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.     

非傍轴双光束势阱产生的辐射力

分析了两束相对传输的非傍轴高斯光束相干叠加形成的双光束势阱对瑞利粒子产生的辐射力,并作了数值计算,结果表明,与傍轴双光束势阱相比,非傍轴双光束势阱的辐射力有明显的不同,纵向辐射力和横向辐射力都增大,y方向平衡点数目由一个增加到多个,且势阱更深,横向辐射力变化趋势更陡,更有利于微粒的精确定位,与非傍轴单光束势阱相比,势阱更深,所产生的辐射力更大,因而更利于控制瑞利粒子。     

Arbitrary direction incident Gaussian beam scattering by multispheres

Based on spherical vector wave functions and their coordinate rotation theory,the field of a Gaussian beam in terms of the spherical vector wave functions in an arbitrary unparallel Cartesian coordinate system is expanded.The beam shape coefficient and its convergence property are discussed in detail.Scattering of an arbitrary direction Gaussian beam by multiple homogeneous isotropic spheres is investigated.The effects of beam waist width,sphere separation distance,sphere number,beam centre positioning,and incident angle for a Gaussian beam with two polarization modes incident on various shaped sphere clusters are numerically studied.Moreover,the scattering characteristics of two kinds of shaped red blood cells illuminated by an arbitrary direction incident Gaussian beam with two polarization modes are investigated.Our results are expected to provide useful insights into particle sizing and the measurement of the scattering characteristics of blood corpuscle particles with laser diagnostic techniques.     

On-axis Gaussian beam scattering by an eccentrically coated conducting cylinder

Based on the generalized Lorenz–Mie theory (GLMT) framework, an exact analytic solution to electromagnetic scattering by an eccentrically coated conducting cylinder is constructed, for oblique incidence of an on-axis Gaussian beam described by a localized beam model. The solution is found by the classical separation of variables technique and the translational addition theorem. For a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis, numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.     

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.     

Scattering of shaped beam by a conducting infinite cylinder with dielectric coating

Based on the generalized Lorenz–Mie theory (GLMT), which provides the general framework and expansion of the incident shaped beam in terms of cylindrical vector wave functions, an analytic solution to the electromagnetic scattering by coated infinite cylinders is constructed for arbitrary incidence of a shaped beam. As an example, for a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis, the scattering characteristics that obviously demonstrate the three-dimensional nature are described in detail, and numerical results of the normalized differential scattering cross section are evaluated.     

任意形状凸粗糙物体高斯光束相干散射研究

研究了任意形状凸粗糙物体对高斯光束的相干散射特性。由平面波谱展开法推导出粗糙面高斯波束散射场表达式．并根据物理光学近似和稳相法原理得到相干散射截面的理论公式。与平面波解不同的是,在公式中引入了波束因子这一表征波束作用的重要参量,该参量与束腰半径、束腰中心与物体中心距离和物体照射面积以及入射、散射方向有关。最后数值计算了1．06μm激光波束对粗糙球的散射,分析了波束因子．介电常量和极化状态对红外激光相干散射截面的影响,重点讨论了波束因子的变化规律。分析表明．当波束半径远大于物体尺寸时,波束入射的结果可退化到平面波情况。     

Calculations of Infrared Laser Beam Scattering from Rough Dielectric Objects

The coherent and incoherent scattering cross sections of Infrared Laser Gaussian beam scattering from arbitrarily shaped convex dielectric objects with rough surfaces are investigated by using plane wave spectrum method and physical optics approximation. In the paper, the infrared laser scattering cross sections of rough sphere are calculated at 10.6 m , and the influence of the beam size, permittivity, and polarization as well as roughness parameters is analyzed numerically. When the beam size is much larger than the size of object, the results in the paper can reduce to those of an incident plane wave. On the other hand, for the case of roughness statistical parameter close to zero, only the forward scattering has a parent difference compared with the result of gaussian beam scattering from smooth sphere.     

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     

离心球对高斯波束的光散射及应用

基于广义米氏理论研究了在轴离心球对高斯波束光散射特性.入射高斯波束的波束因子用积分区域近似法计算,散射场的展开系数由矢量球面波函数的加法定理并求解边界条件得到.以离心球为模型研究了单核生物细胞对高斯波束的散射特性并给出了相关数值模拟,讨论了离心距、波束的束腰半径和核的大小对散射强度角分布和散射、消光系数的影响.     

