Theoretical conversion of the hypergeometric-Gaussian beams family into a high-order spiraling Bessel beams by a curved fork-shaped hologram

  • A. A. A. Ebrahim
  • F. Saad
  • L. Ez-zariy
  • A. Belafhal


Based on the process of the Fresnel diffraction, the possibility of generating a new type of laser beams family by illuminating a curved fork-shaped hologram, with an input hypergeometric-Gaussian beams family of orders n and m is studied in this paper. The theoretical and the numerical results showed that, at the output plane, a high order spiraling Bessel vortex beam is produced. This vortex beam is divergence or non-divergence depending upon the waist position of the input hypergeometric-Gaussian beams, regarding the plane where the curved fork-shaped hologram is situated. Analytical expressions of the amplitude and the intensity distribution of the diffracted wave field are calculated and deduced using the stationary phase method. The actual work generalizes also the Fresnel diffraction study of some subfamilies of the hypergeometric-Gaussian beams family, such as: fundamental Gaussian, hollow Gaussian, modified quadratic Bessel–Gaussian and elegant Laguerre–Gaussian beams.


Fresnel diffraction Hypergeometric-Gaussian beams family Spiraling Bessel beams Curved fork-shaped hologram 



The first and second authors were supported by the Ministry of higher Education and Scientific Research and the Ministry of Education of Yemen.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • A. A. A. Ebrahim
    • 1
  • F. Saad
    • 1
  • L. Ez-zariy
    • 1
  • A. Belafhal
    • 1
  1. 1.Laboratory of Nuclear, Atomic and Molecular Physics, Department of Physics, Faculty of SciencesChouaïb Doukkali UniversityEl JadidaMorocco

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