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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 6 h 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

History
Original Manuscript: November 19, 2004
Manuscript Accepted: January 11, 2005
Published: June 1, 2005

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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References

  1. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Point-group symmetries in electromagnetic scattering,” J. Opt. Soc. Am. A 16, 853–865 (1999). [CrossRef]
  2. F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to homogeneous particles with point-group symmetries,” Appl. Opt. 40, 3110–3123 (2001). [CrossRef]
  3. F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Can simple particle shapes be used to model scalar optical properties of an ensemble of wavelength-sized particles with complex shapes?,” J. Opt. Soc. Am. A 19, 521–531 (2002). [CrossRef]
  4. F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations,” J. Quant. Spectrosc. Radiat. Transf. 74, 167–182 (2002). [CrossRef]
  5. F. M. Kahnert, “Reproducing the optical properties of fine desert dust aerosols using ensembles of simple model particles,” J. Quant. Spectrosc. Radiat. Transf. 85, 231–249 (2004). [CrossRef]
  6. M. Kahnert, A. Kylling, “Radiance and flux simulations for mineral dust aerosols: assessing the error due to using spherical or spheroidal model particles,” J. Geophys. Res. 109, D09203 doi:10.1029/2003JD004318; errata; doi:10.1029/2004JD005311 (2004).
  7. T. Nousiainen, M. Kahnert, B. Veihelmann, “Light scattering modeling of small feldspar aerosol particles using polyhedral prisms and spheroids,” J. Quant. Spectrosc. Radiat. Transf. (to be published).
  8. I. A. Zagorodnov, R. P. Tarasov, “Finite groups in numerical solution of electromagnetic scattering problems on non-spherical particles,” in Light Scattering by Nonspherical Particles: Halifax Contributions (Army Research Laboratory, Adelphi, Md., 2000), pp. 99–102.
  9. T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetic Research (PIER), J. A. Kong, ed. (EMW, Cambridge, Mass., 2002), Vol. 38, pp. 47–95. [CrossRef]
  10. D. M. Bishop, Group Theory and Chemistry (Dover, Mineola, N.Y., 1993).
  11. S. Havemann, A. J. Baran, “Extension of T matrix to scattering of electromagnetic plane waves by non-axisymmetric dielectric particles: application to hexagonal ice cylinders,” J. Quant. Spectrosc. Radiat. Transf. 70, 139–158 (2001). [CrossRef]
  12. M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).
  13. F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003). [CrossRef]
  14. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965). [CrossRef]
  15. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998). [CrossRef]
  16. T. A. Niemen, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1019–1029 (2003). [CrossRef]
  17. D. W. Mackowski, “Discrete dipole moment method for computing the T matrix for nonspherical particles,” J. Opt. Soc. Am. A 19, 881–893 (2002). [CrossRef]
  18. D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996). [CrossRef]
  19. J. D. Dixon, “High speed computation of group characters,” Numer. Math. 10, 446–450 (1965). [CrossRef]
  20. J. J. Cannon, “Computers in group theory: a survey,” Commun. ACM 12, 3–11 (1969). [CrossRef]
  21. D. C. Harris, M. D. Bertolucci, Symmetry and Spectroscopy (Oxford U. Press, New York, 1978).
  22. M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994). [CrossRef]
  23. S. Havemann, A. J. Baran, “Calculation of the phase matrix elements of elongated hexagonal ice columns using the T-matrix method,” in Electromagnetic and Light Scattering—Theory and Applications VII, T. Wriedt, ed. (Universität Bremen, Bremen, Germany, 2003), pp. 107–110.
  24. D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997). [CrossRef] [PubMed]
  25. M. Hamermesh, Group Theory and Its Application to Physical Problems (Dover, New York, 1989).

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