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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 6 — Jun. 1, 2005
  • pp: 1187–1199

Irreducible representations of finite groups in the T-matrix formulation of the electromagnetic scattering problem

Michael Kahnert  »View Author Affiliations


JOSA A, Vol. 22, Issue 6, pp. 1187-1199 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001187


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Abstract

For particles with discrete geometrical symmetries, a group-theoretical method is presented for transforming the matrix quantities in the T-matrix description of the electromagnetic scattering problem from the reducible basis of vector spherical wave functions into a new basis in which all matrix quantities become block diagonal. The notorious ill-conditioning problems in the inversion of the Q matrix are thus considerably alleviated, and the matrix inversion becomes numerically more expedient. The method can be applied to any point group. For the specific example of the D_6h group, it is demonstrated that computations in the new basis are faster by a factor of 3.6 as compared with computations that use the reducible basis. Most importantly, the method is capable of extending the range of size parameters for which convergent results can be obtained by 50%.

© 2005 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(290.5850) Scattering : Scattering, particles

Citation
Michael Kahnert, "Irreducible representations of finite groups in the T-matrix formulation of the electromagnetic scattering problem," J. Opt. Soc. Am. A 22, 1187-1199 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-6-1187

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