OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 2 — Feb. 1, 2008
  • pp: 255–260

Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients

Huayong Zhang and Yiping Han  »View Author Affiliations


JOSA B, Vol. 25, Issue 2, pp. 255-260 (2008)
http://dx.doi.org/10.1364/JOSAB.25.000255


View Full Text Article

Enhanced HTML    Acrobat PDF (118 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The translational addition theorem for the spherical vector wave functions (SVWFs) of the first kind is derived in an integral form by the use of the relations between the SVWFs and cylindrical vector wave functions. The integral representation provides a theoretical procedure for the calculation of the beam shape coefficients in the generalized Lorenz–Mie theory. The beam shape coefficients in the cylindrical or spheroidal coordinates, which correspond to an arbitrarily oriented infinite cylinder or spheroid, can be obtained conveniently by using the addition theorem for the SVWF under coordinate rotations and the expansions of the SVWF in terms of the cylindrical or spheroidal vector wave functions.

© 2008 Optical Society of America

OCIS Codes
(140.3430) Lasers and laser optics : Laser theory
(260.2110) Physical optics : Electromagnetic optics
(290.4020) Scattering : Mie theory

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: August 6, 2007
Manuscript Accepted: December 9, 2007
Published: January 30, 2008

Citation
Huayong Zhang and Yiping Han, "Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients," J. Opt. Soc. Am. B 25, 255-260 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-2-255


Sort:  Year  |  Journal  |  Reset  

References

  1. L. W. Davis, "Theory of electromagnetic beam," Phys. Rev. A 19, 1177-1179 (1979). [CrossRef]
  2. J. P. Barton and D. R. Alexander, "Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989). [CrossRef]
  3. G. Gouesbet, B. Maheu, and G. Gréhan, "Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation," J. Opt. Soc. Am. A 5, 1427-1443 (1988). [CrossRef]
  4. G. Gouesbet, G. Gréhan, and B. Maheu, "Computations of the gn coefficients in the generalized Lorenz-Mie theory using three different methods," Appl. Opt. 27, 4874-4883 (1988). [CrossRef] [PubMed]
  5. G. Gouesbet, G. Gréhan, and B. Maheu, "Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory," J. Opt. Soc. Am. A 7, 998-1003 (1990). [CrossRef]
  6. B. Friedman and J. Russek, "Addition theorems for spherical waves," Q. Appl. Math. 12, 13-23 (1954).
  7. S. Stein, "Addition theorems for spherical wave functions," Q. Appl. Math. 19, 15-24 (1961).
  8. O. R. Cruzan, "Translational addition theorems for spherical vector wave functions," Q. Appl. Math. 20, 33-40 (1962).
  9. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, 1957).
  10. J. H. Bruning and Y. T. Lo, "Multiple scattering of EM waves by spheres part I -- multipole expansion and ray-optical solution," IEEE Trans. Antennas Propag. 19, 378-390 (1971). [CrossRef]
  11. A. Doicu and T. Wriedt, "Computation of the beam-shape coefficients in the generalized Lorenz-Mie theory by using the translational addition theorem for spherical vector wave functions," Appl. Opt. 36, 2971-2978 (1997). [CrossRef] [PubMed]
  12. A. Doicu and T. Wriedt, "Plane wave spectrum of electromagnetic beams," Opt. Commun. 136, 114-124 (1997). [CrossRef]
  13. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  14. H. Y. Zhang, Y. P. Han, and G. X. Han, "Expansion of the electromagnetic fields of a shaped beam in terms of cylindrical vector wave functions," J. Opt. Soc. Am. A 24, 1383-1391 (2007).
  15. Y. Han, H. Zhang, and X. Sun, "Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries," Appl. Phys. B 84, 485-492 (2006). [CrossRef]
  16. Y. P. Han, H. Y. Zhang, and G. X. Han, "Expansion of shaped beam with respect to an arbitrarily oriented spheroidal particle," Opt. Express 15, 735-746 (2007). [PubMed]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  18. C. Flammer, Spheroidal Wave Functions (Stanford U. Press, 1957).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited