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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 5 — May. 1, 2005
  • pp: 849–861

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate

Victor V. Kotlyar, Anton A. Almazov, Svetlana N. Khonina, Victor A. Soifer, Henna Elfstrom, and Jari Turunen  »View Author Affiliations


JOSA A, Vol. 22, Issue 5, pp. 849-861 (2005)
http://dx.doi.org/10.1364/JOSAA.22.000849


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Abstract

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity’s integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to ρ 2 n , where ρ is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with n th -order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity ( n = 2 ) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

© 2005 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics

History
Original Manuscript: July 29, 2004
Revised Manuscript: October 4, 2004
Manuscript Accepted: November 8, 2004
Published: May 1, 2005

Citation
Victor V. Kotlyar, Henna Elfstrom, Jari Turunen, Anton A. Almazov, Svetlana N. Khonina, and Victor A. Soifer, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate," J. Opt. Soc. Am. A 22, 849-861 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-5-849


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References

  1. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974). [CrossRef]
  2. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992). [CrossRef]
  3. V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992). [CrossRef]
  4. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993). [CrossRef]
  5. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]
  6. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997). [CrossRef]
  7. D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997). [CrossRef]
  8. Z. S. Sacks, D. Rozas, G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Soc. Am. B 15, 2226–2234 (1998). [CrossRef]
  9. G. Peele, K. A. Nugent, “X-ray vortex beams: a theoretical analysis,” Opt. Express 11, 2315–2322 (2003). [CrossRef] [PubMed]
  10. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004). [CrossRef]
  11. P. Prudnikov, Y. A. Brichkov, O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983).
  12. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
  13. E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997). [CrossRef]
  14. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef] [PubMed]
  15. R. Oron, N. Davidson, A. A. Friesem, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000). [CrossRef]
  16. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001). [CrossRef]
  17. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).
  18. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994). [CrossRef]
  19. S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, G. W. Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004). [CrossRef] [PubMed]

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