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Sinusoidal Gaussian optical vortex as a superposition of two hypergeometric beams
V.V. Kotlyar 1,2, A.A. Kovalev 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1253 kB

DOI: 10.18287/2412-6179-CO-1008

Pages: 16-21.

Full text of article: Russian language.

Abstract:
We analyze the propagation of hypergeometric beams with a parabolic initial wavefront in a homogeneous medium. While hypergeomentric beams have a central amplitude singularity in the initial plane and are of infinite energy, superposition of two such beams has no singularity and is of finite energy. A particular case of such a superposition we study in detail is a sinusoidal Gaussian beam with a unit topological charge. This beam belongs to the class of elegant laser beams since it is described by the same complex-argument function both in the initial plane and in the Fresnel diffraction zone. The diameter of the first light ring of the sinusoidal Gaussian beam is almost independent of the Gaussian beam waist radius.

Keywords:
optical vortex, hypergeometric beam, beam energy, sinusoidal beam, light ring diameter.

Citation:
Kotlyar VV, Kovalev AA. Sinusoidal Gaussian optical vortex as a superposition of two hypergeometric beams. Computer Optics 2022; 46(1): 16-21. DOI: 10.18287/2412-6179-CO-1008.

Acknowledgements:
This work was supported by the Russian Science Foundation (project No. 18-19-00595, Section "Elegant sinusoidal Gaussian vortex with a unit topological charge", and project No. 22-22-00265, Sections "Hypergeometric beam with an initial parabolic wavefront" and "Linear combination of the hypergeometric beams"), and by the RF Ministry of Science and Higher Education within the State assignment of FSRC “Crystallography and Photonics” RAS (Section "Simulation").

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