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Orbital angular momentum and topological charge of structurally stable laser beams
V.V. Kotlyar 1,2, A.A. Kovalev 1,2, A.M. Telegin 1,2

1 Image Processing Systems Institute, NRC “Kurchatov Institute”,
Molodogvardeyskaya 151, Samara, 443001, Russia;
2 Samara National Research University,
Moskovskoye Shosse 34, Samara, 443086, Russia

 PDF, 1761 kB

DOI: 10.18287/2412-6179-CO-1676

Pages: 940-946.

Full text of article: Russian language.

Abstract:
We analyze various types of structurally stable paraxial laser beams with a finite number of intensity nulls. In more detail, we study structurally stable beams with complex amplitude equal to a complex polynomial of degree n with a Gaussian envelope. We obtain an expression for the orbital angular momentum of such beams and show that for arbitrary complex polynomial coefficients, the topological charge of such beams is equal to the degree of the polynomial, n. As an example of such beams, a rotating Laguerre-Gaussian beam is investigated, whose topological charge is equal to the radial index of the Laguerre polynomial. On the optical axis, such a beam has a nonzero intensity, while all intensity nulls lie on a straight line to the right from the optical axis and rotate counterclockwise by an angle of π/2 upon free-space beam propagation.

Keywords:
structurally stable beam, orbital angular momentum, topological charge.

Citation:
Kotlyar VV, Kovalev AA, Telegin AM. Orbital angular momentum and topological charge of structurally stable laser beams. Computer Optics 2025; 49(6): 940-946. DOI: 10.18287/2412-6179-CO-1676.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #22-12-00137 (theory) and within a government project of the NRC "Kurchatov Institute" (numerical simulation).

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