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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. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2659–2669

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Ljiljana Janicijevic and Suzana Topuzoski  »View Author Affiliations

JOSA A, Vol. 25, Issue 11, pp. 2659-2669 (2008)

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Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges m p and m p , are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the m p th -order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p = 0 ; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.

© 2008 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1970) Diffraction and gratings : Diffractive optics
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Physical Optics

Original Manuscript: June 25, 2008
Manuscript Accepted: August 24, 2008
Published: October 10, 2008

Ljiljana Janicijevic and Suzana Topuzoski, "Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings," J. Opt. Soc. Am. A 25, 2659-2669 (2008)

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  1. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147-1154 (1992). [CrossRef]
  2. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321-327 (1994). [CrossRef]
  3. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Sofier, H. Elfstrom, and J. Turunen, “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). [CrossRef]
  4. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748-1754 (1989). [CrossRef] [PubMed]
  5. J. A. Davis, E. Carcole, and D. M. Cottrell, “Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator,” Appl. Opt. 35, 593-598 (1996). [CrossRef] [PubMed]
  6. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Yu. Moiseev, and V. 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). [CrossRef]
  7. V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis'ma Zh. Eksp. Teor. Fiz. 52, 1037-1039 (1990).
  8. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951-S962 (1992). [CrossRef]
  9. G. F. Brand, “Phase singularities in beams,” Am. J. Phys. 67, 55-60 (1999). [CrossRef]
  10. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217-223 (1995). [CrossRef]
  11. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221-223 (1992). [CrossRef] [PubMed]
  12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992). [CrossRef] [PubMed]
  13. V. V. Kotlyar and A. A. Kovalev, “Family of hypergeometric laser beams,” J. Opt. Soc. Am. A 25, 262-270 (2008). [CrossRef]
  14. N. Friedman, A. Kaplan, and N. Davidson, “Dark optical traps for cold atoms,” in Advances in Atomic, Molecular and Optical Physics (Elsevier Science, 2002), pp. 101-106.
  15. J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B: Lasers Opt. 71, 549-554 (2000). [CrossRef]
  16. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297-301 (2000). [CrossRef]
  17. Lj. Janicijevic and S. Topuzoski, “Diffraction of nondiverging Bessel beams by fork-shaped and rectilinear grating,” in Proceedings of the Sixth International Conference of the Balkan Physical Union (American Institute of Physics, 2007), Vol. 899, pp. 333-334.
  18. Lj. Janicijevic, J. Mozer, and M. Jonoska, “Diffraction properties of circular and linear zone plates with trapezoid profile of the phase layer,” Bulletin des Sociétés des Physiciens de la Rep. Soc. de Macedoine 28, 23-29 (1978) (in Macedonian).
  19. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  20. H. Bateman and A. Erdelyi, Higher Transcendental Functions II (Nauka, 1974).
  21. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964).
  22. D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054-3065 (1997). [CrossRef]
  23. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73-87 (1993). [CrossRef]

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