(46-3) 02 * << * >> * Russian * English * Content * All Issues

Superposition of two Laguerre-Gaussian beams shifted from the optical axis
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

 PDF, 1093 kB

DOI: 10.18287/2412-6179-CO-1057

Pages: 366-374.

Full text of article: Russian language.

Abstract:
Topological charges (TC) of a superposition of two Laguerre-Gauss (LG) beams (0,m) and (0,n) symmetrically shifted from the optical axis are found in this work. It is shown that if m=n, then the TC of the superposition is equal to n. That is, two identical off-axis LG beams have the net TC as that of a single LG beam. If m<n, then the net TC of the superposition can take one of four values: TC1=(m+n)/2, TC2=TC1+1, TC3=TC1+1/2, and TC4=TC1–1/2. Criteria for choosing one of the four TC values are also established. In the absence of the off-axis shift of the two LG beams, the net TC of the superposition is equal to n, i.e. the larger of the two TC. And for an arbitrarily small off-axis shift, the net TC either remains the same as it was before the shift, or decreases by an even number. This is explained by the fact that an even number of optical vortices with TC=–1 "comes" from infinity, which compensate for the same number of optical vortices with TC=+1 in the superposition. It is also interesting that when superimposing two off-axis LG beams with certain tilts to the optical axis such that the superposition is structurally stable, an infinite number of screw dislocations with TC=+1 are formed on some line. The net TC of such a su-perposition is infinite.

Keywords:
screw dislocations, topological charge, optical vortices.

Citation:
Kotlyar VV, Kovalev AA, Nalimov AG. Superposition of two Laguerre-Gaussian beams shifted from the optical axis. Computer Optics 2022; 46(3): 366-374. DOI: 10.18287/2412-6179-CO-1057.

Acknowledgements:
The work was partly funded by the Russian Foundation for Basic Research under grant #18-29-20003 (Section "Structurally stable superposition of off-axis Gaussian vortices"), the Russian Science Foundation grant #18-19-00595 (Section "Superposition of two off-axis LG beams"), and the RF Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS (Section "Simulation").

References:
  1. Nye JF, Berry MV. Dislocations in wave trains. Proc R Soc Lond A 1974; 336: 165-190.
  2. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A–Pure Appl Opt2004; 6(2): 259-268.
  3. Soskin MS, Gorshkov VN, Vasnetsov MV, Malos JT, Heckenberg NR. Topological charge and angular momentum of light beams carrying optical vortices. Phys Rev A1997; 56(5): 4064-4075.
  4. Jesus-Silva AJ, Fonseca EJS, Hickman JM. Study of the birth of a vortex at Frauhofer zone. Opt Lett2012; 37(12): 4552-4554.
  5. Kotlyar VV, Kovalev AA, Volyar AV. Topological charge of a linear combination of optical vortices: topological competition. Opt Express2020; 28(6): 8266-8281. DOI: 10.1364/OE.386401.
  6. Zeng J, Zhang G, Xu Z, Zhao C, Cai Y, Gbur G. Anomalous multi-ramp fractional vortex beams with arbitrary topological charge jumps. Appl Phys Lett 2020; 117: 241103.
  7. Kotlyar VV, Kovalev AA, Nalimov AG, Porfirev AP. Evolution of an optical vortex with an initial fractional topological charge. Phys Rev A 2020; 102(2): 023516. DOI: 10.1103/PhysRevA.102.023516.
  8. Kovalev AA, Kotlyar VV. Optical vortex beams with the infinite topological charge. J Opt 2021; 23(5): 055601. DOI: 10.1088/2040-8986/abf172.
  9. Kovalev AA, Kotlyar VV. Propagation-invariant laser beams with an array of phase singularities. Phys Rev A 2021; 103(6): 063502. DOI: 10.1103/PhysRevA.103.063502.
  10. Indebetouw G. Optical vortices and their propagation. J Mod Opt 1994; 40(1): 73-87.
  11. Abramochkin EG, Volostnikov VG. Spiral-type beams: optical and quantum aspects. OptCommun 1996;125(4-6): 302-323. DOI: 10.1016/0030-4018(95)00640-0.
  12. Kovalev AA, Kotlyar VV. Orbital angular momentum of superposition of identical shifted vortex beams. J Opt Soc Am A 2015; 32(10): 1805-1810. DOI: 10.1364/JOSAA.32.001805.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20