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Sectorial perturbation of vortex beams: Shannon entropy, orbital angular momentum and topological charge

A.V. Volyar1, M.V. Bretsko1, Ya.E. Akimova1, Yu.A. Egorov1, V.V. Milyukov1

Physics and Technology Institute of V.I. Vernadsky Crimean Federal University,  
Academician Vernadsky 4, 295007, Simferopol, Russia

 PDF, 2977 kB

DOI: 10.18287/2412-6179-2019-43-5-723-734

Pages: 723-734.

Full text of article: Russian language.

Transformations of the vortex beams structure subjected to sectorial perturbation were theoretically and experimentally studied. The analysis was based on computing (measuring) the vortex spectrum that enables us to find the orbital angular momentum (OAM) and Shannon entropy (informational entropy). We have revealed that, in the general case, the number of vortices caused by an external perturbation is not related to the topological charge. For arbitrary perturbation, the topological charge remains equal to the initial topological charge of the unperturbed vortex beam. Growth of the vortex number induced by perturbations is associated with the optical uncertainty principle between the sectorial angle and the OAM. The computer simulation has shown that OAM does not depend on the number of vortices induced by perturbations. Moreover, two maxima are formed both in the positive and negative regions of the vortex spectrum. As a result, the OAM does not practically change in a wide range of perturbation angles from 0 to 90 °. However, at large perturbation angles, when the energy is almost equally redistributed between the vortex modes with opposite signs of the topological charge, the OAM rapidly decreases. At the same time, the Shannon entropy monotonically increases with growing perturbation angle. This is due to the fact that the entropy depends only on the number of vortex states caused by external perturbations.

diffractive optics, optical vortices, orbital angular momentum, moments of intensity.

Volyar AV, Bretsko MV, Akimova YaE, Egorov YuA, Milyukov VV. Sectorial perturbation of vortex beams: Shannon entropy, orbital angular momentum and topological charge. Computer Optics 2019; 43(5): 723-734. DOI: 10.18287/2412-6179-2019-43-5-723-734.

The reported study was funded by the Russian Foundation for Basic Research under RFBR grant No. 19-29-01233 and grant ВГ24, "V.I. Vernadsky Crimean Federal University Development Program in 2015–2024".


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