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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21205–21210

ABCD-treatment of a propagating doughnut beam generated by a spiral phase plate

A. Mawardi, S. Hild, A. Widera, and D. Meschede  »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 21205-21210 (2011)

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We apply the Collins-Huygens integral to analytically describe propagation of a doughnut beam generated by a spiral phase plate. Measured beam profiles in free space and through an ABCD-lens system illustrate excellent agreement with theory. Applications range from the creation of optical beams with angular momentum to microscopy to trapping neutral atoms. The method extends to other beam shaping components, too.

© 2011 OSA

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(050.4865) Diffraction and gratings : Optical vortices
(080.4865) Geometric optics : Optical vortices

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: July 29, 2011
Revised Manuscript: September 16, 2011
Manuscript Accepted: September 18, 2011
Published: October 10, 2011

Virtual Issues
Vol. 6, Iss. 11 Virtual Journal for Biomedical Optics

A. Mawardi, S. Hild, A. Widera, and D. Meschede, "ABCD-treatment of a propagating doughnut beam generated by a spiral phase plate," Opt. Express 19, 21205-21210 (2011)

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  1. T. A. Klar and S. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24, 954 (1999) [CrossRef]
  2. T. Kuga, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78, 4713 (1997) [CrossRef]
  3. A. Kaplan, N. Friedman, and N. Davidson, “Optimized single-beam dark optical trap,” J. Opt. Soc. Am. B 19, 1233 (2002) [CrossRef]
  4. P. Xu, X. He, J. Wang, and M. Zhan, “Trapping a single atom in a blue detuned optical bottle beam trap”, Opt. Lett. 35, 2164 (2010) [CrossRef] [PubMed]
  5. D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740 (2003) [CrossRef] [PubMed]
  6. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum, Taylor and Francis, (2003) [CrossRef]
  7. M.R. Dennis, K. O’Holleran, and M.J. Padgettin “Progress in Optics,”  53, 293–363 (2009)
  8. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts”, J. Mod. Opt. 39, 985 (1992) [CrossRef]
  9. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221 (1992) [CrossRef] [PubMed]
  10. E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123 (1991) [CrossRef]
  11. M. Padgett, J. Arlt, N. Simpson, and L. Allen, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,”, Am. J. Phys. 64, 77 (1996) [CrossRef]
  12. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147 (1992) [CrossRef]
  13. M.W. Beijersbergen and et al., “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321 (1994) [CrossRef]
  14. J. H. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968)
  15. D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation Dynamics in Optical Vortices,” J. Opt. Soc. Am. B 14, 3054 (1997) [CrossRef]
  16. Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Soc. Am. 15, (1998)
  17. S. A. Collins, “Lens-System Diffraction Integral Written in Terms of Matrix Optics,” J. Opt. Soc. Am.60, 1168 (1970); A. Siegman, Lasers, University Science Books (Mill Valley 1986), p. 781 [CrossRef]
  18. I. S. Gradshteyn and I. M. Rhyzhik, Table of Integrals, Series, and Products, Academic Press (San Diego1979)

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