(46-5) 06 * << * >> * Russian * English * Content * All Issues

Changing the trajectory of Airy beam sets with spatial carriers
A.O. Frolov 1, А.V. Ustinov 2, S.N. Khonina 1,2

Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34;
IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151

 PDF, 1607 kB

DOI: 10.18287/2412-6179-CO-1139

Pages: 724-732.

Full text of article: Russian language.

In this paper, we study a change in the propagation trajectory of a set of autofocusing laser beams using a fractional Fourier transform. Clusters of displaced bounded Airy-Gaussian beams supplemented by a phase function that deflects the beam similarly to a prism are considered. The shift and phase deviation (according to the carrier spatial frequencies) make it possible to change the propagation trajectory of a set of autofocusing beams. The influence of the parameters under consideration on the properties of autofocusing of a cluster of Airy-Gaussian beams is investigated by means of numerical simulation.

autofocusing properties, sets of Airy-Gaussian beams, fractional Fourier transform.

Frolov AO, Ustinov AV, Khonina SN. Changing the trajectory of Airy beam sets with spatial carriers. Computer Optics 2022; 46(5): 724-732. DOI: 10.18287/2412-6179-CO-1139.

This work was supported by the Russian Foundation for Basic Research under grant No. 20-37-90129 (numerical modeling) and the Ministry of Science and Higher Education within the State assignment of the FSRC "Crystallography and Photonics" RAS (theoretical analysis).


