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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 644–651

Focusing of vortex beams: Lommel treatment

C. J. R. Sheppard  »View Author Affiliations

JOSA A, Vol. 31, Issue 3, pp. 644-651 (2014)

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Focusing of vortex beams by a lens with circular aperture in the paraxial scalar Debye regime is analyzed. The amplitude in the focal region can be expressed naturally in terms of higher order Lommel functions of two variables. Using recurrence relationships, these can then be expressed in terms of low-order Lommel functions. The phase variation in the focal region is investigated, showing some interesting behavior of the Gouy phase anomaly.

© 2014 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(110.2990) Imaging systems : Image formation theory
(260.1960) Physical optics : Diffraction theory
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Diffraction and Gratings

Original Manuscript: October 7, 2013
Manuscript Accepted: January 14, 2014
Published: February 25, 2014

C. J. R. Sheppard, "Focusing of vortex beams: Lommel treatment," J. Opt. Soc. Am. A 31, 644-651 (2014)

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