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Asymmetric hypergeometric laser beams

V.V. Kotlyar1,2, A.A. Kovalev1,2, E.G. Abramochkin3

1 IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS,  
Molodogvardeyskaya 151, 443001, Samara, Russia,  
2 Samara National Research University,
Moskovskoye Shosse 34, 443086, Samara, Russia,  
3 Samara Branch of P.N. Lebedev Physical Institute of Russian Academy of Sciences, Samara, Russia

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DOI: 10.18287/2412-6179-2019-43-5-735-740

Pages: 735-740.

Full text of article: Russian language.

Abstract:
Here we study asymmetric Kummer beams (aK-beams) with their scalar complex amplitude being proportional to the Kummer function (a degenerate hypergeometric function). These beams are an exact solution of the paraxial propagation equation (Schrödinger-type equation) and obtained from the conventional symmetric hypergeometric beams by a complex shift of the transverse coordinates. On propagation, the aK-beams change their intensity weakly and rotate around the optical axis. These beams are an example of vortex laser beams with a fractional orbital angular momentum (OAM), which depends on four parameters: the vortex topological charge, the shift magnitude, the logarithmic axicon parameter and the degree of the radial factor. Changing these parameters, it is possible to control the beam OAM, either continuously increasing or decreasing it.

Keywords:
optical vortex, asymmetric laser beam, Kummer function, hypergeometric function, logarithmical axicon, orbital angular momentum.

Citation:
Kotlyar VV, Kovalev AA, Abramochkin EG. Asymmetric hypergeometric laser beams. Computer Optics 2019; 43(5): 735-740. DOI: 10.18287/2412-6179-2019-43-5-734-740.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #18-19-00595 ("Shifted Kummer beams"), the Russian Foundation for Basic Research under grant # 18-29-20003 ("Orbital angular momentum of the asymmetrical Kummer beam"), and the RF Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS under agreement 007-ГЗ/Ч3363/26 ("Numerical simulation").

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