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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 1 — Jan. 1, 2009
  • pp: 142–146

Hollow vortex beams

Shunichi Sato and Yuichi Kozawa  »View Author Affiliations

JOSA A, Vol. 26, Issue 1, pp. 142-146 (2009)

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Hollow beam formation of radially and azimuthally polarized vortex beams, which has arbitrary topological charge, is analytically discussed under the strong focusing condition. The expressions for the electric fields of the focused vector-vortex beams are obtained based on a vector diffraction theory. The order of the Bessel function of the first kind appearing in the expressions indicates the ability to form hollow beams. Similar discussion is applied for different vortex beams, which are expressed by linear combination of radially and azimuthally polarized beams. Calculations of intensity profiles across the focus are also presented.

© 2008 Optical Society of America

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(260.5430) Physical optics : Polarization
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Physical Optics

Original Manuscript: October 2, 2008
Revised Manuscript: November 12, 2008
Manuscript Accepted: November 12, 2008
Published: December 22, 2008

Shunichi Sato and Yuichi Kozawa, "Hollow vortex beams," J. Opt. Soc. Am. A 26, 142-146 (2009)

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  1. K. S. Youngworth and T. G. Brown, “Focusing of high numerical apterture cylindrical-vector beams,” Opt. Express 7, 77-87 (2000). [CrossRef] [PubMed]
  2. G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spatial phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190-196 (2007). [CrossRef]
  3. H. Kawauchi, Y. Kozawa, S. Sato, T. Sato, and S. Kawakami, “Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate,” Opt. Lett. 33, 399-401 (2008). [CrossRef] [PubMed]
  4. L. E. Helseth, “Focusing of atoms with strongly confined light potentials,” Opt. Commun. 212, 343-352 (2002). [CrossRef]
  5. G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 31, 11440-11445 (2006). [CrossRef]
  6. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959). [CrossRef]
  7. G. N. Watson, Theory of Bessel Functions (Cambridge U. Press, 1944).
  8. L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1-8 (2006). [CrossRef]

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