Superposition of Kummer beams

produced by a spiral phase plate

from Goriís flattened-Gaussian beams


F. Khannous, L. Ez-zariy, H. Nebdi, M. Khouilid, A. Belafhal*

Laboratory of Nuclear, Atomic and Molecular Physics
Department of Physics, Faculty of Sciences, ChouaÔb Doukkali University,

P. B 20, 24000 El Jadida, Morocco

* Corresponding author. E-mail:

Received: 13 March 2013; revised version accepted: 10 September 2013



    In this work, using a Spiral Phase Plate (SPP) the superposition of Kummer beams as a novel family of doughnut beams and solution of Helmholtz equation is generated from Goriís flattened-Gaussian (GFTG) beams. Based on Collins-Huygens integral formula an analytical expression of the produced superposition of Kummer beams through a paraxial optical ABCD is developed. The propagations of GFTG beams through an SPP followed by a free space and by a lens system are numerically investigated respectively. The propagation of GTFG beams through an optical system without SPP and the propagation of Gaussian beams travelling an SPP followed by an optical system are derived as particular cases of our main finding. The propagation of GTFG beams in an SPP, followed by a free space and through a telescope, is also given, in the work, as examples of numerical simulations.


Keywords: Superposition of Kummer beams; Spiral Phase Plate; Goriís flattened-Gaussian beams; ABCD-treatment; Telescope.

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