Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems: I. General formulation

The generalized Lorenz-Mie theory in the strict sense describes the interaction between an illuminating arbitrary shaped beam and a homogeneous sphere characterized by its diameter d and its complex refractive index m. It relies on the method of separation of variables expressed in spherical coordinates. Other generalized Lorenz-Mie theories (for other kinds of scatterers) expressed in spherical coordinates are available too. In these theories, the illuminating beam is expressed by using expansions with expansion coefficients depending on some fundamental coefficients named beam shape coefficients, more specifically spherical beam shape coefficients. In this paper we present a general formulation for the transformation of spherical beam shape coefficients through rotations of coordinate systems.     

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.     

Asymptotic quantum inelastic generalized Lorenz-Mie theory

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane wave illumination. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz-Mie theory and (ii) elastic cross-sections in an associated quantum generalized Lorenz-Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz-Mie theory, which is presented in this paper.     

离轴多层球对高斯波束的光散射

根据广义米氏理论，将入射的高斯波束按矢量球谐函数展开，获得了波束因子（展开系数）ｇｍｎ，ＴＭ和ｇｍｎ，ＴＥ的一般表达式。应用ｇｍｎ的局域近结果和散射系数ａｎｍ和ｂｎｍ的迭代公式与算法，研究了多层有耗介质球的光散射。讨论了波束宽度与球形粒子的尺寸和位置对散射系数和散射强度角分布的影响。     

Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems. IV. Plane waves

This paper is the fourth of a series devoted to the transformation of beam shape coefficients through rotations of coordinate systems. These coefficients are required to express electromagnetic fields of laser beams in expanded forms, for instance for use in some generalized Lorenz-Mie theories. The main result of Part I has been the theorem of transformation of beam shape coefficients under rotations. Part II dealt with the special case of on-axis axisymmetric beams. Part III dealt with other special cases, namely when the Euler angles specifying the rotation are given some special values. The present Part IV studies another special case, namely the one of plane waves viewed as special on-axis axisymmetric beams, and can therefore be viewed as a special case of Part II. Unexpectedly, it is found that, in general, although plane waves are fairly trivial, their expansions require using non trivial beam shape coefficients, exactly as required when dealing with arbitrary shaped beams.     

Generalized lorenz-mie theory and applications

Many optical sizing techniques rely on particle/laser interactions. The classical Lorenz-Mie theory describing sphere/plane wave interactions is therefore misleading when designing instruments and processing data when the particle size is not small enough with respect to beam diameters. In such cases the use of the generalized Lorenz-Mie theory is required. After summarizing essential features of the generalized Lorenz-Mie theory for sphere/arbitray wave interactions, this paper describes applications of the theory with some emphasis on the analysis of phase-Doppler anemometers.     

均匀椭球粒子对拉盖尔-高斯光束的散射特性研究

基于广义Mie理论, 研究了椭球粒子对在轴入射的拉盖尔-高斯光束的散射特性. 通过局域近似法求解椭球坐标系中的波束因子, 计算得到了波束因子之间满足的普遍关系. 对散射强度随椭球粒子不同尺寸参数和扁圆程度的变化特性进行了数值计算, 并针对不同拓扑荷时的散射强度进行了对比分析. 结果表明: 当椭球粒子尺寸在与入射光波长可比拟的范围内变化时, 散射强度随尺寸参数的增大而增大, 随椭球长短轴之比和拓扑荷的增大而减小. 本文的理论研究能够为拉盖尔-高斯光束在粒径测量、大气激光通信、 大气遥感等领域的应用提供更准确的粒子模型和参考价值. 关键词： 椭球粒子 拉盖尔-高斯光束 波束因子 散射强度     

Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems. V. Localized beam models

This paper is the fifth of a series of papers devoted to the transformation of beam shape coefficients through rotations of coordinate systems. These coefficients are required to express electromagnetic fields of laser beams in expanded forms, for use in some generalized Lorenz-Mie theories, or in other light scattering approaches such as Extended Boundary Condition Method. Part I was devoted to the general formulation. Parts II, III, IV were devoted to special cases, namely axisymmetric beams, special values of Euler angles, and plane waves respectively. The present Part V is devoted to the study of localized approximation and localized beam models, and of their behavior under the rotation of coordinate systems.     

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     

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。     

高斯波束对双层粒子的辐射俘获力

从广义米理论出发，将入射高斯波束用矢量球谐函数展开.根据对电磁场动量的讨论，得出了高斯波束对多层球形粒子的辐射俘获力的表示式，并就单高斯波束对在轴双层有吸收粒子受到的辐射俘获力进行了数值模拟，讨论了束腰半径、吸收系数、内外层相对厚度对俘获情况的影响. 关键词： 辐射俘获力 多层球形粒子 光镊 高斯波束     

高斯波束致微粒旋转的理论研究

基于偏振光波是左旋光子与右旋光子组成的, 从广义米理论出发, 得出了偏振高斯波束对球形粒子的辐射俘获力和力矩的表示式. 分析了微粒在圆偏振高斯波束照射时产生两种不同旋转的原因, 并结合光子的量子特性进行了解释. 对圆偏振高斯波束中粒子的两种力矩进行了数值模拟, 讨论了粒子半径、折射率、吸收系数和束腰半径对力矩及光致旋转的影响. 关键词： 光致旋转 力矩 高斯波束 光子     

理论模拟有核细胞对高斯光束偏振散射特性的影响

利用双层球形粒子模拟了有核细胞;根据广义米理论(GLMT),对入射激光束(高斯光束)利用矢量球谐函数进行展开;利用分离变量法研究了有核细胞对高斯光束的散射特性的影响.数值计算了高斯光束正入射时,斯托克斯散射矩阵中各元素的角分布,并与平面波入射情况进行了比较.     

Interaction Between Shaped Beams and an Infinite Cylinder,including a discussion of Gaussian beams

The theory of interaction between a shaped beam and an infinite cylinder arbitrarily located in it is presented. The same approach as for the generalized Lorenz-Mie theory is first used. In particular, variable separability is assumed in solving the wave equation. The special case of Gaussian beams, however, implies that, unexpectedly, a special class of non-separable scalar potentials is required for some kinds of beams.     

A transparent macroscopic sphere is cross-sectionally equivalent to a superposition of two quantum-like radial potentials

We consider two frameworks (i) the electromagnetic generalized Lorenz-Mie theory describing the interaction between an electromagnetic arbitrary shaped beam and a homogeneous, non-magnetic sphere, with an isotropic, linear, material and (ii) a quantum generalized Lorenz-Mie theory describing the interaction between a quantum eigen-arbitrary shaped beam and a quantum radial potential. For the time being, we restrict ourselves in this paper to elastic scattering cross-sections. We then demonstrate that a transparent macroscopic sphere in the first framework is equivalent to a superposition of two quantum-like radial potentials in the second framework. The restrictive meaning of “quantum-like” will be discussed when appropriate.     

Evaluation of a Particle Sizing Technique Based on Laser Sheets

The use of a laser sheet (or elliptical Gaussian beam) in meas-urement techniques is of growing interset. Some of these techniques take advantage of the wavefront curvature of such beams as in a dual-crylindrical wave system (DCW). Nevertheless, up to now, the analysis of the properties of the light scattered by spherical particles form the beam has been carried out largely by using geometrical optics or classical Lorenz-Mie theory. In this paper, the generalized Lorenz-Mie theory (GLMT) is applied to the analysis of an existing DCW measurement system. Differences between the results predicted by classical approaches and by GLMT are emphasized.