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Spiral phase plate with multiple singularity centers
V.V. Kotlyar 1,2, A.A. Kovalev 1,2, E.S. Kozlova 1,2, A.P. Porfirev 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, 1400 kB

DOI: 10.18287/2412-6179-CO-774

Pages: 901-908.

Full text of article: Russian language.

Abstract:
We investigate a multispiral phase plate (MSPP) with multiple centers of phase singularity arbitrarily located in the MSPP plane. Equations to describe the topological charge of an optical vortex in the initial plane immediately behind the MSPP and orbital angular momentum (OAM) normalized relative to the beam power are derived. The topological charge in the initial plane is found as a sum of the topological charges of all singularities if their centers are located inside a finite-radius circular aperture. If the phase singularity centers are partially located on the boundary of a circular diaphragm limiting the MSPP, the total topological charge is found as the sum of all singularities divided by 2. Total OAM that the vortex carries depends on the location of the singularity centers: the farther from the center of the plate the singularity center is located, the smaller is its contribution to the OAM. If all singularity centers are located on the boundary of the diaphragm limiting MSPP, then the OAM of the vortex beam equals zero, although in this case the topological charge of the beam is nonzero.

Keywords:
spiral phase plate, optical vortex, orbital angular momentum.

Citation:
Kotlyar VV, Kovalev AA, Kozlova ES, Porfirev AP. Spiral phase plate with multiple singularity centers. Computer Optics 2020; 44(6): 901-908. DOI: 10.18287/2412-6179-CO-774.

Acknowledgements:
The work was partly funded by the Russian Foundation for Basic Research under project # 18-29-20003 (section "Topological charge calculation"), the Russian Science Foundation under project # 18-19-00595 (section "Orbital angular momentum calculation"), and the Russian Federation Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS (section "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. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A-Pure Appl Op 2004; 6(2): 259-268.
  3. 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: 8185.
  4. 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: 083605.
  5. Willner AE, Huang H, Yan Y, Ren Y, Ahmed N, Xie G, Bao C, Li L, Cao Y, Zhao Z, Wang J, Lavery MPJ, Tur M, Ramachandran S, Molisch AF, Ashrafi N, Ashrafi S Optical communications using orbital angular momentum beams. Adv Opt Photonics 2015; 7: 66-106.
  6. Rodriguez-Herrera OG, Lara D, Bliokh KY, Ostrovskaya EA, Dainty C. Optical nanoprobing via spin-orbit interaction of light. Phys Rev Lett 2010; 104: 253601.
  7. Aksenov VP, Kolosov VV, Pogutsa CE. The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment. J Opt 2013; 15: 044007.
  8. Bazhenov V, Vasnetsov MV, Soskin MS. Laser-beam with screw dislocations in the wavefront. JETP Lett 1990; 53: 429-431.
  9. Khonina SN, Kotlyar VV, Shinkarev MV, Soifer VA, Uspleniev GV. The rotor phase filter. J Mod Opt 1992; 39(5): 1147-1154. DOI: 10.1080/09500349214551151.
  10. Kotlyar VV, Kovalev AA, Porfirev AP. Topological stability of optical vortices diffracted by a random phase screen. Computer Optics 2019; 43(6): 917-925. DOI: 10.18287/2412-6179-2019-43-6-917-925.
  11. 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.
  12. 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.
  13. 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.
  14. Wen J, Wang L, Yang X, Zhang J, Zhu S. Vortex strength and beam propagation factor of fractional vortex beams. Opt Express 2019; 27(4): 5893-5904.
  15. 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.
  16. Indebetouw G. Optical vortices and their propagation. J Mod Opt 1993; 40(1): 73-87.
  17. Abramochkin E, Volostnikov V. Spiral-type beams. Opt Commun 1993; 102(3-4): 336-350. DOI: 10.1016/0030-4018(93)90406-U.
  18. Kovalev AA, Kotlyar VV, Kalinkina DS. Orbital angular momentum and topological charge of a Gaussian beam with multiple optical vortices. Computer Optics 2020; 44(1): 34-39. DOI: 10.18287/2412-6179-CO-632.
  19. 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.
  20. Leach J, Yao E, Padgett MJ. Observation of the vortex structure of a non-integer vortex beam. New J Phys 2004; 6: 71.
  21. 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.
  22. Kovalev AA, Kotlyar VV. Fresnel and Fraunhofer diffraction of a Gaussian beam with several polarization singularities. Computer Optics 2018; 42(2): 179-189. DOI: 10.18287/2412-6179-2018-42-2-179-189.
  23. Gradshteyn IS, Ryzhik IM. Table of integrals, series, and products. 7th ed. New York: Academic Press; 2007. ISBN: 978-0-12-373637-6.
  24. Kotlyar V, Kovalev A, Porfirev A, Kozlova E. Orbital angular momentum of a laser beam behind an off-axis spiral phase plate. Opt Lett 2019; 44(15): 3673-3676. DOI: 10.1364/OL.44.003673.
  25. Kotlyar VV, Almazov AA, Khonina SN, Soifer VA, Elfstrom H, Turunen J. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. J Opt Soc Am A 2005; 22(5): 849-861. DOI: 10.1364/JOSAA.22.000849.
  26. Volyar A, Bretsko M, Akimova Ya, Egorov Yu. Digital sorting perturbed Laguerre-Gaussian beams by radial number. J Opt Soc Am A 2020; 37(6): 959-968.

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