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Topological charge of superposition of optical vortices described by a geometric sequence
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, 1410 kB

DOI: 10.18287/2412-6179-CO-1152

Pages: 864-871.

Full text of article: Russian language.

Abstract:
Here, we investigate coaxial superpositions of Gaussian optical vortices that can be described by a geometric sequence. For all superpositions analyzed, a topological charge (TC) is derived. In the initial plane, the TC can be either integer or half-integer, acquiring an integer value upon free-space propagation of the light field. Generally, the geometric sequence of optical vortices (GSOV) has three integer parameters and one real parameter. Values of these four parameters define the TC of the GSOV. Upon free-space propagation, the intensity pattern of the GSOV is not conserved, but can have intensity petals whose number is equal to one of the four beam parameters. If the GSOV has a unit real parameter, all constituent angular harmonics in the superposition have the same weight. In this case, the TC of the superposition is equal to the average index of the constituent angular harmonics. For instance, if the TC of the first and of the last angular harmonics, respectively, equals k and n, then the total TC of the superposition in the initial plane will be (n + k) /2, becoming equal to n upon free-space propagation.

Keywords:
optical vortex, superposition, geometric sequence, topological charge.

Citation:
Kotlyar VV, Kovalev AA. Topological charge of a superposition of optical vortices described by a geometric sequence. Computer Optics 2022; 46(6): 864-871. DOI: 10.18287/2412-6179-CO-1152.

Acknowledgements:
The work was funded by the Russian Science Foundation grant 22-12-00137 (theory), as well as by the Ministry of Science and Higher Education of the Russian Federation within the government project of the FSRC “Crystallography and Photonics” RAS (simulation).

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