Electromagnetic Fields in a Bi-Isotropic Medium Inside and Outside a Metallic Sphere

The problem on an electromagnetic resonator that is a metallic (perfectly conducting) sphere filled with a bi-isotropic medium has been solved. Exact analytic solutions for monochromatic fields inside the sphere and a transcendent condition for the natural frequencies of the resonator have been found. The problem on the scattering of a plane, circularly polarized wave in a bi-isotropic medium at a metallic sphere has also been solved.     

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.     

球形粒子在Bessel波束照射下的轴向辐射力计算和分析

通过声散射理论,将水中粒子的Bessel波束声散射场的分波序列(PWS)表达公式加以推广,进而推导出声辐射力的表达公式,获得了液体球及弹性球在Bessel波束下声辐射力的变化规律。通过观察不同散射角形态函数,可发现声辐射力的产生与粒子背向散射抑制程度有关。对于液体球粒子,球壳厚度及材料介质对粒子声辐射力有着重要的影响,同时Bessel波束波锥角越大,产生负声辐射力的可能性越大。对于弹性球和弹性单层壳粒子,声辐射力的产生与其本身的共振特征存在很大的关系。同时,通过改变球壳内介质及壳层厚度的方法,可增加产生的负声辐射力的频率范围及幅值强度.      

Curle's equation and acoustic scattering by a sphere

Recent papers have initiated interesting comparisons between aeroacoustic theory and the results of acoustic scattering problems. In this paper, we consider some aspects of these comparisons for acoustic scattering by a sphere. We give a derivation of Curle's equation for a specific class of linear acoustic scattering problems, and, in response to previous claims to the contrary, give an explicit confirmation of Curle's equation for plane wave scattering by a stationary rigid sphere of arbitrary size in an inviscid fluid. We construct the complete solution for scattering by a rigid sphere in a viscous fluid, and show that the neglect of viscous terms in Curie's equation yields an incomplete prediction of the far field dipole pressure. We also consider the null field solution of the sphere scattering problem, and give its extension to the vorticity modes associated with viscosity. Finally, we construct a solution for an elastic sphere in a viscous fluid, and show that the rigid sphere/null field solution is recovered from the limit of infinite longitudinal and shear wave speeds in the elastic solid.     

Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images

Human B-cells play an important role in the immune system, and because of their relatively simple structures with a nearly spherically shaped cell membrane and a large nucleus, they provide a good case to study on how the details of cell structure affect light scattering properties. A finite-difference-time-domain (FDTD) method is used to calculate angle-resolved light scattering distributions from a B-cell. Published FDTD simulations to date have used a smooth shape with a certain degree of symmetry to approximate the actual cell shape. In contrast, for this work, the shapes of the cell and its nucleus were determined from confocal microscopy measurements. An automated procedure was developed to construct a realistic three-dimensional structure of a B-cell from a stack of two-dimensional confocal images. The angle-resolved Mueller matrix elements of the B-cell were calculated and averaged for 30 different angles of incidence using a parallel FDTD code. These results were compared with those from a homogeneous and a coated sphere. Scattering from the two sphere models and the B-cell were very similar for scattering angles less than 5°, and the coated sphere and B-cell agreed well for scattering angles up to 20°. However, at larger angles, the scattering from the B-cell was a much smoother function of angle than scattering from either sphere model. Additionally, the homogeneous sphere results were the most similar to the B-cell results for most angles between 120° and 150°, and at angles greater than 150°, the B-cell scattered more light than either of the spheres. These results yield strong evidence that accurate modeling of light scattering by biological cells requires not only the high accuracy of the employed numerical method but the realistic cellular structure as input information as well.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

Acoustic scattering from two spheres,one with a small radius

The scattering of a plane acoustic wave from an acoustically penetrable or impenetrable (soft or hard) sphere separated at a distance from another sphere, also penetrable or impenetrable (soft or hard), of acoustically small radius, is examined. The penetrable spheres and the surrounding medium are fluids or fluidlike; i.e., they do not support shear waves. Separation of variables, in conjunction with translational addition theorems for spherical wave functions, is used. Analytical expressions are obtained for the scattered pressure field and the scattering cross sections. Numerical results are given for penetrable and impenetrable spheres, showing the influence of the small sphere on the scattering cross sections of the other sphere. Published in Russian in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 1, pp. 38–49. The text was submitted by the authors in English.     

