(45-4) 01 * << * >> * Russian * English * Content * All Issues

Structural stability of spiral beams and fine structure of an energy flow
A.V. Volyar 1, E.G. Abramochkin 2, E.V. Razueva 2, Ya.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, 2146 kB

DOI: 10.18287/2412-6179-CO-885

Pages: 482-489.

Full text of article: Russian language.

Abstract:
The problem of structural stability of wave systems with great numbers of degrees of freedom directly concerns the issue of redistribution of energy fluxes in structured vortex beams that ensure their stability under propagating and focusing. A special place in this variety is occupied by spiral vortex beams capable of mapping complex figures, letters and even words. Spiral beams contain an infinite set of Laguerre-Gauss beams with a strong sequence of topological charges and radial numbers, their amplitudes and phases are tightly matched. Therefore, the problem of structural stability plays a special role for their applications.
     Using a combination of theory and computer simulation, supported by experiment, we ana-lyzed the structure of critical points in energy flows for two main types of spiral beams: triangular beams with zero radial number and triangular beams with complex framing of their faces with both quantum numbers. Structural stability is provided by triads of critical points, both inside and outside the triangle, which direct the light flux along the triangular generatrix and hold the framing when rotating the beam. The experiment showed that a simple triangular spiral beam turns out to be stable even with small alignment inaccuracies, whereas a complex triangular beam with a fram-ing requires careful alignment

Keywords:
optical vortices, twisting paraxial beams, optical currents.

Citation:
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.

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. Abramochkin E, Volostnikov V. Spiral-type beams: optical and quantum aspects. Opt Commun 1996; 125: 302-323. DOI: 10.1364/OPN.31.6.000024.
  2. Forbes A. Structured light tailored for purpose. Opt Photon News 2020; 6: 24-31. DOI: 10.1364/OPN.31.6.000024.
  3. Nye JF, Berry MV. Dislocations in wave trains. Proc R Soc Lond A 1974; 336: 165-190. DOI: 10.1098/rspa.1974.0012.
  4. Baranova NB, Mamaev AY, Pilipetsky NF, Shkunov VV, Zel'dovich BYa. Wave-front dislocations: topological limitations for adaptive systems with phase conjugation. J Opt Soc Am 1983; 73(5): 525-528. DOI: 10.1364/JOSA.73.000525.
  5. Bazhenov VYu, Vasnetsov MV, Soskin MS. Laser beams with screw dislocations in their wavefronts. JETP Lett 1990; 52: 429-431.
  6. Soskin MS, Vasnetsov MV. Singular optics. Prog Opt 2001; 42: 219-276.
  7. Rubinsztein-Dunlop H, Forbes A, Berry MV, Dennis MR, Andrews DL, Mansuripur M, Denz C, Alpmann C, Banzer P, Bauer T, Karimi E, Marrucci L, Padgett M, Ritsch-Marte M, Litchinitser NM, Bigelow NP, Rosales-Guzmán C, Belmonte A, Torres JP, Neely TW, Baker M, Gordon R, Stilgoe AB, Romero J, White AG, Fickler R, Willner AE, Xie G, McMorran B, Weiner AM. Roadmap on structured light. J Opt 2017; 19: 013001. DOI: 10.1088/2040-8978/19/1/013001.
  8. 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: Science & Appl 2019; 8: 90. DOI: 10.1038/s41377-019-0194-2.
  9. Abramochkin EG, Razueva EV, Volostnikov VG. Application of spiral laser beams for beam shaping problem. Current Research in Optics and Photonics: Selected Papers from Int Conf Adv Optoelectronics & Lasers 2006; 6: 275-278. DOI: 10.1109/LFNM.2006.252042.
  10. Afanasiev KN, Abramochkin EG, Korobtsov AV, Kotova SP, Losevsky NN, Razueva EV, Volostnikov VG. Vortical laser tweezers with predetermined intensity structure. Proc SPIE 2007; 6644: 664410. DOI 10.1117/12.733864.
  11. Grover G, Mohrman W, Piestun R. Real-time adaptive drift correction for superresolution localization microscopy. Opt Express 2015; 23: 23887-23898.
  12. Rodrigo JA, Alieva T, Abramochkin E, Castro I. Shaping of light beams along curves in three dimensions. Opt Express 2013; 21: 20544-20555. DOI: 10.1364/OE.21.020544.
  13. Dennis MR, King RP, Jack B, O'Holleran K, Padgett MJ. Isolated optical vortex knots. Nat Phys 2010; 6: 118-121. DOI: 10.1038/nphys1504.
  14. Abramochkin EG, Volostnikov VG, Spiral light beams. Physics–Uspekhi 2004; 47(12): 1177-1203. DOI: 10.1070/PU2004v047n12ABEH001802.
  15. Razueva E, Abramochkin E. Multiple-twisted spiral beams. J Opt Soc Am A 2019; 36(6): 1089-1097. DOI: 10.1364/JOSAA.36.001089.
  16. Päakkönen P, Lautanen J, Honkanen M, Kuittinen M, Turunen J, Khonina SN, Kotlyar VV, Soifer VA, Friberg AT. Rotating optical fields: experimental demonstration with diffractive optics. J Mod Opt 1998; 45(11): 2355-2369. DOI: 10.1080/09500349808231245.
  17. Berry MV. Optical currents. J Opt A-Pure Appl Opt 2009; 11: 094001. DOI: 10.1088/1464-4258/11/9/094001.
  18. Berry MV. Curvature of wave streamlines. J Phys A Math Theor 2013, 46: 395202.
  19. Arnold VI, Khesin BА. Topological methods in hydrodynamics. New York: Springer; 1998.
  20. Berry MV, Dennis MR. Stream function for optical energy flow. J Opt 2011; 13: 064004. DOI: 10.1088/2040-8978/13/6/064004.
  21. Poston T, Stewart I. Catastrophe theory and its applications. London: Pitman; 1978.
  22. Brychkov YuA. Handbook of special functions: derivatives, integrals, series and other formulas. Boca Raton FL: CRC Press; 2008.
  23. Volyar A, Bretsko M, Akimova Ya, Egorov Yu. Measurement of the vortex spectrum in a vortex-beam array without cuts and gluing of the wavefront. Opt Lett 2018; 43(22): 5635-5638. DOI: 10.1364/OL.43.005635.
  24. Volyar A, Bretsko M, Akimova Ya, Egorov Yu. Measurement of the vortex and orbital angular momentum spectra with a single cylindrical lens. Appl Opt 2019; 58: 5748-5755. DOI: 10.1364/AO.58.005748.
  25. Volyar A, Abramochkin E, Bretsko M, Akimova Ya, Egorov Yu. 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.
  26. Siegman AE. Hermite-Gaussian functions of complex argument as optical beam eigenfunctions. J Opt Soc Am 1973; 63(9): 1093-1094. DOI: 10.1364/JOSA.63.001093.
  27. Wünsche A. Generalized Gaussian beam solutions of paraxial optics and their connection to a hidden symmetry. J Opt Soc Am A 1989; 6(9): 1320-1329. DOI: 10.1364/JOSAA.6.001320.

© 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