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Optical phase singularities and superluminal motion in unbounded space
V.V. Kotlyar 1,2, A.A. Kovalev 1,2, A.G. Nalimov 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

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DOI: 10.18287/2412-6179-CO-879

Pages: 654-660.

Full text of article: Russian language.

Abstract:
In this paper, we summarize a remarkable result obtained by Soskin et al. in Phys Rev A 56, 4064 (1997). We show that for an on-axis superposition of two different-waist Laguerre-Gauss beams with numbers (0, n) and (0, m), the topological charge equals TC=m up to a plane where the waist radii become the same, given that the beam (0, m) has a greater waist radius, changing to TC=n after this plane. This occurs because in the initial plane the superposition has an on-axis op-tical vortex with TC=m and on different axis-centered circles there are (n – m) vortices with TC= +1 and (n – m) vortices with TC= –1. On approaching the above-specified plane, the vortices with TC= -1 "depart" to infinity with a higher-than-light speed, with the TC of the total beam becoming equal to TC=n. If, on the contrary, the beam (0, m) has a smaller waist, then the total TC equals n on a path from the initial plane up to a plane where the waist radii become the same, changing to TC=m after the said plane. This occurs because after the said plane, n–m vortices with TC= –1 "arrive" from infinity with a higher-than-light speed.

Keywords:
optical vortex, hidden phase, screw dislocation, topological charge.

Citation:
Kotlyar VV, Kovalev AA, Nalimov AG. Optical phase singularities and superluminal motion in unbounded space. Computer Optics 2021; 45(5): 654-660. DOI: 10.18287/2412-6179-CO-879.

Acknowledgements:
The work was partly funded by the Russian Foundation for Basic Research under grant #18-29-20003 (theoretical analysis) and the RF Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS (numerical simulation).

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