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Topological charge of optical vortices devoid of radial symmetry
V.V. Kotlyar 1,2, 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, 1336 kB

DOI: 10.18287/2412-6179-CO-719

Pages: 510-518.

Full text of article: Russian language.

Abstract:
Here we theoretically obtain values of the topological charge (TC) for vortex laser beams devoid of radial symmetry: asymmetric Laguerre-Gaussian (LG) beams, Bessel-Gaussian (BG) beams, Kummer beams, and vortex Hermite-Gaussian (HG) beams. All these beams consist of conventional modes, namely, LG, BG, or HG modes, respectively. However, all these modes have the same TC equal to that of a single constituent mode n. Orbital angular momenta (OAM) of all these beams, normalized to the beam power, are different and changing differently with varying beam asymmetry. However, for arbitrary beam asymmetry, TC remains unchanged and equals n. Superposition of just two HG modes with the adjacent numbers (n, n+1) and with the phase retardation of (pi)/2 yields a modal beam with the TC equal to – (2n+1). Numerical simulation confirms the theoretical predictions.

Keywords:
topological charge, optical vortex, asymmetric beam.

Citation:
Kotlyar VV, Kovalev AA. Topological charge of optical vortices devoid of radial symmetry. Computer Optics 2020; 44(4): 510-518. DOI: 10.18287/2412-6179-CO-719.

Acknowledgements:
This work was partly funded by the Russian Foundation for Basic Research under project No. 18-29-20003 (section “Derivation of the topological charge of asymmetric optical vortices”), the Russian Science Foundation under project No. 18-19-00595 (section “Derivation of the topological charge of Hermite-Gaussian vortex beams”, and the RF Ministry of Science and Higher Education within a government project of FSRC “Crystallography and Photonics” RAS (section “Numerical simulation results”).

