieu beam produces asymmetrical scattering as a function of scattering angles θ and ?. The geometrical properties of the scattering Mathieu beam are noted.     

Scattering of electromagnetic waves by a bi-isotropic sphere

The scattering of a plane electromagnetic wave at a bi-isotropic sphere is studied, and exact analytical representations are obtained for the fields inside and outside the sphere. Expressions corresponding to Rayleigh scattering can be used to find the effective values of the material parameters of a heterogeneous composite medium consisting of small bi-isotropic spheres randomly disseminated throughout a homogeneous dielectric.V. D. Kuznetsov Siberian Institute of Physics and Technology, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 108–112, October, 1994.     

有限波束作用下掩埋球体的散射声场计算

计算并分析了海底掩埋物体的三维散射声场。采用“等效垂直线列阵”方法来进行有限波束的建模,并将浅海波导中点声源散射声场的波数积分计算方法,推广到有限波束作用下海底掩埋物体的散射场计算,本文导出了物体位于沉积层中的散射声场计算公式。计算结果表明,在波导中垂直面内的散射声场,与沉积层中点源形成的声场非常相似;当距离较远时,散射声波呈柱面波衰减。文章还分析利用海面反射以提高散射能量的可能性,表明波束指向性及波束宽度对散射声场有较大影响。     

Scattering of a general partially coherent beam from a diffuse target in atmospheric turbulence

The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a general rotationally symmetric beam as a sum of Gaussian–Schell model(GSM) beams, the mean intensity of the general beam propagating over a distance in an atmospheric turbulence is formulated. Expressions for the degree of coherence(DOC) and the normalized intensity variance of the scattered field of a general beam from a rough surface in turbulence are derived based on the extended Huygens–Fresnel principle. The general expressions reduce to the well-known forms for a GSM beam. Another example for the general beam used in this paper is the collimated flat-topped beam. The results of both kinds of beams show that the intensity profile on the target plane is a key factor affecting the statistical characteristics of the speckle field.A larger beam spot on the target plane induces a smaller coherence length and a smaller normalized intensity variance of the received field. As turbulence gets stronger, the coherence length becomes smaller, and the normalized intensity variance firstly increases and declines to unity finally.     

具有轨道角动量光束入射下的单球粒子散射研究

根据广义Mie理论,研究了具有轨道角动量拉盖尔-高斯光束（LGB）的空间传输特性以及单粒子散射特性.在单体球粒子对高斯光束散射研究的基础上,分析了在自由空间不同传输距离LGB光束的光强分布情况,在不考虑散射和波束相移关系的情况下,将LGB作为入射高斯光束,通过对波束入射时的散射衰减截面求解得到波束因子,利用矢量球谐函数对入射高斯波束进行展开,从而研究了单球粒子在在轴条件下对具轨道角动量高斯波束入射的散射问题.通过数值计算,讨论了散射强度及角分布在不同波束宽度情况下对其散射特性的影响,并与平面波的情况做了对比.结果表明,当波束束腰半径较小时,束腰半径对衰减率的影响较大,而当束腰半径远大于粒子半径时,接近于平面波的情况. 关键词： 广义Mie理论 轨道角动量 Laguerre-Gauss光束 单球粒子     

Scattering of a spherical wave by a small sphere: an elementary solution

Wave scattering by objects that are small compared to the wavelength (Rayleigh scattering) is usually studied for plane incident waves. However, knowledge of the full Green's function of the problem becomes necessary when the separation of scatterers from either an interface or each other is comparable to the scatterers' dimensions. Here, an elementary analytic solution is derived for diffraction of a spherical sound wave by a small, soft sphere. The approximate solution is obtained from asymptotic expansions of an exact solution, holds everywhere outside the sphere, and reduces to classical results due to Kelvin and Rayleigh in appropriate special cases.     

聚焦部分相干涡旋光束作用在介质球上的光阱力

应用部分相干理论推导了部分相干贝塞尔涡旋光束经过透镜聚焦后的光强分布表达式。在雷利散射范围内,利用光作用在介质球上的梯度力和散射力公式,主要讨论了拓扑荷数、相干长度、参数α以及介质球的大小选择对于梯度力和散射力的影响。数值模拟结果表明,作用在介质球上的梯度力和散射力随着拓扑荷数、相干长度或参数α的增大而减小。当拓扑荷数为0,1时,稳定的3维光阱能被获得,并且能被应用于操控折射率低于周围媒介的粒子。     

聚焦部分相干涡旋光束作用在介质球上的光阱力(英文)

应用部分相干理论推导了部分相干贝塞尔涡旋光束经过透镜聚焦后的光强分布表达式。在雷利散射范围内,利用光作用在介质球上的梯度力和散射力公式,主要讨论了拓扑荷数、相干长度、参数α以及介质球的大小选择对于梯度力和散射力的影响。数值模拟结果表明,作用在介质球上的梯度力和散射力随着拓扑荷数、相干长度或参数α的增大而减小。当拓扑荷数为0,1时,稳定的3维光阱能被获得,并且能被应用于操控折射率低于周围媒介的粒子。     

