Xu Y L
Appl Opt. 1995 Jul 20;34(21):4573-88. doi: 10.1364/AO.34.004573.
We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.
我们针对由任意数量、任意构型的球体组成的聚集体的电磁散射经典问题，提出了一种全面的解决方案。这些球体是各向同性且均匀的，但大小和组成可能不同。入射电磁波的轮廓是任意的。该分析基于单个球体的米氏理论框架以及现有的球矢量波函数加法定理。经典的米氏理论得到了推广。将扩展的米氏理论同时应用于聚集体中的所有球形组分，会导致一组关于未知相互作用系数的耦合线性方程。我们提出了一种渐近迭代技术来求解这些系数。通过再次使用平移加法定理，利用相互作用散射系数构建整个聚集体的总散射场。在一般情况下，推导了严格的截面解析表达式；在沿z轴传播的平面入射波的特殊情况下，推导了振幅散射矩阵所有元素的严格解析表达式。作为示例，我们展示了一些初步的数值结果，并将它们与先前发表的实验室散射测量结果进行比较。
