(45-4) 02 * << * >> * Russian * English * Content * All Issues

Optical beams with an infinite number of vortices
V.V. Kotlyar 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, 2104 kB

DOI: 10.18287/2412-6179-CO-858

Pages: 490-496.

Full text of article: Russian language.

Abstract:
In optical data transmission with using vortex laser beams, data can be encoded by the topo-logical charge, which is theoretically unlimited. However, the topological charge of a single sepa-rate vortex is limited by possibilities of its generating. Therefore, in this work, we analyze light beams with an unbounded (countable) set of optical vortices. The summary topological charge of such beams is infinite. Phase singularities (isolated intensity nulls) in such beams typically have a unit topological charge and reside equidistantly (or not equidistantly) on a straight line in the beam cross section. Such beams are form-invariant and, on propagation in space, change only in scale and rotate. Orbital angular momentum of such multivortex beams is finite, since only a finite number of optical vortices fall into the area, where the Gaussian beam has a notable intensity. Other phase singularities are located in the periphery (and at the infinity), where the intensity is almost zero.

Keywords:
optical vortex, topological charge, shape-invariant beam, multivortex beam, orbital angular momentum.

Citation:
Kotlyar VV. Optical beams with an infinite number of vortices. Computer Optics 2021; 45(4): 490-496. DOI: 10.18287/2412-6179-CO-858.

Acknowledgements:
This work was supported by the Russian Foundation for Basic Research under project No. 18-29-20003 (Section "Gaussian beam with a vortex-argument cosine envelope function"), the Russian Science Foundation under project No. 18-19-00595 (Section "Gaussian beam with a vortex-argument Bessel envelope function"), and the RF Ministry of Science and Higher Education within a government project of FSRC "Crystallography and Photonics" RAS (Section "Shape-invariant Gaussian beams").

References:
  1. Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 1992; 45(11): 8185-8189.
  2. Courtial J, Dholakia K, Allen L, Padgett MJ. Gaussian beams with very high orbital angular momentum. Opt Commun 1997; 144: 210-213.
  3. Campbell G, Hage B, Buchler B, Lam P. Generation of high-order optical vortices using directly machined spiral phase mirrors. Appl Opt 2012; 51: 873-876.
  4. Chen Y, Fang Z, Ren Y, Gong L, Lu R. Generation and characterization of a perfect vortex beam with a large topological charge through a digital micromirror device. Appl Opt 2015; 54: 8030-8035.
  5. Wang C, Ren Y, Liu T, Luo C, Qiu S, Li Z, Wu H. Generation and measurement of high-order optical vortices by using the cross phase. Appl Opt 2020; 59: 4040-4047.
  6. Chen D, Miao Y, Fu H, He H, Tong J, Dong J. High-order cylindrical vector beams with tunable topological charge up to 14 directly generated from a microchip laser with high beam quality and high efficiency. APL Photonics 2019; 4: 106106.
  7. Kotlyar VV, Kovalev AA, Porfirev AP. Astigmatic transforms of an optical vortex for measurement of its topological charge. Appl Opt 2017; 56(14): 4095-4104. DOI: 10.1364/AO.56.004095.
  8. Kumar P, Nishchal N. Modified Mach-Zehnder interferometer for determining the high-order topological charge of Laguerre-Gaussian vortex beams. J Opt Soc Am A 2019; 36: 1447-1455.
  9. Li Y, Han Y, Cui Z. Measuring the topological charge of vortex beams with gradually changing-period spiral spoke grating. IEEE Photon Technol Lett 2020; 32(2): 101-104.
  10. Nape I, Sephton B, Huang YW, Vallés A, Qiu CW, Ambrosio A, Capasso F, Forbes A. Enhancing the modal purity of orbital angular momentum photons. APL Photon 2020; 5: 070802.
  11. Hong S, Lee YS, Choi H, Quan C, Li Y, Kim S, Oh K. Hollow silica photonic crystal fiber guiding 101 orbital angular momentum modes without phase distortion in C+ L band. J Lightw Technol 2020; 38(5): 1010-1018.
  12. Fickler R, Campbell G, Buchler B, Lam PK, Zeilinger A. Quantum entanglement of angular momentum states with quantum numbers up to 10010. Proc Natl Acad Sci USA 2016; 113(48): 13642-13647.
  13. Serna J, Movilla J. Orbital angular momentum of partially coherent beams. Opt Lett 2001; 26: 405-407.
  14. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A: Pure Appl Opt 2004; 6(2): 259-268.
  15. Indebetouw G. Optical vortices and their propagation. J Mod Opt 1993; 40(1): 73-87.
  16. Abramochkin EG, Volostnikov VG. Spiral-type beams: optical and quantum aspects. Opt Commun 1996; 125(4-6): 302-323.
  17. Abramochkin EG, Volostnikov VG. Modern optics of Gaussian beams [In Russian]. Moscow: "Fizmatlit" Publisher; 2010.
  18. Siegman AE. Lasers. University Science; 1986.
  19. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex astigmatic Fourier-invariant Gaussian beams. Opt Express 2019; 27(2): 657-666. DOI: 10.1364/OE.27.000657.
  20. Prudnikov AP, Brychkov YA, Marichev OI. Integrals and Series, Special Functions. New York: Gordon and Breach; 1981.

© 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