References:
  1. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex laser beams. Boca Raton: CRC Press; 2018. ISBN: 978-1-138-54211-2.
  2. Li S, Pan X, Ren Y, Liu H, Yu S, Jing J. Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement. Phys Rev Lett 2020; 124(8): 083605. DOI: 10.1103/PhysRevLett.124.083605.
  3. Hiekkamaki M, Prabhakar S, Fickler R. Near-perfect measuring of full-field transverse-spatial modes of light. Opt Express 2019; 27(22): 31456-31464. DOI: 10.1364/OE.27.031456.
  4. Li S, Li X, Zhang L, Wang G, Zhang L, Liu M, Zeng C, Wang L, Sun Q, Zhao W, Zhang W. Efficient optical angular momentum manipulation for compact multiplexing and demultiplexing using a dielectric metasurface. Adv Opt Mater 2020; 8(8): 1901666. DOI: 10.1002/adom.201901666.
  5. Pryamikov A, Alagashev G, Falkovich G, Turitsyn S. Light transport and vortex-suppoted wave-guiding in micro-structured optical fibers. Sci Rep 2020; 10: 2507. DOI: 10.1038/s41598-020-59508-z.
  6. Dai K, Li W, Morgan KS, Li Y, Miller JK, Watkins RJ, Johnson EG. Second-harmonic generation of asymmetric Bessel-Gaussian beams carrying orbital angular momentum. Opt Express 2020; 28: 2536-2546. DOI: 10.1364/OE.381679.
  7. Dimitrov N, Zhekova M, Paulus GG, Dreischuh A. Inverted field interferometer for measuring the topological charges of optical vortices carried by short pulses. Opt Commun 2020; 456: 124530. DOI: 10.1016/j.optcom.2019.124530.
  8. Watkins RJ, Dai K, White G, Li W, Miller JK, Morgan KS, Johnson EG. Experimental probing of turbulence using a continuous spectrum of asymmetric OAM beams. Opt Express 2020; 28(2): 924-935. DOI: 10.1364/OE.380405.
  9. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A: Pure Appl Opt 2004; 6(2): 259-268. DOI: 10.1088/1464-4258/6/2/018.
  10. Allen L, Beijersbergen M, Spreeuw R, Woerdman J. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 1992; 45(11): 8185. DOI: 10.1103/PhysRevA.45.8185.
  11. Kotlyar VV, Kovalev AA, Pofirev 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.
  12. Hickmann JM, Fonseca EJS, Soares WC, Chavez-Cerda S. Unveiling a truncated optical lattice associated with a triangular aperture using lights orbital angular momentum. Phys Rev Lett 2010; 105: 053904. DOI: 10.1103/PhysRevLett.105.053904.
  13. Alperin SN, Niederriter RD, Gopinath JT, Siemens ME. Quantitative measurement of the orbital angular momentum of light with a single, stationary lens. Opt Lett 2016; 41(21): 5019-5022. DOI: 10.1364/OL.41.005019.
  14. Kotlyar VV, Kovalev AA, Porfirev AP. Calculation of fractional orbital angular momentum of superpositions of optical vortices by intensity moments. Opt Express 2019; 27(8): 11236-11251. DOI: 10.1364/OE.27.011236.
  15. Kotlyar VV, Khonina SN, Soifer VA. Light field decomposition in angular harmonics by means of diffractive optics. J Mod Opt 1998; 45(7): 1495-1506. DOI: 10.1080/09500349808230644.
  16. Volyar AV, Bretsko MV, Akimova YaE, Egorov YuA. Beyond the light intensity or intensity moments and measurements of the vortex spectrum in complex light beams. Computer Optics 2018; 42(5): 736-743. DOI: 10.18287/2412-6179-2017-42-5-736-743.
  17. Volyar AV, Bretsko MV, Akimova YaE, Egorov YuA, Milyukov VV. Sectorial perturbation of vortex beams: Shannon entropy, orbital angular momentum and topological charge. Computer Optics 2019; 43(5): 723-734. DOI: 10.18287/2412-6179-2019-43-5-723-734.
  18. Siegman AE. Lasers. Sausalito, CA: University Science Books; 1986.
  19. Gori F, Guattary G, Padovani C. Bessel-Gauss beams. Opt Commun 1987; 64(6): 491-495. DOI: 10.1016/0030-4018(87)90276-8.
  20. Soskin MS, Gorshkov VN, Vastnetsov MV, Malos JT, Heckenberg NR. Topological charge and angular momentum of light beams carring optical vortex. Phys Rev A 1997; 56(5): 4064-4075. DOI: 10.1103/PhysRevA.56.4064.
  21. Kovalev AA, Kotlyar VV, Porfirev AP. Asymmetric Laguerre-Gaussian beams. Phys Rev A 2016; 93(6): 063858. DOI: 10.1103/PhysRevA.93.063858.
  22. Kotlyar VV, Kovalev AA, Skidanov RV, Soifer VA. Asymmetric Bessel-Gauss beams. J Opt Soc Am A 2014; 31(9): 1977-1983. DOI: 10.1364/JOSAA.31.001977.
  23. Kotlyar VV, Kovalev AA, Abramochkin EG. Kummer laser beams with a transverse complex shift. J Opt 2020; 22(1): 015606. DOI: 10.1088/2040-8986/ab5ef1.
  24. Kotlyar VV, Kovalev AA. Hermite-Gaussian modal laser beams with orbital angular momentum. J Opt Soc Am A 2014; 31(2): 274-282. DOI: 10.1364/JOSAA.31.000274.
  25. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex Hermite-Gaussian laser beams. Opt Lett 2015; 40(5): 701-704. DOI: 10.1364/OL.40.000701.
  26. 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.
  27. Volostnikov VG, Abramochkin EG. The modern optics of the Gaussian beams [In Russian]. Moscow: “Fizmatlit” Publisher; 2010. ISBN: 978-5-9221-1216-1.
  28. Gradshteyn IS, Ryzhik IM. Table of integrals, series, and products. New York: Academic; 1965.

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