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Optics Letters

Optics Letters


  • Vol. 36, Iss. 17 — Sep. 1, 2011
  • pp: 3482–3484

Simplified expressions of the T-matrix integrals for electromagnetic scattering

Walter R. C. Somerville, Baptiste Auguié, and Eric C. Le Ru  »View Author Affiliations

Optics Letters, Vol. 36, Issue 17, pp. 3482-3484 (2011)

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The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.

© 2011 Optical Society of America

OCIS Codes
(290.0290) Scattering : Scattering
(290.5850) Scattering : Scattering, particles
(290.5825) Scattering : Scattering theory

ToC Category:

Original Manuscript: July 15, 2011
Revised Manuscript: August 10, 2011
Manuscript Accepted: August 15, 2011
Published: September 1, 2011

Walter R. C. Somerville, Baptiste Auguié, and Eric C. Le Ru, "Simplified expressions of the T-matrix integrals for electromagnetic scattering," Opt. Lett. 36, 3482-3484 (2011)

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  1. P. C. Waterman, Phys. Rev. D 3, 825 (1971). [CrossRef]
  2. P. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975). [PubMed]
  3. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990). [CrossRef]
  4. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves (Wiley, 2000). [CrossRef]
  5. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles, 3rd ed. (Cambridge University, 2002).
  6. A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles: Null-field Method with Discrete Sources: Theory and Programs, Springer Series in Optical Sciences (Springer, 2006), Vol.  124.
  7. P. C. Waterman, Proc. IEEE 53, 805 (1965). [CrossRef]
  8. M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, J. Quant. Spectrosc. Radiat. Transfer 88, 357 (2004).
  9. J. B. Schneider and I. C. Peden, IEEE Trans. Antennas Propag. 36, 1317 (1988). [CrossRef]
  10. F. Kahnert, J. Stamnes, and K. Stamnes, Appl. Opt. 40, 3110 (2001). [CrossRef]
  11. R. Boyack and E. C. Le Ru, Phys. Chem. Chem. Phys. 11, 7398 (2009). [CrossRef] [PubMed]
  12. B. N. Khlebtsov and N. G. Khlebtsov, J. Phys. Chem. C 111, 11516 (2007). [CrossRef]
  13. P. W. Barber, R. K. Chang, and H. Massoudi, Phys. Rev. B 27, 7251 (1983). [CrossRef]
  14. P. W. Barber, R. K. Chang, and H. Massoudi, Phys. Rev. Lett. 50, 997 (1983). [CrossRef]
  15. P. C. Waterman, J. Acoust. Soc. Am. 45, 1417 (1969). [CrossRef]
  16. B. Peterson and S. Ström, Phys. Rev. D 10, 2670 (1974). [CrossRef]
  17. B. Peterson and S. Ström, Phys. Rev. D 8, 3661 (1973). [CrossRef]
  18. A. Doicu and T. Wriedt, Optics Commun. 139, 85 (1997). [CrossRef]
  19. A. Doicu and T. Wriedt, J. Quant. Spectrosc. Radiat. Transfer 111, 466 (2010). [CrossRef]
  20. F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 043824 (2010). [CrossRef]
  21. D. Petrov, Y. Shkuratov, and G. Videen, Opt. Lett. 32, 1168 (2007). [CrossRef] [PubMed]
  22. M. Mishchenko and L. Travis, Optics. Commun. 109, 16 (1994). [CrossRef]
  23. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

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