## Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems |

JOSA A, Vol. 30, Issue 6, pp. 1273-1280 (2013)

http://dx.doi.org/10.1364/JOSAA.30.001273

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### Abstract

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie’s theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold–silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

© 2013 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.4430) General : Numerical approximation and analysis

(260.2110) Physical optics : Electromagnetic optics

(260.3910) Physical optics : Metal optics

(290.5890) Scattering : Scattering, stimulated

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: January 24, 2013

Revised Manuscript: April 4, 2013

Manuscript Accepted: April 23, 2013

Published: May 31, 2013

**Citation**

Mandiaye Fall, Salim Boutami, Alain Glière, Brian Stout, and Jerome Hazart, "Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems," J. Opt. Soc. Am. A **30**, 1273-1280 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-6-1273

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