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在椭球坐标中任意取向、定位和形状的光束的扩展。

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates.

作者信息

Xu Feng, Ren Kuanfang, Cai Xiaoshu

机构信息

Institute of Particle and Two-phase Flow Measurement Technology, University of Shanghai for Science and Technology, Shanghai, China.

出版信息

J Opt Soc Am A Opt Image Sci Vis. 2007 Jan;24(1):109-18. doi: 10.1364/josaa.24.000109.

Abstract

Within the framework of the generalized Lorenz-Mie theory (GLMT), the incident shaped beam of an arbitrary orientation and location is expanded in terms of the spheroidal vector wave functions in given spheroidal coordinates. The beam shape coefficients (BSCs) in spheroidal coordinates are computed by the quadrature method. The classical localization approximation method for BSC evaluation is found to be inapplicable when the Cartesian coordinates of the beam and the particle are not parallel to each other. Once they are parallel, all the symmetry relationships existing for the BSCs in spherical coordinates (spherical BSCs) [J. Opt. Soc. Am. A11, 1812 (1994)] still pertain to the BSCs in spheroidal coordinates (spheroidal BSCs). In addition, the spheroidal BSCs computed by our method are verified by comparing them with those evaluated by Asano and Yamamoto for plane wave incidence [Appl. Opt.14, 29 (1975)]. Furthermore, formulas are given for field reconstruction from the spheroidal BSCs, and consistency is found between the original incident fields and the reconstructed ones.

摘要

在广义洛伦兹 - 米氏理论(GLMT)的框架内,任意取向和位置的入射成形光束在给定椭球坐标下根据椭球矢量波函数展开。椭球坐标下的光束形状系数(BSCs)通过求积法计算。当光束和粒子的笛卡尔坐标彼此不平行时,发现用于BSC评估的经典局部近似方法不适用。一旦它们平行,球坐标下BSCs(球形BSCs)[《美国光学学会志》A11, 1812 (1994)] 存在的所有对称关系仍然适用于椭球坐标下的BSCs(椭球BSCs)。此外,通过将我们方法计算的椭球BSCs与浅野和山本针对平面波入射所评估的结果[《应用光学》14, 29 (1975)]进行比较,验证了我们方法计算的结果。此外,给出了从椭球BSCs进行场重建的公式,并且发现原始入射场与重建场之间具有一致性。

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