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JOURNALS // Computer Optics // Archive

Computer Optics, 2022 Volume 46, Issue 6, Pages 864–871 (Mi co1079)

This article is cited in 3 papers

DIFFRACTIVE OPTICS, OPTICAL TECHNOLOGIES

Topological charge of superposition of optical vortices described by a geometric sequence

V. V. Kotlyarab, A. A. Kovalevab

a Image Processing Systems Institute of the RAS - Branch of the FSRC "Crystallography and Photonics" RAS, Samara, Russia, Samara
b Samara National Research University

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

Received: 22.04.2022
Accepted: 25.05.2022

DOI: 10.18287/2412-6179-CO-1152



© Steklov Math. Inst. of RAS, 2025