Pseudo-Gaussian cylindrical acoustical beam – Axial scattering and radiation force on an elastic cylinder

Making use of the addition theorem for the cylindrical wave functions and the complex-source-point method in cylindrical coordinates, an exact solution to the Helmholtz equation is derived, which corresponds to a tightly focused (or collimated) cylindrical quasi-Gaussian beam with arbitrary waist. The solution is termed “quasi-Gaussian” to make a distinction from the standard Gaussian beam solution obtained in the paraxial approximation. The advantage of introducing this new solution is the efficient and fast computational modeling of tightly focused or quasi-collimated cylindrical wave-fronts depending on the dimensionless waist parameter kw₀, where k is the wavenumber of the acoustical radiation. Moreover, a closed-form partial-wave series expansion is obtained for the incident field, which has the property that the axial scattering (i.e. along the direction of wave propagation) and the axial acoustic radiation force (which is a time-averaged quantity) on a cylinder, can be calculated without any approximations in the limit of linear acoustical waves in a nonviscous fluid. Examples are found where the extinction in the radiation force function plot is found to be correlated with conditions giving reduction of the backscattering from an elastic cylinder. Those results are useful in beam-forming design, particle manipulation in acoustic tweezers operating with focused cylindrical beams, and the prediction of the scattering and radiation forces on a cylindrical particle or liquid bridges.     

Theoretical comparison of optical traps created by standing wave and single beam

We used generalised Lorenz–Mie scattering theory (GLMT) to compare submicron-sized particle optical trapping in a single focused beam and a standing wave. We focus especially on the study of maximal axial trapping force, minimal laser power necessary for confinement, axial trap position, and axial trap stiffness in dependency on trapped sphere radius, refractive index, and Gaussian beam waist size. In the single beam trap (SBT), the range of refractive indices which enable stable trapping depends strongly on the beam waist size (it grows with decreasing waist). On the contrary to the SBT, there are certain sphere sizes (non-trapping radii) that disable sphere confinement in standing wave trap (SWT) for arbitrary value of refractive index. For other sphere radii we show that the SWT enables confinement of high refractive index particle in wider laser beams and provides axial trap stiffness and maximal axial trapping force at least by two orders and one order bigger than in SBT, respectively.     

Acoustic beam scattering and excitation of sphere resonance: Bessel beam example

The exact partial wave series for the scattering by a sphere centered on an ideal Bessel beam was recently given by Marston ["Scattering of a Bessel beam by a sphere," J. Acoust. Soc. Am. 121, 753-758 (2007)]. That series is applied here to solid elastic spheres in water and to an empty spherical shell in water. The examples are selected to illustrate the effect of varying the beam's conical angle so as to modify the coupling to specific resonances in the response of each type of sphere considered. The backscattering may be reduced or increased depending on properties of the resonance and of the specular contribution. Changing the conical angle is equivalent to changing the beamwidth. Some applications of the Van de Hulst localization principle to the interpretation of the partial wave series and to the interpretation of the scattering dependence on the beam's conical angle are discussed. Some potential applications to the analysis of the scattering by spheres of more general axisymmetric beams are noted.     

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.     

Gaussian beam scattering by a chiral sphere

Based on the generalized Lorenz–Mie theory that provides the general framework, an analytic solution to Gaussian beam scattering by a chiral sphere is constructed, by expanding the incident Gaussian beam, scattered fields and internal fields in terms of spherical vector wave functions. The unknown expansion coefficients are determined by a system of equations derived from the boundary conditions. For a localized beam model, numerical results of the normalized differential scattering cross section are presented.     

紧聚焦条件下相干反斯托克斯拉曼散射信号场的矢量分析

在相干反斯托克斯拉曼散射(coherent anti-Stokes Raman scattering,CARS)显微镜中,共线传输的紧聚焦高斯光束激发具有不同形状和尺寸的待测样品所产生的CARS信号场的空间分布决定了整体系统的结构特点.建立了紧聚焦条件下球形样品产生CARS信号场的理论模型.利用矢量波动方程分析了紧聚焦条件下线偏振的高斯光束的光场强度和相位分布.利用格林函数求解该模型中CARS信号场的矢量波动方程,模拟计算得到了不同直径球形样品的远场CARS信号场的空间分布.理论分析和模拟计算结果表明,对于小体积的球形样品,前向和背向传输的CARS信号场强度接近,因此采用大数值孔径物镜背向探测方式即可获得高对比度图像.对于大体积球形样品,CARS信号场的强度大幅增强,且发射方向主要集中在前向的一定立体角内.因此,采用小数值孔径物镜即可有效收集前向传输的CARS信号.     

双球粒子对任意入射单波束及双波束的散射

基于广义Lorenz-Mie理论,研究了双介质球粒子对任意角度入射波束的散射.将入射波束用球矢量波函数展开,推导了双介质球形粒子对任意入射单波束的散射方程;将该方法进一步推广,研究了双波束任意入射时的情况.以Gauss波束为例,对以上理论进行了数值验证,比较分析了单波束及双波束任意入射时散射特性随入射方向、球心距等参数的变化关系.     

双球粒子对任意入射单波束及双波束的散射

基于广义Lorenz-Mie理论,研究了双介质球粒子对任意角度入射波束的散射.将入射波束用球矢量波函数展开,推导了双介质球形粒子对任意入射单波束的散射方程;将该方法进一步推广,研究了双波束任意入射时的情况.以Gauss波束为例,对以上理论进行了数值验证,比较分析了单波束及双波束任意入射时散射特性随入射方向、球心距等参数的变化关系. 关键词： 广义波束因子 双球粒子 Gauss波束     

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。     

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.