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Topological charge of optical vortices and their superpositions

V.V. Kotlyar 1,2, A.A. Kovalev  1,2, A.V. Volyar  3

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 Physics and Technology Institute of V.I. Vernadsky Crimean Federal University,

Academician Vernadsky 4, 295007, Simferopol, Russia

 PDF, 1603 kB

DOI: 10.18287/2412-6179-CO-685

Pages: 145-154.

Full text of article: Russian language.

Abstract:
An optical vortex passed through an arbitrary aperture (with the vortex center found within the aperture) or shifted from the optical axis of an arbitrary axisymmetric carrier beam is shown to conserve the integer topological charge (TC). If the beam contains a finite number of off-axis optical vortices with different TCs of the same sign, the resulting TC of the beam is shown to be equal to the sum of all constituent TCs. For a coaxial superposition of a finite number of the Laguerre-Gaussian modes (n, 0), the resulting TC equals that of the mode with the highest TC (including sign). If the highest positive and negative TCs of the constituent modes are equal in magnitude, then TC of the superposition is equal to that of the mode with the larger (in absolute value) weight coefficient. If both weight coefficients are the same, the resulting TC equals zero. For a coaxial superposition of two different-amplitude Gaussian vortices, the resulting TC equals that of the constituent vortex with the larger absolute value of the weight coefficient amplitude, irrespective of the relation between the individual TCs.

Keywords:
topological charge (TC), optical vortex, diaphragm, displacement, optical vortices superposition.

Citation:
Kotlyar VV, Kovalev AA, Volyar AV. Topological charge of optical vortices and their superpositions. Computer Optics 2020; 44(2): 145-154. DOI: 10.18287/2412-6179-CO-685.

Acknowledgements:
This work was supported by the Russian Foundation for Basic Research under RFBR grants ## 18-29-20003 ("TC of an optical vortex passing through an amplitude mask" and "TC of a coaxial superposition of optical vortices"), 19-29-01233 ("TC of an optical vortex with the initially fractional charge"), and 18-07-01129 ("TC of an optical vortex with multiple phase-singularity centers" and "TC in an arbitrary plane"), the Russian Science Foundation under # grant 17-19-01186 ("TC of an off-axis optical vortex" and "TC of an elliptic vortex in the Gaussian beam"), and the Ministry of Science and Higher Education of the Russian Federation within a government project of the Federal Research Center for Crystallography and Photonics of the Russian Academy of Sciences under agreement 007-ГЗ/Ч3363/26 ("TC of superposition of two Gaussian optical vor-tices").

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