T-matrix methods, with incident and scattered fields described as sums of multipolar fields, are attractive computational methods for many scattering problems due to their versatility, accuracy, and computational efficiency, especially for repeated calculations. However, numerical difficulties often hamper their use for non-spherical particles with large aspect ratios. Further, even if far-field scattering can be accurately calculated, it can be impossible to accurately calculate near-fields. The use of spheroidal wavefunctions, instead of the commonly-used spherical wavefunctions, can be a useful solution for these problems. However, the mathematical complexity of spheroidal wavefunctions, and the challenging task of accurate numerical calculation of them, are significant barriers to their use. We have developed a computational package of MATLAB routines for performing electromagnetic scattering calculations using spheroidal wavefunctions. These allow the determination of light scattering by non-spherical particles with high aspect ratios that would be inaccessible for double precision calculation using spherical wavefunctions. We demonstrate that our codes can be successfully used for cylinders of aspect ratios from 1/10 and 10, and for metal nanoparticles. We include routines for interoperability with regular T-matrix codes and packages such as our optical tweezers toolbox.

中文翻译：

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使用球状波函数从扁平或细长的粒子中散射聚焦光的计算工具箱


T 矩阵方法将入射场和散射场描述为多极场之和，由于其多功能性、准确性和计算效率，尤其是对于重复计算，对于许多散射问题来说，是有吸引力的计算方法。然而，数值上的困难往往会阻碍它们在具有大纵横比的非球形颗粒中的使用。此外，即使可以准确计算远场散射，也可能无法准确计算近场。使用球面波函数而不是常用的球面波函数可能是这些问题的有用解决方案。然而，球状波函数的数学复杂性以及精确数值计算的艰巨任务是其使用的重大障碍。我们开发了一个 MATLAB 例程的计算包，用于使用球面波函数执行电磁散射计算。这些允许测定具有高纵横比的非球形粒子的光散射，而这对于使用球面波函数进行双精度计算是无法实现的。我们证明我们的代码可以成功地用于纵横比为 1/10 和 10 的圆柱体以及金属纳米颗粒。我们包括与常规 T 矩阵代码和软件包（例如我们的光镊工具箱）互操作的例程。