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Orbital angular momentum burst control in astigmatic structured beams in ABCD-matrix transforms
A.V. Volyar 1, M.V. Bretsko 1, S.I. Khalilov 1, Y.E. Akimova 1

1 Physics and Technology Institute of V.I. Vernadsky Crimean Federal University,
295007, Simferopol, Republic of Crimea, Russia, Academician Vernadsky 4

 PDF, 1872 kB

DOI: 10.18287/2412-6179-CO-1411

Pages: 171-179.

Full text of article: Russian language.

Abstract:
We developed and experimentally implemented an ABCD matrix formalism for describing structural transformations and orbital angular momentum of structured Laguerre-Gaussian beams in an astigmatic optical system containing cylindrical and corrective spherical lenses. It was shown that the matrix formalism not only agrees well with the method of integral astigmatic transformations, but also significantly expands the scope of its application. It was found that a corrective spherical lens is capable of not only separating the vortex and astigmatic components of the orbital angular momentum, but also transforming a structurally unstable astigmatic Laguerre-Gaussian beam after a cylindrical lens into a structurally stable one, provided that the form of fast oscillations and bursts of the orbital angular momentum is preserved.

Keywords:
vortex beams; ABCD-matrix, structured light; orbital angular momentum.

Citation:
Volyar AV, Bretsko MV, Khalilov SI, Akimova YE. Orbital angular momentum burst control in astigmatic structured beams in ABCD-matrix transforms. Computer Optics 2024; 48(2): 171-179. DOI: 10.18287/2412-6179-CO-1411.

Acknowledgements:
The authors thank E. Abramochkin for the useful discussion.

References:
  1. Kogelnik H, Li T. Laser beams and resonators. Appl Opt 1966; 5(10): 1550-1567. DOI: 10.1364/AO.5.001550.
  2. Siegman AE. Lasers. Mill Valley, CA: University Science Books; 1986. ISBN: 0-935702-11-5.
  3. Soifer VA, Golub MA. Laser beam mode selection by computer-generated holograms. Boca Raton: CRC Press; 1994. ISBN: 0-8493-2476-9.
  4. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex laser beams. Boca Raton, FL: Taylor & Francis Groop LLC; 2019. DOI: 10.1201/9781351009607.
  5. Forbes A, de Oliveira M, Dennis MR. Structured light. Nat Photonics 2021; 15: 253-262. DOI: 10.1038/s41566-021-00780-4.
  6. Shen Y, Yang X, Naidoo D, Fu X, 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.382994.
  7. Fadeyeva T, Rubass A, Egorov Y, Swartzlander JrG. Quadrefringence of optical vortices in a uniaxial crystal. J Opt Soc Am A 2008; 25(7): 1634-1641. DOI: 10.1364/JOSAA.25.001634.
  8. Fadeyeva T, Alexeyev C, Rubass A, Volyar A. Vector erf-Gaussian beams: Fractional optical vortices and asymmetric TE and TM modes. Opt Lett 2012; 37(9): 1397-1399. DOI: 10.1364/OL.37.001397.
  9. Collins SA. Lens-system diffraction integral written in terms of matrix optics. J Opt Soc Am 1970; 60(9): 1168-1177. DOI: 10.1364/JOSA.60.001168.
  10. Bélanger PA. Beam propagation and the ABCD ray matrices. Opt Lett 1991; 16(4): 196-198. DOI: 10.1364/OL.16.000196.
  11. Taché JP. Derivation of ABCD law for Laguerre-Gaussian beams. Appl Opt 1987; 26(14): 2698-2700. DOI: 10.1364/AO.26.002698.
  12. Alieva T, Bastiaans MJ. Alternative representation of the linear canonical integral transform. Opt Lett 2005; 30(24): 3302-3304. DOI: 10.1364/OL.30.003302.
  13. Alieva T, Bastiaans MJ. Mode mapping in paraxial lossless optics. Opt Lett 2005; 30(12): 1461-1463. DOI: 10.1364/OL.30.001461.
  14. Beijersbergen MW, Allen L, van der Veen HELO, Woerdman JP. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt Commun 1993; 96(1): 123-132. DOI: 10.1016/0030-4018(93)90535-D.
  15. Courtial J, Padgett MJ. Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes. Opt Commun 1999; 159(1): 13-18. DOI: 10.1016/S0030-4018(98)00599-9.
  16. Khonina SN, Karpeev SV, Ustinov AV. Functional enhancement of mode astigmatic converters on the basis of application of diffractive optical elements [In Russian]. Izvestia of Samara Scientific Center of the Russian Academy of Sciences 2009; 11(5): 13-23.
  17. Abramochkin E, Volostnikov V. Beam transformations and nontransformed beams. Opt Commun 1991; 83(1): 123-135. DOI: 10.1016/0030-4018(91)90534-K.
  18. Abramochkin E, Razueva E, Volostnikov V. General astigmatic transform of Hermite–Laguerre–Gaussian beams. J Opt Soc Am A 2010; 27(11): 2506-2513. DOI: 10.1364/JOSAA.27.002506.
  19. Abramochkin E, Volostnikov V. Modern optics of Gaussian beams [In Russian]. Moscow: “Fizmatlit” Publisher; 2010. ISBN: 978-5-9221-1216-1.
  20. Wada A, Ohtani T, Miyamoto Y, Takeda M. Propagation analysis of the Laguerre-Gaussian beam with astigmatism. J Opt Soc Am A 2005; 22(12): 2746-2755. DOI: 10.1364/JOSAA.22.002746.
  21. Bekshaev AYa, Soskin MS, Vasnetsov MV. Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams. J Opt Soc Am A 2003; 20(8): 1635-1643. DOI: 10.1364/JOSAA.20.001635.
  22. 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(90): 90. DOI: 10.1038/s41377-019-0194-2.
  23. Alieva T, Bastiaans MJ. Orthonormal mode sets for the two-dimensional fractional Fourier transformation. Opt Lett 2007; 32(10): 1226-1228. DOI: 10.1364/OL.32.001226.
  24. Volyar A, Abramochkin E, Akimova Y, Bretsko M. Astigmatic-invariant structured singular beams. Photonics 2022; 9(11): 842. DOI: 10.3390/photonics9110842.
  25. Volyar A, Abramochkin E, Bretsko M, Khalilov S, Akimova Y. General astigmatism of structured LG beams: Evolution and transformations of the OAM super-bursts. Photonics 2023; 10(7): 727. DOI: 10.3390/photonics10070727.
  26. Bekshaev AYa, Soskin MS, Vasnetsov MV. Transformation of higher-order optical vortices upon focusing by an astigmatic lens. Opt Commun 2004; 241(4): 237-247. DOI: 10.1016/j.optcom.2004.07.023.
  27. Kotlyar VV, Kovalev AA. Orbital angular momentum of paraxial propagation-invariant laser beams. J Opt Soc Am A 2022; 39(6): 1061-1065. DOI: 10.1364/JOSAA.457660.
  28. 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.
  29. Anan’ev YuA, Bekshaev AYa. Theory of intensity moments for arbitrary light beams. Opt Spectrosc 1994; 76(4): 558-568.
  30. Fadeyeva TA, Rubass AF, Aleksandrov RV, Volyar AV. Does the optical angular momentum change smoothly in fractional-charged vortex beams? J Opt Soc Am B 2014; 31(4): 798-805. DOI: 10.1364/JOSAB.31.000798.

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