(45-2) 04 * << * >> * Russian * English * Content * All Issues

Astigmatic transformation of a set of edge dislocations embedded in a Gaussian beam
V.V. Kotlyar 1,2, A.A. Kovalev 1,2, A.G. Nalimov 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, 1483 kB

DOI: 10.18287/2412-6179-CO-849

Pages: 190-199.

Full text of article: Russian language.

Abstract:
It is theoretically shown how a Gaussian beam with a finite number of parallel lines of intensity nulls (edge dislocations) is transformed using a cylindrical lens into a vortex beam that carries orbital angular momentum (OAM) and has a topological charge (TC). In the initial plane, this beam already carries OAM, but does not have TC, which appears as the beam propagates further in free space. Using an example of two parallel lines of intensity nulls symmetrically located relative to the origin, we show the dynamics of the formation of two intensity nulls at the double focal length: as the distance between the vertical lines of intensity nulls is being increased, two optical vortices are first formed on the horizontal axis, before converging to the origin and then diverging on the vertical axis. At any distance between the zero-intensity lines, the optical vortex has the topological charge TC=–2, which conserves at any on-axis distance, except the initial plane. When the distance between the zero-intensity lines changes, the OAM that the beam carries also changes. It can be negative, positive, and at a certain distance between the lines of intensity nulls OAM can be equal to zero. It is also shown that for an unlimited number of zero-intensity lines, a beam with finite OAM and an infinite TC is formed.

Keywords:
orbital angular momentum, topological charge, zero intensities, optical vortex.

Citation:
Kotlyar VV, Kovalev AA, Nalimov AG. Astigmatic transformation of a set of edge dislocations embedded in a Gaussian beam. Computer Optics 2021; 45(2): 190-199. DOI: 10.18287/2412-6179-CO-849.

Acknowledgements:
The work was partly funded by the Russian Foundation for Basic Research under grant #18-29-20003 (Sections "Complex amplitude at the double focal distance" and "Orbital angular momentum"), the Russian Science Foundation grant #18-19-00595 (Section "Astigmatic cosine-Gauss beam"), and the RF Ministry of Science and Higher Education within a state contract with the FSRC "Crystallography and Photonics" RAS (Section "Simulation").

References:
  1. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex laser beams. CRC Press, 2018. ISBN: 978-1-138-54211-2.
  2. Vasara A, Turunen J, Friberg AT. Realization of general nondiffracting beams with computer-generated holograms. JOpt Soc Am A 1989; 6(11): 1748-1754.
  3. Heckenberg NR, McDaff R, Smith CP, White AG. Generation of optical phase singularities by computer-generated holograms. Opt Lett 1998; 17(3): 221-223.
  4. Bazhenov VY, Soskin MS, Vasnetsov MV. Screw dislocations in light wavefronts. J Mod Opt 1992; 39(5): 985-990.
  5. Abramochkin E, Volostnikov V. Beam transformation and nontransformed beams. Opt Commun 1991; 83(1,2): 123-35. DOI: 10.1016/0030-4018(91)90534-K.
  6. Khonina SN, Kotlyar VV, Uspleniev GV, Shinkarev MV, Soifer VA. The phase rotor filter. J Mod Opt 1992; 39(5): 1147-1154. DOI: 10.1080/09500349214551151.
  7. Beijersbergen MV, Coerwinkel RPC, Kristensen M, Woerdman JP. Helical-wavefront laser beams produced with a spiral phase plate. Opt Commun 1994; 112(5-6): 321-327.
  8. Fedotowsky A, Lehovec K. Optimal filter design for annular imaging. Appl Opt 1974; 13(12): 2919-2923.
  9. Khonina SN, Kotlyar VV, Soifer VA, Shinkaryev MV, Uspleniev GV. Trochoson. Opt Commun 1992; 91(3-4): 158-162.
  10. Marrucci L, Manzo C, Paparo D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys Rev Lett 2006; 96(16): 163905.
  11. Naik DN, Viswanahan NK. Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer. J Opt 2016; 18(9): 095601.
  12. Zhu L, Wang J. Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators. Sci Rep 2015; 4: 7441.
  13. Devlin RC, Ambrosio A, Rubin A, Mueller JB, Capasso F. Arbitrary spin-to-orbital angular momentum conversion of light. Science 2017; 358: 896-901.
  14. Miao P, Zhang Z, Sun J, Walasik W, Longhi S, Litchintser NM, Feng L. Orbital angular momentum microlaser. Science 2016; 353: 464-467.
  15. Vaity P, Aadhi A, Singh RP. Formation of optical vortices through superposition of two Gaussian beams. Appl Opt 2013; 52(27): 6652-6656.
  16. Zhang J, Guo Z, Li R, Wang W, Zhang A, Liu J, Qu S, Gao J. Circular polarization analyzer based on the combined coaxial Archimedes’ spiral structure. Plasmonics 2015; 10(6): 1256-1261.
  17. Zhang J, Guo Z, Zhou K, Ran L, Zhu L, Wang W, Sun Y, Shen F, Gao J, Liu S. Circular polarization analyzer based on an Archimedean nano-pinholes array. Opt Express 2015; 23(23): 30523-30531.
  18. Zhan H, Li J, Guo K, Guo Z. Generation of acoustic vortex beams with designed Fermat’s spiral diffraction grating. J Acoust Soc Am 2019; 146(6): 4237-4243.
  19. 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): 214.
  20. Petrov DV. Vortex-edge dislocation interaction in a linear medium. Opt Commun 2001; 188(5-6): 307-312.
  21. Petrov DV. Splitting of an edge dislocation by an optical vortex. Opt Quantum Electron 2002; 34: 759-773.
  22. He D, Yan H, Lu B. Interaction of the vortex and edge dislocation embedded in a sosh-Gaussian beam. Opt Commun 2009; 282(20): 4035-4044.
  23. Chen H, Wang W, Gao Z, Li W. Splitting of an edge dislocation by a vortex emergent from a nonparaxial beam. J Opt Soc Am B 2019; 36(10): 2804-2809.
  24. Kotlyar VV, Kovalev AA, Porfirev AP, Kozlova ES. Three different types of astigmatic Hermite-Gaussian beams with orbital angular momentum. J Opt 2019; 21(11): 115601. DOI: 10.1088/2040-8986/ab42b5.
  25. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex astigmatic Fourier-invariant Gaussian beams. Opt Express 2019; 27(2): 657-666. DOI: 10.1364/OE.27.000657.
  26. Courtial J, Dholakia K, Allen L, Padgett MJ. Gaussian beams with very high orbital angular momentum. Opt Commun 1997; 144(4-6): 210-213.
  27. Kotlyar VV, Kovalev AA, Porfirev  AP. Elliptic Gaussian optical vortices. Phys Rev A 2017; 95: 053805. DOI: 10.1103/PhysRevA.95.053805.
  28. Lin J, Dellinger J, Genevet P, Cluzel B, de Fornel F, Capasso F. Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave. Phys Rev Lett 2012; 109(9): 093904.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20