  1. Berry МV, Balazs NL. Nonspreding wave packets. Am J Phys 1979; 47(3): 264-267. DOI: 10.1119/1.11855.
  2. Siviloglou GA, Christodoulides DN. Accelerating finite energy Airy beams. Opt Lett 2007; 32(8): 979-981. DOI: 10.1364/OL.32.000979.
  3. Saari P. Laterally accelerating Airy pulses. Opt Express 2008; 16(4): 10303-10308. DOI: 10.1364/OE.16.010303.
  4. Bandres MA. Accelerating beams. Opt Lett 2009; 34(24): 3791-3793. DOI: 10.1364/OL.34.003791.
  5. Vallée O, Soares M. Airy functions and applications in physics. London: Imperial College Press; 2004. ISBN: 1-86094-478-7.
  6. Baumgartl J, Mazilu M, Dholakia K. Optically mediated particle clearing using Airy wavepackets. Nat Photonics 2008; 2(11): 675-678. DOI: 10.1038/nphoton.2008.201.
  7. Khonina SN, Skidanov RV, Moiseev OYu. Airy laser beams generation by binary-coded diffractive optical elements for microparticles manipulation. Computer Optics 2009; 33(2): 138-146.
  8. Zheng Z, Zhang B-F, Chen H, Ding J, Wang H-T. Optical trapping with focused Airy beams. Appl Opt 2011; 50(1): 43-49. DOI: 10.1364/AO.50.000043.
  9. Vettenburg T, Dalgarno HIC, Nylk J, Coll-Llado C, Ferrier DEK, Čižmár T, Gunn-Moore FJ, Dholakia K. Light-sheet microscopy using an Airy beam. Nat Methods 2014; 11(5): 541-544. DOI: 10.1038/nmeth.2922.
  10. Piksarv P, Marti D, Le T, Unterhuber A, Forbes LH, Andrews MR, Stingl A, Drexler W, Andersen PE, Dholakia K. Integrated single- and two-photon light sheet microscopy using accelerating beams. Sci Rep 2017; 7(1): 1435. DOI: 10.1038/s41598-017-01543-4.
  11. Dowski ER, Cathey WT. Extended depth of field through wave-front coding. Appl Opt 1995; 34(11): 1859-1866. DOI: 10.1364/AO.34.001859.
  12. Pan C, Chen J, Zhang R, Zhuang S. Extension ratio of depth of field by wavefront coding method. Opt Express 2008; 16(17): 13364-13371. DOI: 10.1364/oe.16.013364.
  13. Khonina SN, Volotovskiy SG, Dzyuba AP, Serafimovich PG, Popov SB, Butt MA. Power phase apodization study on compensation defocusing and chromatic aberration in the imaging system. Electronics 2021; 10(11): 1327. DOI: 10.3390/electronics10111327.
  14. Mathis A, Courvoisier F, Froehly L, Furfaro L, Jacquot M, Lacourt PA, Dudley JM. Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams. Appl Phys Lett 2012; 101(7): 071110. DOI: 10.1063/1.4745925.
  15. Courvoisier S, Götte N, Zielinski B, Winkler T, Sarpe C, Senftleben A, Bonacina L, Wolf JP, Baumert T. Temporal Airy pulses control cell poration. APL Photon 2016; 1(4): 046102. DOI: 10.1063/1.4948367.
  16. Rose P, Diebel F, Boguslawski M, Denz C. Airy beam induced optical routing. Appl Phys Lett 2013; 102(10): 101101. DOI: 10.1063/1.4793668.
  17. Banders MA, Gutierrez-Vega JC. Airy-Gauss beams and their transformation by paraxial optical systems. Opt Express 2007; 15(25): 16719-16728. DOI: 10.1364/OE.15.016719.
  18. Khonina SN, Volotovsky SG. Bounded 1D Airy beams: Laser fan. Computer Optics 2008; 32(2): 168-174.
  19. Efremidis NK, Christodoulides DN. Abruptly autofocusing waves. Opt Lett 2010; 35(23): 4045-4047. DOI: 10.1364/OL.35.004045.
  20. Davis JA, Cottrell DM, Sand D. Abruptly autofocusing vortex beams. Opt Express 2012; 20(12): 13302-13310. DOI: 10.1364/OE.20.013302.
  21. Vaveliuk P, Lencina A, Rodrigo JA, Matos OM. Symmetric Airy beams. Opt Lett 2014; 39(8): 2370-2373. DOI: 10.1364/OL.39.002370.
  22. Jiang Y, Zhao S, Yu W, Zhu X. Abruptly autofocusing property of circular Airy vortex beams with different initial launch angles. J Opt Soc Am A 2018; 35(6): 890-894. DOI: 10.1364/JOSAA.35.000890.
  23. Khonina SN. Mirror and circular symmetry of autofocusing beams. Symmetry 2021; 13(10): 1794. DOI: 10.3390/sym13101794.
  24. Zhang P, Prakash J, Zhang Z, Mills MS, Efremidis NK, Christodoulides DN, Chen Z. Trapping and guiding microparticles with morphing autofocusing Airy beams. Opt Lett 2011; 36(15): 2883-2885. DOI: 10.1364/OL.36.002883.
  25. Manousidaki M, Papazoglou DG, Farsari M, Tzortzakis S. Abruptly autofocusing beams enable advanced multiscale photo-polymerization. Optica 2016; 3(5): 525-530. DOI: 10.1364/OPTICA.3.000525.
  26. Panagiotopoulos P, Papazoglou DG, Couairon A, Tzortzakis S. Sharply autofocused ring-Airy beams trans-forming into non-linear intense light bullets. Nat Commun 2013; 4: 2622. DOI: 10.1038/ncomms3622.
  27. Li P, Liu S, Peng T, Xie G, Gan X, Zhao J. Spiral autofocusing Airy beams carrying power-exponent phase vortices. Opt Express 2014; 22(7): 7598-7606. DOI: 10.1364/OE.22.007598.
  28. Khonina SN, Ustinov AV. Fractional Airy beams. J Opt Soc Am A 2017; 34(11): 1991-1999. DOI: 10.1364/JOSAA.34.001991.
  29. Khonina SN, Porfirev AP, Ustinov AV. Sudden autofocusing of superlinear chirp beams. J Opt 2018; 20(2): 025605. DOI: 10.1088/2040-8986/aaa075.
  30. Brimis A, Makris KG, Papazoglou DG. Tornado waves. Opt Lett 2020; 45(2): 280-283. DOI: 10.1364/OL.45.000280.
  31. Khonina SN, Porfirev AP, Ustinov AV, Butt MA. Generation of complex transverse energy flow distributions with autofocusing optical vortex beams. Micromachines 2021; 12(3): 297. DOI: 10.3390/mi12030297.
  32. Lü B, Ma H. Beam propagation properties of radial laser arrays. J Opt Soc Am A 2000; 17(11): 2005-2009. DOI: 10.1364/JOSAA.17.002005.
  33. Song L, Yang Z, Li X, Zhang S. Controllable Gaussian-shaped soliton clusters in strongly nonlocal media. Opt Express 2018; 26(15): 19182-19198. DOI: 10.1364/OE.26.019182.
  34. Suarez RA, Neves AA, Gesualdi MR. Generation and characterization of an array of Airy-vortex beams. Opt Commun 2019; 458: 124846.
  35. Song L, Yang Z, Zhang S, Li X. Dynamics of rotating Laguerre-Gaussian soliton arrays. Opt Express 2019; 27(19): 26331-26345. DOI: 10.1364/OE.27.026331.
  36. Suarez RA, Neves AA, Gesualdi MR. Optimizing optical trap stiffness for Rayleigh particles with an Airy array beam. J Opt Soc Am B 2020; 37(2): 264-270. DOI: 10.1364/JOSAB.379247.
  37. Frolov AO, Khonina SN. Modeling the propagation of sets of autofocusing laser beams. Proc SPIE 2021; 11793: 117930I. DOI: 10.1117/12.2592792.
  38. Namias V. The fractional order Fourier transform and its application to quantum mechanics. IMA J Appl Math 1980; 25(3): 241-265. DOI: 10.1093/imamat/25.3.241.
  39. Mendlovic D, Ozaktas HM. Fractional Fourier transformations and their optical implementation. I. J Opt Soc Am A 1993; 10(9): 1875-1881. DOI: 10.1364/JOSAA.10.001875.
  40. Haskel M, Stern A. Evaluation of the influence of arbitrary masks on the output field of optical systems using ABCD matrices. J Opt Soc Am A 2017; 34(4): 609-613. DOI: 10.1364/JOSAA.34.000609.
  41. 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.
  42. Khonina SN, Striletz AS, Kovalev AA, Kotlyar VV. Propagation of laser vortex beams in a parabolic optical fiber. Proc SPIE 2010; 7523: 75230B. DOI: 10.1117/12.854883.
  43. Monin EO, Ustinov AV, Khonina SN. Propagation modeling of vortex generalized Airy beams in parabolic fiber. Proc Progress in Electromagnetics Research Symposium 2018; F134321: 583-589. DOI: 10.1109/PIERS.2017.8261809.
  44. Ustinov AV, Khonina SN. Generalized lens: Calculation of distribution on the optical axis. Computer Optics 2013; 37(3): 307-315.
  45. Kirilenko MS, Zubtsov RO, Khonina SN,
    Calculation of eigenfunctions of a bounded fractional Fourier transform, Computer Optics, 2015; 39(3): 332-338.  DOE: 10.18287/0134-2452-2015-39-3-332-338.

© 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