粗糙体目标激光束散射场的互相关函数统计特征

依据高斯波束体目标散射特征,研究了粗糙体目标高斯波束散射场量的互相关函数统计特征。在激光波束入射下,通过数值方法讨论圆球类目标、不同半径、不同材料、不同入射波束极化等条件下,散射场量的互相关函数随散射角变化情况。数值计算结果表明:金属薄膜材料比非金属镀漆材料互相关函数量值要大,金属材料球体目标的后向散射互相关函数值较大,而非金属镀漆材料球体互相关函数值较小。材料表面的粗糙度和目标尺寸对互相关函数影响较大,而入射光的极化方式对相关函数有影响但影响较小。     

Electromagnetic scattering as a radiation reaction problem

Electromagnetic scattering is treated as a dynamical problem, by equating the external torque exerted by the incident wave on the sphere to the self torque due to the radiated (scattered) wave. ForI _mech=0,our scattering amplitude is equal to the usualP-wave amplitude of the electromagnetic scattering on an infinitely conducting sphere. The poles of the scattering amplitude, in particular their dependence onI _mech, are studied. For example, a pole on the positive imaginary axis, which usually corresponds to a bound state, corresponds to a runaway solution in our case. Non-decaying resonances are also discussed.     

平面上方分层小球的光散射计算

本文基于扩展的Mie理论方法求解平面上方分层小球的散射问题。通过建立小球和平面的模型,解决小球和平面的边界条件问题,并利用矢量波函数展开的方法求得了散射场。强调了小球与表面的相互作用。利用Mie理论方法得到了分层小球的散射场系数,通过计算平面上小球的散射模型,得到了平面上分层小球的散射场分布。结论给出了分层介质小球的微分散射截面图。     

Gas molecule-molecule interaction and the gas-surface scattering effect on the rarefied gas flow through a slit into a vacuum

The effect of the gas molecule-molecule interaction and the gas-surface scattering on the gas flow through a slit into a vacuum are investigated in a wide range of the gas rarefaction using the direct simulation Monte Carlo method. To study the gas molecule-molecule interaction influence, we used the variable hard sphere and variable soft sphere models defined for an inverse-power-law potential and the generalized hard sphere model defined for the 12–6 Lennard-Jones potential. The Maxwell, Cercignani-Lampis, and Epstein models were used to simulate the gas-surface scattering. This study demonstrates that the gas molecule-molecule interaction can have a significant influence on the rarefied gas flow through a slit, while the influence of the gas-surface scattering is negligibly small. The presented numerical results are in agreement with the corresponding experimental ones. The article is published in the original.     

Mie theory with spatial dispersion

The classícal Mie theory for the scattering and absorption of electromagnetic radiation by a sphere is extended to the case of a dieelectric sphere which exhibits spatial dispersion. This is achieved by imposing the usual Maxwell boundary conditions as well as Pekar's additional boundary conditions at the surface of the sphere.     

Diffraction of electromagnetic plane wave by a slit in a homogeneous bi-isotropic medium

We investigated the diffraction of an electromagnetic plane wave by an infinite slit embedded in a homogeneous bi-isotropic medium. With the aim of deriving explicit expressions for the left- and right-handed Beltrami fields, we used the Fourier integral transform, the Wiener–Hopf technique and the steepest descent asymptotic method. The electric and magnetic fields, E and H, were determined from the Beltrami fields. Our graphical results indicate that the strength of both electric and magnetic fields reduces with the dissipation of bi-isotropic medium. While matching the diffraction pattern with the existing plane wave solution, the objective was, and is, to see how well spherical wave solution performs when it is developed for plane wave solution.     

