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Optical vortices with an infinite number of screw dislocations
A.A. Kovalev 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, 1354 kB

DOI: 10.18287/2412-6179-CO-866

Pages: 497-505.

Full text of article: Russian language.

Abstract:
In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

Keywords:
optical vortex, screw dislocation, topological charge, form-invariant beam, multivortex beam, orbital angular momentum.

Citation:
Kovalev AA. Optical vortex beams with an infinite number of screw dislocations. Computer Optics 2021; 45(4): 497-505. DOI: 10.18287/2412-6179-CO-866.

Acknowledgements:
This work was supported by the Russian Foundation for Basic Research under project No. 18-29-20003 (Section "Cosine optical vortex with a parabolic argument"), the Russian Science Foundation under project No. 18-19-00595 (Section "Higher-order cosine optical vortex"), and the RF Ministry of Science and Higher Education under the government project of FSRC "Crystallography and Photonics" RAS (Section "Astigmatic cosine optical vortex with a parabolic argument").

References:
  1. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A-Pure Appl Opt 2004; 6(2): 259-268.
  2. Nye JF, Berry MV. Dislocations in wave trains. Proc Math Phys Eng Sci 1974; 336(1605): 165-190.
  3. Fickler R, Campbell G, Buchler B, Lam PK, Zeilinger A. Quantum entanglement of angular momentum states with quantum numbers up to 10010. Proc Nation Acad Sciences USA 2016; 113(48): 13642-13647.
  4. Basisty IV, Bazhenov VYu, Soskin MS, Vasnetsov MV. Optics of light beams with screw dislocations. Opt Commun 1993; 103: 422-428.
  5. Shen Y, Wang X, Xie Z, Min C, Fu X, Liu Q, Gong M, Yuan X. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light Sci Appl 2019; 8: 90.
  6. Hickmann JM, Fonseca EJS, Soares WC, Chávez-Cerda S. Unveiling a truncated optical lattice associated with triangular aperture using light’s orbital angular momentum. Phys Rev Lett 2010; 105: 053904.
  7. De Araujo LEE, Anderson ME. Measuring vortex charge with a triangular aperture. Opt Lett 2011; 36: 787-789.
  8. Melo LA, Jesus-Silva AJ, Chávez-Cerda S, Ribeiro PHS, Soares WC. Direct measurement of the topological charge in elliptical beams using diffraction by a triangular aperture. Sci Rep 2018; 8: 6370.
  9. Vaity P, Banerji J, Singh RP. Measuring the topological charge of an optical vortex by using a titled convex lens. Phys Lett A 2013; 377: 1154-1156.
  10. 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.
  11. Shen D, Zhao D. Measuring the topological charge of optical vortices with a twisting phase. Opt Lett 2019; 44(9): 2334-2337.
  12. Liu G, Wang K, Lee Y, Wang D, Li P, Gou F, Li Y, Tu C, Wu S, Wang H. Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate. Opt Lett 2018; 43: 823-826.
  13. 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.
  14. Lan B, Liu C, Rui D, Chen M, Shen F, Xian H. The topological charge measurement of the vortex beam based on dislocation self-reference interferometry. Phys Scr 2019; 94: 055502.
  15. Kodatskii B, Sevryugin A, Shalimov E, Tursunov I, Venediktov V. Comparative study of reference wave lacking measurement of topological charge of the incoming optical vortex. Proc SPIE 2019; 11153: 111530G.
  16. Kovalev AA, Kotlyar VV, Porfirev AP. Orbital angular momentum and topological charge of a multi-vortex Gaussian beam. J Opt Soc Am A 2020; 37(11): 1740-1747. DOI: 10.1364/JOSAA.401561.
  17. Fu S, Zhai Y, Zhang J, Liu X, Song R, Zhou H, Gao C. Universal orbital angular momentum spectrum analyzer for beams. PhotoniX 2020; 1: 19.
  18. Soskin MS, Gorshkov VN, Vasnetsov MV, Malos JT, Heckenberg NR. Topological charge and angular momentum of light beams carrying optical vortices. Phys Rev A 1997; 56(5): 4064-4075.
  19. Jesus-Silva AJ, Fonseca EJS, Hickman JM. Study of the birth of a vortex at Frauhofer zone. Opt Lett 2012; 37(12): 4552-4554.
  20. Kotlyar VV, Kovalev AA, Volyar AV. Topological charge of a linear combination of optical vortices: topological competition. Opt Express. 2020; 28(6): 8266-8281. DOI: 10.1364/OE.386401.
  21. Zeng J, Zhang H, 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.
  22. 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.
  23. Wang H, Liu L, Zhou C, Xu J, Zhang M, Teng S, Cai Y. Vortex beam generation with variable topological charge based on a spiral slit. Nanophotonics 2019; 8(2): 317-324.
  24. Zhang Z, Qiao X, Midya B, Liu K, Sun J, Wu T, Liu W, Agarwal R, Jornet JM, Longhi S, Litchinitser NM, Feng L. Tunable topological charge vortex microlaser. Science 2020; 368: 760-763.
  25. Zhang K, Wang Y, Yuan Y, Burokur SN. A Review of orbital angular momentum vortex beams generation: from traditional methods to metasurfaces. Appl Sci 2020; 10: 1015.
  26. Abramochkin EG, Volostnikov VG. Spiral-type beams: optical and quantum aspects. Opt Commun 1996; 125: 302-323.
  27. Alexeyev CN, Egorov YuA, Volyar AV. Mutual transformations of fractional-order and integer-order optical vortices. Phys Rev A 2017; 96: 063807.

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