Scattering of partially polarized light by aligned atoms

A compact expression for the cross section of scattering of an arbitrarily polarized light by aligned atomic systems is obtained, in which the dependence on the geometric parameters and the Stokes parameters specifying the state of partial polarization of the incident radiation is represented in explicit form. The effect of atomic alignment and the processes of dissipation of the light energy on the polarization specific features and the angular distribution of the scattered light is investigated. In particular, it is shown that, if a dissipative channel is accessible, the angular distribution and the degree of linear polarization of scattered light depend on the degree of circular polarization of the incident radiation η₂. Dissipative processes also induce the circular polarization of the light scattered by aligned atoms when η₂=0.     

多孔介质球对声波的散射

本文利用Biot多孔介质理论,研究了多孔介质球对平面声波的散射。首先,从多孔介质球的形式函数(formfunction)出发,考虑了开孔(open-pore)和闭孔(sealed-pore)两种边界条件下的多孔介质球的散射;其次,对多孔介质球的散射功率进行了理论推导,并数值计算了散射功率与ka的关系。结果表明:形式函数曲线是非常复杂的,开孔和闭孔两种边界条件下的多孔介质球形式函数存在着重要的差异,在闭孔条件下出现了许多尖峰(peak)和尖谷(dip),而且散射功率也高于开孔条件下的散射功率。     

Acoustic radiation from a fluid-filled, subsurface vascular tube with internal turbulent flow due to a constriction

The vibration of a thin-walled cylindrical, compliant viscoelastic tube with internal turbulent flow due to an axisymmetric constriction is studied theoretically and experimentally. Vibration of the tube is considered with internal fluid coupling only, and with coupling to internal-flowing fluid and external stagnant fluid or external tissue-like viscoelastic material. The theoretical analysis includes the adaptation of a model for turbulence in the internal fluid and its vibratory excitation of and interaction with the tube wall and surrounding viscoelastic medium. Analytical predictions are compared with experimental measurements conducted on a flow model system using laser Doppler vibrometry to measure tube vibration and the vibration of the surrounding viscoelastic medium. Fluid pressure within the tube was measured with miniature hydrophones. Discrepancies between theory and experiment, as well as the coupled nature of the fluid-structure interaction, are described. This study is relevant to and may lead to further insight into the patency and mechanisms of vascular failure, as well as diagnostic techniques utilizing noninvasive acoustic measurements.     

Scattering from a Bounded Plasma

The electromagnetic scattering from a bounded plasma column in a rectangular waveguide is investigated. Using image and boundary value techniques, equations are formulated for reflection, transmission and attenuation coefficients. Numerical results obtained from computations are in good agreement with results obtained using alternative formulations elsewhere.     

Electromagnetic scattering from a spatially dispersive sphere

The problem of the scattering of a plane, monochromatic, linearly polarized, electromagnetic wave incident from vacuo onto a linear, homogeneous, non-magnetic, spatially dispersive sphere whose dielectric function is of the form is solved within the framework of Maxwell's theory.     

Scattering processes and electrical conductivity of partially ionized hydrogen plasma

We consider partially ionized hydrogen plasma for the density region n_e = (10¹⁸ ÷ 10²²) cm^—3. The cross sections for scattering processes between the particles are calculated within the partial wave method. Charged particles in the system (electrons, protons) interact via an effective potential that takes into account threeparticle correlations. The Buckingham polarization potential is used to describe electron‐atom and proton‐atom interactions. The electrical conductivity is determined using the Chapman‐Enskog method. The results are compared with other available data.     

Scattering measurements from a dissolving bubble

A laboratory-scale study on acoustic scattering from a single bubble undergoing dissolution in undersaturated fresh water is presented. Several experiments are performed with the acoustic source driven with five-cycle tone bursts, center frequency of 120 kHz, to insonify a single bubble located on axis of the combined beam of the set of transducers. The bubble is placed on a fine nylon thread located in the far field of the transducer set, arranged in bistatic configuration, in a tank filled with undersaturated water. Backscattered waveforms from the bubble target are acquired every few seconds for several hours until the bubble has completely dissolved, and detailed dissolution curves are produced from the acoustic data. The rate of bubble dissolution is calculated using the solution developed by Epstein and Plesset [J. Chem. Phys. 18, 1505-1509 (1950)]. The results of the experiments performed are in agreement with the calculations.     

Scattering from impurities in a crystal

A time independent scattering theory for a particle in a crystal with impurity is given. It is shown that the scattered wave is the solution of a Lippman Schwinger equation, and that the existence of bound states or narrow resonances is related more to the band structure than to the form of the impurity potential.