近似声斗篷的多层介质覆盖水中弹性球壳的声散射

对水中弹性球壳的低频覆盖层消声效果和消声机理进行研究。声斗篷(Acoustic cloak)是各向异性的超常材料,根据有效介质近似理论(Effective MediumApproximationTheory),采用各向同性多层介质近似各向异性材料的声斗篷,推导出覆盖多层介质水中弹性球壳散射声场的解析表达式,计算了弹性球壳覆盖多层介质前后的散射形态函数、谐振模态以及声场分布,分析了覆盖前后球壳的声散射特性和声传播机理。研究表明,覆盖层内的声波在多层介质之间的声传播方向发生改变,声场形成弯曲变形,声能流绕过目标,这不仅极大的降低了低频散射强度,而且使到达弹性体表面的声场强度非常小,散射频响中除了0阶子波产生的第一个谐振峰外,无法激发弹性球壳的其它谐振模态,有效的抑制弹性球壳的谐振散射。      

Seismic scattering from a spherical inclusion eccentrically located within a homogeneous,spherical host: theoretical derivation

Abstract

The scattered fields from a spherical body eccentrically located within an otherwise homogeneous host sphere are derived by satisfying the boundary conditions at both interfaces simultaneously. The source, which may be composed of any linear combination of S and P waves, is also located arbitrarily within the host sphere. The scattering system may have applications in seismic scattering, by cavities or dense bodies located near the Earth surface or to the Slichter mode.     

多层球对高斯波束散射的德拜级数研究

基于广义洛伦兹-米氏理论,利用多层球粒子散射系数的德拜级数展开公式,提出了一种新的研究多层球粒子对高斯波束散射的方法。计算结果与已有的广义洛伦兹-米氏理论算法的计算结果吻合得很好。利用该方法有效分离了折射率分布满足指数变化规律的多层球粒子对高斯波束散射的远区散射场中多阶彩虹的干涉强度分布。数值模拟了双层球的归一化双一阶彩虹强度分布以及各层的一阶彩虹艾里结构。最后分析讨论了高斯波束的入射位置和束腰半径对多层球单阶彩虹强度分布的影响。     

The discrete ordinates method for anisotropic scattering in the neutron transport theory: The critical sphere problem

The spherical harmonics method for anisotropic scattering in the neutron transport theory related to the critical sphere problem was investigated by Yildiz [The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem. JQSRT 2001;71:25-37]. Some numerical results and figures that they provided are incorrect. The correct numerical results for the critical radius are obtained and tabulated for different scattering parameters by using the discrete ordinates method.     

Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere

Arbitrary electromagnetic (EM) scattering of a zero-order Bessel beam by a homogeneous water sphere in air is investigated. The radial components of the electric and magnetic scattering fields are expressed using a partial wave series involving the beam-shape coefficients, scattering coefficients of the sphere, and half-conical angle of the wavenumber components of the beam. The 3D scattering directivity plots in the far-field region are evaluated using a numerical integration procedure. It is shown here that shifting the sphere off the axis of wave propagation breaks the symmetry in the directivity patterns. Moreover, the scattering strongly depends on the half-cone angle of the beam. This investigation could provide a useful test of finite element codes for the evaluation of EM scattering and radiation forces, which are important in optical tweezers and related particle manipulation applications.     

Acoustic beam interaction with a rigid sphere: The case of a first-order non-diffracting Bessel trigonometric beam

Mathematical expressions for the acoustic scattering, instantaneous (linear), and time-averaged (nonlinear) forces resulting from the interaction of a new type of Bessel beam, termed here a first-order non-diffracting Bessel trigonometric beam (FOBTB) with a sphere, are derived. The beam is termed “trigonometric” because of the dependence of its phase on the cosine function. The FOBTB is regarded as a superposition of two equi-amplitude first-order Bessel vortex (helicoidal) beams having a unit positive and negative order (known also as topological charge), respectively. The FOBTB is non-diffracting, possesses an axial null, a geometric phase, and has an azimuthal phase that depends on cos(?±?₀), where ?₀ is an initial arbitrary phase angle. Beam rotation around its wave propagation axis can be achieved by varying ?₀. The 3D directivity patterns are computed, and the resulting modifications of the scattering are illustrated for a rigid sphere centered on the beam's axis and immersed in water. Moreover, the backward and forward acoustic scattering by a sphere vanish for all frequencies. The present paper will shed light on the novel scattering properties of an acoustical FOBTB by a sphere that may be useful in particle manipulation and entrapment, non-destructive/medical imaging, and may be extended to other potentially useful applications in optics and electromagnetism.