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Reconstruction of stable states of spiral vortex beams
A.V. Volyar 1, E.G. Abramochkin 2, Y.E. Akimova 1, M.V. Bretsko 1

1 Physics and Technology Institute (Academic Unit) of V.I. Vernadsky Crimean Federal University,
Academician Vernadsky 4, Simferopol, Republic of Crimea, 295007, Russia;
2 Lebedev Physical Institute, Novo-Sadovaya 221, Samara, 443034, Russia

 PDF, 2888 kB

DOI: 10.18287/2412-6179-CO-1032

Pages: 5-15.

Full text of article: Russian language.

Abstract:
Using an asymptotic approach and an experiment supported by computer simulation, we analyzed processes of restoring structural stability and transitions to new stable states of spiral vortex beams subject to perturbations by curly apertures. Using a tetragonal beam as an example, we considered three perturbation scenarios: 1) asymmetric perturbation, when an opaque screen covers the caustic only on one side of the square, 2) symmetric perturbation, when the curly aperture covers the entire beam except for a narrow caustic region, and 3) symmetric perturbation, when the curly aperture screens only a narrow region of the caustic without affecting the rest of the beam. At the same time, the asymptotic calculation was carried out for all types of polygonal beams. It was shown that if the curly aperture did not destroy the caustic region of the spiral beam, it was able to self-heal in the far diffraction zone. If the perturbation even locally destroyed a part of the caustics, then the perturbed beam passed into a new stable state through chains of creation and annihilation of optical vortices (dislocation reactions).

Keywords:
structural stability, spiral beam, vortex spectrum.

Citation:
Volyar AV, Abramochkin EG, Akimova YE, Bretsko MV. Reconstruction of stable states of spiral vortex beams. Computer Optics 2022; 46(1): 5-15. DOI: 10.18287/2412-6179-CO-1032.

Acknowledgements:
This work was supported by the Russian Foundation for Basic Research and the Ministry Council of the Republic of Crimea under project No. 20-47-910002 (Section “Basic and symmetrical spiral beams”), project No. 20-37-90066 (Section “Fine structure of optical currents”), and projects Nos. 20-37-90068 and 19-29-01233 (Section “Experiment”).

