Frezza F, Mangini F
J Opt Soc Am A Opt Image Sci Vis. 2015 Jul 1;32(7):1379-83. doi: 10.1364/JOSAA.32.001379.
In this paper, a generalization of the vectorial spherical-harmonics expansion of an inhomogeneous elliptically polarized plane wave is presented. The solution has been achieved using the Legendre functions generalized via hypergeometric and gamma functions, shifting the difficulty to the determination of only expansion coefficients. In order to validate the presented method, a Matlab code has been implemented. To compare the results a Mie scattering by a sphere is considered, then a truncation criterion for the numerical evaluation of the series is proposed, and the Mie scattering coefficients by perfectly conducting and dielectric spheres excited by an inhomogeneous elliptically polarized plane wave are shown.
本文提出了非均匀椭圆偏振平面波矢量球谐展开的一种推广形式。该解是通过利用经由超几何函数和伽马函数推广的勒让德函数得到的，将难点转移到仅确定展开系数上。为了验证所提出的方法，已实现了一个Matlab代码。为了比较结果，考虑了球体的米氏散射，然后提出了级数数值评估的截断准则，并给出了由非均匀椭圆偏振平面波激发的理想导电球体和介质球体的米氏散射系数。
