OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 11 — Nov. 1, 2006
  • pp: 2803–2809

Partial-wave expansions of angular spectra of plane waves

James A. Lock  »View Author Affiliations


JOSA A, Vol. 23, Issue 11, pp. 2803-2809 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002803


View Full Text Article

Enhanced HTML    Acrobat PDF (106 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Focused electromagnetic beams are frequently modeled by either an angular spectrum of plane waves or a partial-wave sum of spherical multipole waves. The connection between these two beam models is explored here. The partial-wave expansion of an angular spectrum containing evanescent components is found to possess only odd partial waves. On the other hand, the partial-wave expansion of an alternate angular spectrum constructed so as to be free of evanescent components contains all partial waves but describes a propagating beam with a small amount of standing-wave component mixed in. A procedure is described for minimizing the standing-wave component so as to more accurately model a purely forward propagating experimental beam.

© 2006 Optical Society of America

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(290.4020) Scattering : Mie theory

ToC Category:
Scattering

History
Original Manuscript: March 16, 2006
Revised Manuscript: May 22, 2006
Manuscript Accepted: May 23, 2006

Citation
James A. Lock, "Partial-wave expansions of angular spectra of plane waves," J. Opt. Soc. Am. A 23, 2803-2809 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-11-2803


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 48-51.
  2. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980), pp. 561-564.
  3. C. Yeh, S. Colak, and P. Barber, "Scattering of sharply focused beams by arbitrarily shaped dielectric particles: an exact solution," Appl. Opt. 21, 4426-4433 (1982). [CrossRef] [PubMed]
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), p. 121.
  5. J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988). [CrossRef]
  6. G. Gouesbet, B. Maheu, and G. Grehan, "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]
  7. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), pp. 122-125.
  8. D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson Prentice Hall, 2005), p. 418.
  9. K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer, 2003), pp. 84-85, Eqs. (354) and (355).
  10. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1965), p. 761, Eq. (6.738.1).
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 43-45.
  12. O. R. Cruzan, "Translational addition theorems for spherical vector wave functions," Q. Appl. Math. 20, 33-40 (1962), App. B, Eqs. (B.1) and (B.2).
  13. A. Messiah, Quantum Mechanics (Wiley, 1966), Vol. 1, p. 497, Eqs. (B.99)-(B.101).
  14. Ref. , p. 684, Eq. (6.561.14).
  15. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1965), p. 545, Eq. (10.33b).
  16. A. Messiah, Quantum Mechanics (Wiley, 1966), Vol. 2, pp. 1057-1059, Eqs. (C.16), (C.22), (C.23a), and (C.23b).
  17. J. A. Lock, "Excitation of morphology-dependent resonances and van de Hulst's localization principle," Opt. Lett. 24, 427-429 (1999). [CrossRef]
  18. A. Messiah, Quantum Mechanics (Wiley, 1966), Vol. 1, p. 497, Eq. (B105).
  19. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1965), pp. 629-630, Eqs. (11.174) and (11.175).
  20. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1965), p. 716, Eq. (6.631.1).
  21. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1965), p. 753, Eq. (13.134).
  22. B. Maheu, G. Grehan, and G. Gousebet, "Ray localization in Gaussian beams," Opt. Commun. 70, 259-262 (1989). [CrossRef]
  23. G. Gouesbet, J. A. Lock, and G. Grehan, "Partial-wave representations of laser beams for use in light-scattering calculations," Appl. Opt. 34, 2133-2143 (1995). [CrossRef] [PubMed]
  24. J. A. Lock and J. T. Hodges, "Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle," Appl. Opt. 35, 4283-4290 (1996). [CrossRef] [PubMed]
  25. J. A. Lock and J. T. Hodges, "Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle," Appl. Opt. 35, 6605-6616 (1996). [CrossRef] [PubMed]
  26. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), pp. 208-209.

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited