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Optics Letters

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  • Editor: Alan E. Willner
  • Vol. 35, Iss. 21 — Nov. 1, 2010
  • pp: 3652–3654

Constraints on spheroidal beam wavefunctions

John Lekner and Rufus Boyack  »View Author Affiliations


Optics Letters, Vol. 35, Issue 21, pp. 3652-3654 (2010)
http://dx.doi.org/10.1364/OL.35.003652


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Abstract

The oblate spheroidal wavefunctions proposed by Rodríguez-Morales and Chávez-Cerda are shown to be possible representations of physical beams only when the angular function S m n ( β , η ) has odd n m . This condition makes S m n odd in η, which ensures the convergence of integrals of physical quantities over a cross section of the beam. The odd n m condition also makes S m n ( β , η ) zero in the focal plane z = 0 outside the circle ρ = b , and thus allows for the physically necessary discontinuity in phase at z = 0 on the ellipsoidal surfaces of otherwise constant phase. Only a subset of the oblate spheroidal functions can be exact representations of nonparaxial scalar beams.

© 2010 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(140.3410) Lasers and laser optics : Laser resonators
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: August 10, 2010
Revised Manuscript: September 27, 2010
Manuscript Accepted: September 28, 2010
Published: October 26, 2010

Citation
John Lekner and Rufus Boyack, "Constraints on spheroidal beam wavefunctions," Opt. Lett. 35, 3652-3654 (2010)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-21-3652


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References

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  2. C. Flammer, Spheroidal Wavefunctions (Stanford U. Press, 1957).
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  11. A. April, J. Opt. Soc. Am. A 27, 76 (2010). [CrossRef]
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