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FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR THREE DIMENSIONAL ELECTROMAGNETIC SCATTERING PROBLEM

Department of Physics and William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, P. R. China

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H. H. ZHENG

Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, P. R. China

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J. J. XIAO

Department of Electronic and Information Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, P. R. China

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Z. F. LIN

Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, P. R. China

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, and

C. T. CHAN

Department of Physics and William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, P. R. China

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https://doi.org/10.1142/S2047684112500388Cited by:3 (Source: Crossref)

Abstract

We developed a fast numerical algorithm for solving the three-dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary element method. Nyström's quadrature rule with a triangular grid is employed to linearize the integral equations, which are then solved by using a right-preconditioned iterative method. We apply the fast multipole technique to accelerate the matrix-vector multiplications in the iterations. We demonstrate the broad applications and accuracy of this method with practical examples including dielectric, plasmonic and metallic objects. We then apply the method to investigate the plasmonic properties of a silver torus and a silver split-ring resonator under the incidence of an electromagnetic plane wave. We show the silver torus can be used as a trapping tool to bind small dielectric or metallic particles.

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