贝塞尔梁球面波展开的径向正交与有限级数的等价性。

IF 1.4 3区物理与天体物理 Q3 OPTICS

Journal of The Optical Society of America A-optics Image Science and Vision Pub Date : 2023-06-01 DOI:10.1364/JOSAA.491597

Jianxin Lin, Shiliang Zhong, Jianqi Shen

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引用次数: 1

摘要

最近提出了用径向正交法来计算异形梁的梁形系数。本文利用球面贝塞尔函数在0到无穷区间内的积分，用r -正交法推导出一种新的BSCs。基于贝塞尔梁的标量描述，证实了r正交法与有限级数法的等价性。标量函数的球面波展开式简化了r -正交和FS中BSC的表达式，加快了数值BSC的计算速度。作为一个副产品，相关的勒让德函数的FS展开式被建立，这是我们在文献中没有发现的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Equivalence between radial quadrature and finite series for spherical wave expansion of Bessel beams.

The radial quadrature method was recently proposed for formulating the beam shape coefficients (BSCs) for shaped beams. A new deduction of BSCs using the R-quadrature method is presented in this paper, using the integral of the spherical Bessel functions in the interval ranging from zero to infinity. Based on the scalar description of the Bessel beam, the equivalence between the R-quadrature and the finite series (FS) method is confirmed. The spherical wave expansion of the scalar function allows us to simplify the formulation of the BSCs in the R-quadrature and the FS and to speed up the numerical BSC calculation. As a by-product, FS expansions of the associated Legendre functions are established, which we do not find in the literature.

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来源期刊

Journal of The Optical Society of America A-optics Image Science and Vision 物理-光学

CiteScore

3.40

自引率

10.50%

发文量

417

审稿时长

3 months

期刊介绍： The Journal of the Optical Society of America A (JOSA A) is devoted to developments in any field of classical optics, image science, and vision. JOSA A includes original peer-reviewed papers on such topics as: * Atmospheric optics * Clinical vision * Coherence and Statistical Optics * Color * Diffraction and gratings * Image processing * Machine vision * Physiological optics * Polarization * Scattering * Signal processing * Thin films * Visual optics Also: j opt soc am a.