References:
  1. Lit JWY, Tremblay R. Focal depth of a transmitting axicon. J Opt Soc Am 1973; 63(4): 445-449. DOI: 10.1364/JOSA.63.000445.
  2. Sheppard CJR, Wilson T. Depth of field in scanning microscope. Opt Lett 1978; 3(3): 115-117. DOI: 10.1364/OL.3.000115.
  3. 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: 1-29. DOI: 10.1038/s41377-019-0194-2.
  4. Garces-Chavez V, McGloin D, Melville H, Sibbett W, Dholakia K. Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam. Nature 2002; 419: 145-147. DOI: 10.1038/nature01007.
  5. Fahrbach FO, Simon P, Rohrbach A. Microscopy with self-reconstructing beams. Nat Photon 2010; 4: 780-785. DOI: 10.1038/nphoton.2010.204.
  6. Nape I, Otter E, Valles A, Rosales-Guzman C, Cardano F, Denz C, Forbes A. Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states. Opt Express 2018; 26(21): 26946-26960. DOI: 10.1364/OE.26.026946.
  7. McLaren M, Mhlanga T, Padgett MJ, Roux FS, Forbes A. Self-healing of quantum entanglement after an obstruction. Nat Commun 2014; 5: 3248. DOI: 10.1038/ncomms4248.
  8. Duocastella M, Arnold CB. Bessel and annular beams for materials processing. Laser Photonics Rev 2012; 6(5): 607-621. DOI: 10.1002/lpor.201100031.
  9. Simon DS. A guided tour of light beams. From lasers to optical knots. Bristol: Morgan & Claypool Publishers; 2016. ISBN: 978-1-6817-4436-0.
  10. Nelson W, Palastro J, Davis C, Sprangle P. Propagation of Bessel and Airy beams through atmospheric turbulence. J Opt Soc Am A 2014; 31(3): 603-609. DOI: 10.1364/JOSAA.31.000603.
  11. Soifer VA, Korotkova О, Khonina SN, Shchepakina ЕА. Vortex beams in turbulent media: Review. Computer Optics 2016; 40(5): 605-624. DOI: 10.18287/2412-6179-2016-40-5-605-624.
  12. Mphuthi N, Botha R, Forbes A. Are Bessel beams resilient to aberrations and turbulence? J Op Soc Am A 2018; 35(6): 1021-1027. DOI: 10.1364/JOSAA.35.001021.
  13. Aiello A, Agarwal GS. Wave-optics description of self-healing mechanism in Bessel beams. Opt Lett 2014; 39(24): 6819-6822. DOI: 10.1364/OL.39.006819.
  14. Chu X. Analytical study on the self-healing property of Bessel beam. Eur Phys J D 2012; 66: 259. DOI: 10.1140/epjd/e2012-30343-6.
  15. Wu G, Pang X. Self-healing properties of partially coherent Schell-model beams. IEEE Photon J 2017; 9(6): 6501311. DOI:10.1109/JPHOT.2017.2772350.
  16. Anguiano-Morales M, Martínez A, Iturbe-Castillo MD, Chávez-Cerda S, Alcalá-Ochoa N. Self-healing property of a caustic optical beam. Appl Opt 2007; 46(34): 8284-8290. DOI: 10.1364/AO.46.008284.
  17. Vaveliuk P, Martínez-Matos Ó, Ren Y-X, Lu R-D. Dual behavior of caustic optical beams facing obstacles. Phys Rev A 2017; 95(6): 063838. DOI: 10.1103/PhysRevA.95.063838.
  18. Nye JF. Natural focusing and fine structure of light: caustics and wave dislocations. Bristol: Institute of Physics; 1999. ISBN 0-7503-0610-6.
  19. Berry MV. Upsill C catastrophe optics: Morphologies of caustics and their diffraction patterns. Progress in Optics 1980; 18: 257-346. DOI: 10.1016/S0079-6638(08)70215-4.
  20. Forbes A, Oliveira M, Dennis MR. Structured light. Nat Photon 2021; 15: 253-262. DOI: 10.1038/s41566-021-00780-4.
  21. Shen Yi, Yang Xi, Naidoo D, Fu Xing, Forbes A. Structured ray-wave vector vortex beams in multiple degrees of freedom from a laser. Optica 2020; 7(7): 820-831. DOI: 10.1364/OPTICA.414397.
  22. Shen Yi, Wang Zh, Fu Xing, Naidoo Dar, Forbes A. SU(2) Poincaré sphere: A generalized representation for multidimensional structured light. Phys Rev A 2020; 102(3): 031501. DOI: 10.1103/PhysRevA.102.031501.
  23. Abramochkin EG, Volostnikov VG. Spiral light beams. Physics-Uspekhi 2004; 47(12): 1177-1203. DOI: 10.1070/PU2004v047n12ABEH001802.
  24. Razueva E, Abramochkin E. Multiple-twisted spiral beams. J Opt Soc Am A 2019; 36(6): 1089-1097. DOI: 10.1364/JOSAA.36.001089.
  25. Rodrigo JA, Alieva T, Abramochkin E, Castro I. Shaping of light beams along curves in three dimensions. Opt Express 2013; 21(18): 20544-20555. DOI: 10.1364/OE.21.020544.
  26. Berry MV, Nye JF, Wright FJ. The elliptic umbilic diffraction catastrophe. Philos Trans Royal Soc A 1979; 291(1382): 453-484. DOI: 10.1098/rsta.1979.0039.
  27. Nye JF. Dislocation lines in the hyperbolic umbilic diffraction catastrophe. Proc Math Phys Eng Sci 2006; 462(2072): 2299-2313. DOI: 10.1098/rspa.2006.1683.
  28. Volyar AV, Abramochkin EG, Razueva EV, Akimova YaE, Bretsko MV. Structural stability of spiral beams and fine structure of an energy flow. Computer Optics 2021; 45(4): 482-489. DOI: 10.18287/2412-6179-CO-885.
  29. Volyar AV, Akimova YaE. Transformations of structurally stable states of spiral beams subjected to sector perturbations. Computer Optics: accepted for publication.
  30. Poston T, Stewart I. Catastrophe theory and its applications. London: Pitman; 1978.
  31. Volyar A, Bretsko M, Akimova Ya, Egorov Yu. Orbital angular momentum and informational entropy in perturbed vortex beams. Opt Lett 2019; 44(29): 5687-5680. DOI: 10.1364/OL.44.005687.
  32. Arnold VI, Gusein-Zade SM, Varchenko AN. Singularities of differentiable maps. Basel: Birkhäuser, 1988.
  33. Berry MV. Wave dislocation reactions in non-paraxial Gaussian beams. J Mod Opt 1998; 45(9): 1845-1858. DOI: 10.1080/09500349808231706.
  34. Volyar A, Bretsko M, Akimova Ya, Egorov Yu. Digital sorting perturbed Laguerre–Gaussian beams by radial numbers. J Opt Soc Am A 2020; 37(6): 959-968. DOI: 10.1364/JOSAA.391153.
  35. Volyar AV, Abramochkin EG, Egorov YuA, Bretsko MV, Akimova YaE. Digital sorting of Hermite-Gauss beams: mode spectra and topological charge of a perturbed Laguerre-Gauss beam. Computer Optics 2020; 44(4): 501-509. DOI: 10.18287/2412-6179-CO-747.
  36. Volyar A, Abramochkin E, Egorov Yu, Bretsko M, Akimova Ya. Fine structure of perturbed Laguerre–Gaussian beams: Hermite–Gaussian mode spectra and topological charge. Appl Opt 2020; 59(25): 7680-7687. DOI: 10.1364/AO.396557.
  37. Born M, Wolf E. Principles of optics. 7th ed. Cambridge: Cambridge University Press; 1999. ISBN: 0-521-64222-1.
  38. Temme NM. Asymptotic methods for integrals. Singapore: World Scientific Publishing Co Pte Ltd; 2014. ISBN: 978-981-4612-15-9.

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