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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 8 — Aug. 10, 2007

Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate

Victor V. Kotlyar, Alexey A. Kovalev, Roman V. Skidanov, Oleg Yu. Moiseev, and Victor A. Soifer  »View Author Affiliations


JOSA A, Vol. 24, Issue 7, pp. 1955-1964 (2007)
http://dx.doi.org/10.1364/JOSAA.24.001955


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Abstract

We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n = 10 ) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 μ m .

© 2007 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(140.7010) Lasers and laser optics : Laser trapping

ToC Category:
Diffraction and Gratings

History
Original Manuscript: November 15, 2006
Manuscript Accepted: December 30, 2006
Published: June 13, 2007

Virtual Issues
Vol. 2, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Victor V. Kotlyar, Alexey A. Kovalev, Roman V. Skidanov, Oleg Yu. Moiseev, and Victor A. Soifer, "Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate," J. Opt. Soc. Am. A 24, 1955-1964 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-24-7-1955

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