$T$ --计算球形粒子团簇二次谐波的矩阵方法
$T$-matrix method for calculation of second-harmonic generation in clusters of spherical particles
摘要：
本文提出了一种$T$ -矩阵方法，用于数值计算由中心对称光学材料组成的任意分布的球形粒子团簇的二次谐波。在基波和二次谐波（SH）频率的电磁场展开在一系列的矢量球面波函数，和单球$T$ -矩阵元素的计算施加场边界条件的表面上的粒子。与以往的方法不同，我们计算SH场，同时考虑到本地表面和非本地体极化源，这使得人们能够准确地描述在任意团簇的球形粒子SH的产生。我们的数值方法可以用来有效地分析各种光学材料，包括金属，电介质，半导体和极化激元材料制成的球形颗粒的集群。
英文摘要：
In this article, we present a $T$-matrix method for numerical computation of second-harmonic generation from clusters of arbitrarily distributed spherical particles made of centrosymmetric optical materials. The electromagnetic fields at the fundamental and second-harmonic (SH) frequencies are expanded in series of vector spherical wave functions, and the single sphere $T$-matrix entries are computed by imposing field boundary conditions at the surface of the particles. Different from previous approaches, we compute the SH fields by taking into account both local surface and nonlocal bulk polarization sources, which allows one to accurately describe the generation of SH in arbitrary clusters of spherical particles. Our numerical method can be used to efficiently analyze clusters of spherical particles made of various optical materials, including metallic, dielectric, semiconductor, and polaritonic materials.
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