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.

在本文中，我们提出了一种T矩阵方法，用于计算由中心对称光学材料制成的任意分布的球形粒子簇产生的第二谐波产生的数值。通过一系列矢量球面波函数和单球面T扩展基频和二次谐波（SH）频率上的电磁场通过在粒子表面施加场边界条件来计算-矩阵项。与以前的方法不同，我们通过考虑局部表面和非局部体极化源来计算SH场，这使人们可以准确地描述任意球形颗粒簇中SH的生成。我们的数值方法可用于有效地分析由各种光学材料（包括金属，电介质，半导体和极化子材料）制成的球形颗粒的团簇。