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.     

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.     

激光对含偏心核球形粒子的辐射俘获力

利用偏心球形粒子对任意角度入射有形波束散射的理论,从广义米理论出发,根据电磁场的动量守恒及麦克斯韦张量,推导了任意入射波束对偏心球形粒子辐射俘获力的级数表达式,并以高斯波束为例,就离轴入射有吸收偏心球形粒子时的辐射俘获力进行了数值模拟,讨论了束腰半径、吸收系数、内核的相对大小及位置对俘获情况的影响. 关键词： 广义米理论 偏心球 辐射俘获力 光镊     

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.     

Debye Series Formulation for Generalized Lorenz‐Mie Theory with the Bromwich Method

The formulation of the Debye series ready for implementation in generalized Lorenz‐Mie theory (theory of interaction between an arbitrary shaped beam and a homogeneous sphere) is presented in the framework of the Bromwich method.     

Measurements of Beam Shape Coefficients in Generalized Lorenz-Mie Theory and the Density-Matrix Approach. Part 2: The Density-Matrix Approach

In Part 1, it was demonstrated that intensity measurements on an actual beam in the laboratory allow one to determine so-called density matrices related to the beam shape coefficients encoding the beam and used in many expressions of the generalized Lorenz-Mie theory. In this paper, expressions in the generalized Lorenz-Mie theory are rewritten and it is shown that they can be expressed in terms of the density matrices rather than in terms of beam shape coefficients, leading to what is called the density matrix approach to the generalized Lorenz-Mie theory. The possibility of rewriting the generalized Lorenz-Mie theory in terms of quantities describing the illuminating beam and experimentally measurable in the laboratory offers new opportunities in optical characterization.     

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。     

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.     

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     

T-matrix formulation and generalized Lorenz-Mie theories in spherical coordinates

There has been recently a growing interest in the development of what is usually known as the T-matrix method (better to be named: T-matrix formulation), in connection with studies concerning light scattering by nonspherical particles. Another line of research has been devoted to the development of generalized Lorenz-Mie theories dealing with the interaction between arbitrary electromagnetic shaped beams and some regular particles, allowing one to solve Maxwell’s equations by using a method of separation of variables. Both lines of research are conjointly considered in this paper. Results of generalized Lorenz-Mie theories in spherical coordinates (for homogeneous spheres, multilayered spheres, spheres with an eccentrically located spherical inclusion, assemblies of spheres and aggregates) are modified from scalar results in the framework of the Bromwich method to vectorial expressions using vector spherical wave functions (VSWFs) in order to match the T-matrix formulation, and to express the T-matrix. The results obtained are used as a basis to clarify statements, some of them erroneous, concerning the T-matrix formulation and to provide recommendations for better terminologies.     

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     

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.     

On the structures of some light scattering theories depending on whether or not the Bromwich formulation may be used,e.g. spherical versus spheroidal coordinates

The generalized Lorenz–Mie theories for a homogeneous sphere (interaction between an electromagnetic arbitrary shaped beam and a sphere defined by its diameter and its complex refractive index), and for other particles as well (such as cylindrical particles, with circular or elliptical cross-sections) have been developed by using the Bromwich method. Conversely, this method cannot be used for spheroidal particles. Whether it is possible or not to use the Bromwich method implies a certain number of consequences concerning (i) the definition of TM- and TE-waves, (ii) the definition of genuine beam shape coefficients to describe the beam, (iii) the possibility of developing a localized beam model to describe the illuminating beam. These three issues may be enlightened by referring to the properties of the Bromwich method.     

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     

Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion

A generalized Lorenz-Mie theory framework (GLMT) is applied to the study of Gaussian beam scattering by a spherical particle with an embedded spheroid at the center. By virtue of a transformation between the spherical and spheroidal vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are presented.     

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.