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Fourier-invariant autofocused Laguerre-Gaussian beams
V.V. Kotlyar 1,2, E.G. Abramochkin 1,2, A.A. Kovalev 1,2, E.S. Kozlova 1,2, A.A. Savelyeva 1,2

1 Image Processing Systems Institute, NRC "Kurchatov Institute",
443001, Samara, Russia, Molodogvardeyskaya 151;
2 Samara National Research University,
443086, Samara, Russia, Moskovskoye Shosse 34;
3 Lebedev Physical Institute,
443011, Samara, Russia, Novo-Sadovaya 221

 PDF, 1210 kB

DOI: 10.18287/2412-6179-CO-1374

Pages: 180-185.

Full text of article: Russian language.

Abstract:
We study a new Laguerre - Gaussian (LG) beam, which differs from conventional LG mode beams that preserve the structure of the intensity distribution up to scale. The proposed beam does not retain its structure upon free-space propagation but shows some interesting properties. This beam is Fourier invariant and has extended dark regions in the initial (waist) plane and in the far field. Thus, while maintaining the beam topological charge, the effective diameter of the central dark intensity spot can be increased or decreased by changing the radial index of the Laguerre polynomial. In addition, this beam has the property of autofocusing, that is, at the Rayleigh distance from the waist, the intensity distribution has the form of a light ring (for any value of the radial index) with a minimum diameter and maximum intensity on the ring. This beam can be used to manipulate microparticles without using an additional focusing spherical lens.

Keywords:
optical vortex, Laguerre-Gaussian beam, Fourier transform, Fresnel transform.

Citation:
Kotlyar VV, Abramochkin EG, Kovalev AA, Kozlova ES, Savelyeva AA. Fourier-invariant autofocused Laguerre-Gaussian beams. Computer Optics 2024; 48(2): 180-185. DOI: 10.18287/2412-6179-CO-1374.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #22-12-00137 (Sections “Fresnel transform from Laguerre–Gaussian beam with enlarged dark area” and “Simulation”) and within a state contract with the NRC "Kurchatov Institute" (Sections “Introduction” and “Conclusion”).

References:
  1. Prentice PA, MacDonald MP, Frank TG, Cuschieri A, Spalding GC, Sibbett W, Campbell PA, Dholakia K. Manipulation and filtration of low index particles with holographic Laguerre–Gaussian optical trap arrays. Opt Express 2004; 12: 593-600. DOI: 10.1364/OPEX.12.000593.
  2. Doster T, Watnik AT. Laguerre–Gauss and Bessel–Gauss beams propagation through turbulence: analysis of channel efficiency. Appl Opt 2016; 55: 10239-10246. DOI: 10.1364/AO.55.010239.
  3. Ferlic NA, Iersel M, Paulson DA, Davis CC. Propagation of Laguerre–Gaussian and Im–Bessel beams through atmospheric turbulence: A computational study. Proc SPIE 2020; 11506: 115060H. DOI: 10.1117/12.2567348.
  4. Ghaderi GAM, Mahmoudi M. Laguerre–Gaussian modes generated vector beam via nonlinear magneto-optical rotation. Sci Rep 2021; 11: 5972. DOI: 10.1038/s41598-021-85249-8.
  5. Cao M, Yu Y, Zhang L, Ye F, Wang Y, Wei D, Zhang P, Guo W, Zhang S, Gao H, Li F. Demonstration of CNOT gate with Laguerre Gaussian beams via four-wave mixing in atom vapor. Opt Express 2014; 22: 20177-20184. DOI: 10.1364/OE.22.020177.
  6. Dedecker P, Muls B, Hofkens J, Enderlein J, Hotta J. Orientational effects in the excitation and de-excitation of single molecules interacting with donut-mode laser beams. Opt Express 2007; 15: 3372-3383. DOI: 10.1364/OE.15.003372.
  7. Bokor N, Iketaki Y, Watanabe T, Fujii M. Investigation of polarization effects for high-numerical-aperture first-order Laguerre–Gaussian beams by 2D scanning with a single fluorescent microbead. Opt Express 2005; 13: 10440-10447. DOI: 10.1364/OPEX.13.010440.
  8. Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP, Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys Rev A 1992; 45: 8185-8189. DOI: 10.1103/PhysRevA.45.8185.
  9. Zhou G, Ru G. Orbital angular momentum density of an elegant Laguerre–Gaussian beam. Prog Electromagn Res 2013; 141: 751-768. DOI: 10.2528/PIER13051608.
  10. Abramochkin E, Razueva E, Volostnikov V. General astigmatic transform of Hermite–Laguerre–Gaussian beams. J Opt Soc Am A 2010; 27: 2506-2513. DOI: 10.1364/JOSAA.27.002506.
  11. Kovalev AA, Kotlyar VV, Porfirev AP. Asymmetric Laguerre–Gaussian beams. Phys Rev A 2016; 93: 063858. DOI: 10.1103/PhysRevA.93.063858.
  12. 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: 1397-1399. DOI: 10.1364/OL.37.001397.
  13. Kotlyar VV, Abramochkin EG, Kovalev AA, Savelyeva AA. Product of Two Laguerre–Gaussian Beams. Photonics 2022; 9: 496. DOI: 10.3390/photonics9070496.
  14. Bisson JF, Senatsky Y, Ueda KI. Generation of Laguerre–Gaussian modes in Nd:YAG laser using diffractive optical pumping. Laser Phys Lett 2015: 2(7): 327-333. DOI: 10.1002/lapl.200510008.
  15. Lin D, Daniel JMO, Clarkson WA. Controlling the handedness of directly excited Laguerre–Gaussian modes in a solid-state laser. Opt Lett 2014; 39(13): 3903-3906. DOI: 10.1364/OL.39.003903.
  16. Thirugnanasambandam MP, Senatsky Y. Generation of very-high order Laguerre–Gaussian modes in Yb:YAG ceramic laser. Laser Phys Lett 2010; 7(9): 637-643. DOI: 10.1002/lapl.201010044.
  17. Wang M, Ma Y, Sheng Q, He X, Liu J, Shi W, Yao J, Omatsu T. Laguerre–Gaussian beam generation via enhanced intracavity spherical aberration. Opt Express 2021; 29: 27783-27790. DOI: 10.1364/OE.436110.
  18. Abramochkin E, Volostnikov V. Beam transformations and nontransformed beams. Opt Commun 1991; 83: 123-135. DOI: 10.1016/0030-4018(91)90534-K.
  19. Matsumoto N, Ando T, Inoue T, Ohtake Y, Fukuchi N, Hara T. Generation of high-quality higher-order Laguerre–Gaussian beams using liquid-crystal-on-silicon spatial light modulators. J Opt Soc Am A 2008; 25: 1642-1651. DOI: 10.1364/JOSAA.25.001642.
  20. Kotlyar V, Kovalev A. Orbital angular momentum of paraxial propagation-invariant laser beams. J Opt Soc Am A 2022; 39: 1061-1065. DOI: 10.1364/JOSAA.457660.
  21. 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: 727. DOI: 10.3390/photonics10070727.
  22. Prudnikov AP, Brychkov YA, Marichev OI. Integrals and series, Special functions. New York: Gordon and Breach; 1981.

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