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

  • Vol. 21, Iss. 9 — Sep. 1, 2004
  • pp: 1805–1810

On the angular-spectrum representation of multipole wave fields

Riccardo Borghi  »View Author Affiliations


JOSA A, Vol. 21, Issue 9, pp. 1805-1810 (2004)
http://dx.doi.org/10.1364/JOSAA.21.001805


View Full Text Article

Enhanced HTML    Acrobat PDF (144 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The closed-form expression of the angular spectrum of multipole fields, both scalar and vectorial, of any order and degree, evaluated across a plane orthogonal to an arbitrary (fixed) direction, is provided. Such a result has been obtained by starting from the Weyl representation of multipole fields and using suitable transformation rules. Moreover, as far as the vectorial case is concerned, knowledge of the (vectorial) transverse angular spectrum allows one to gain some insight into the polarization structure of the multipole fields evaluated across a typical plane. Such information could be useful, for instance, in those problems dealing with the interaction between planar partially reflecting surfaces and waves.

© 2004 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: February 11, 2004
Revised Manuscript: April 13, 2004
Manuscript Accepted: April 13, 2004
Published: September 1, 2004

Citation
Riccardo Borghi, "On the angular-spectrum representation of multipole wave fields," J. Opt. Soc. Am. A 21, 1805-1810 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-9-1805


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Weyl, “Ausbreitung elektromagnetischer Wallen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919). [CrossRef]
  2. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  3. A. J. Devaney, E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974). [CrossRef]
  4. P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986). [CrossRef]
  5. T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998). [CrossRef]
  6. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, Oxford, UK, 1966).
  7. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), Sec. 13.2.1.
  8. A. T. Friberg, E. Wolf, “Angular spectrum representation of scattered electromagnetic fields,” J. Opt. Soc. Am. 73, 26–32 (1983). [CrossRef]
  9. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), Sec. 3.2.4.
  10. A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Sec. 2.13.
  11. E. Wolf, M. Nieto-Vesperinas, “Analiticity of the angular spectrum amplitude of scattered fields and some of its consequences,” J. Opt. Soc. Am. A 2, 886–890 (1985). [CrossRef]
  12. Note that the definition given in Eq. (7) is intended to be valid when m>0.Spherical harmonics evaluated for negative values of mare given by (38)Yl,m(α, β)=(-1)mYl,-m*(α, β),with the asterisk denoting the complex conjugate.
  13. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. (Academic, New York, 2000), Sec. 8.81.
  14. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998).
  15. C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (Wiley, New York, 1977).

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 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited