Efficient and accurate numerical-projection of electromagnetic multipoles for scattering objects

Wenfei Guo; Zizhe Cai; Zhongfei Xiong; Weijin Chen; Yuntian Chen

doi:10.1007/s12200-023-00102-2

Efficient and accurate numerical-projection of electromagnetic multipoles for scattering objects

Front Optoelectron. 2023 Dec 29;16(1):48. doi: 10.1007/s12200-023-00102-2.

Authors

Wenfei Guo¹, Zizhe Cai¹, Zhongfei Xiong², Weijin Chen³, Yuntian Chen^{4

5

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Affiliations

¹ School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, China.
² School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, China. xiongzf94@outlook.com.
³ Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Singapore.
⁴ School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, China. yuntian@hust.edu.cn.
⁵ Wuhan National Laboratory of Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China. yuntian@hust.edu.cn.
⁶ Optics Valley Laboratory, Wuhan, 430074, China. yuntian@hust.edu.cn.

Abstract

In this paper, we develop an efficient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration. Firstly, we briefly review the principles of multipole decomposition, highlighting two numerical projection methods including surface and volume integration. Secondly, we discuss the Lebedev and Gaussian quadrature methods, provide a detailed recipe to select the quadrature points and the corresponding weighting factor, and illustrate the integration accuracy and numerical efficiency (that is, with very few sampling points) using a unit sphere surface and regular tetrahedron. In the demonstrations of an isotropic dielectric nanosphere, a symmetric scatterer, and an anisotropic nanosphere, we perform multipole decomposition and validate our numerical projection procedure. The obtained results from our procedure are all consistent with those from Mie theory, symmetry constraints, and finite element simulations.

Keywords: Light scattering; Multipole decomposition; Numerical quadrature.