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Applied Physics B

, 125:188 | Cite as

Bound states of chirped Airy–Gaussian beams in a medium with a parabolic potential

  • Xiaoqin Bai
  • Yuhao Wang
  • Jing Zhang
  • Yan XiaoEmail author
Article
  • 14 Downloads

Abstract

Starting from the normalized dimensionless linear parabolic (Schrödinger-like) equation, by means of split-step Fourier numerical simulation, in this paper we investigate the interaction between two chirped Airy–Gaussian (CAiG) beams in a medium with a parabolic potential. We find that a parabolic potential provides interesting effects and supports the bound states of two CAiG beams. We also study the effect of chirps and found that large enough chirps will weaken the energy of bound states. Moreover, initial parameters of the beams, initial interval, amplitudes, and distribution factor, are taken into consideration as well.

Notes

References

  1. 1.
    M.V. Berry, N.L. Balazs, Nonspreading wave packets. Am. J. Phys. 47, 264 (1979)ADSCrossRefGoogle Scholar
  2. 2.
    G.A. Siviloglou, D.N. Christodoulides, Accelerating finite energy airy beams. Opt. Lett. 32, 979 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    G.A. Siviloglou, J. Broky, A. Dogariu, D.N. Christodoulides, Observation of accelerating Airy beams. Phys. Rev. Lett. 99, 213901 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    G.A. Siviloglou, J. Broky, A. Dogariu et al., Ballistic dynamics of Airy beams. Opt. Lett. 33, 207 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    J. Broky, G.A. Siviloglou, A. Dogariu et al., Self-healing properties of optical Airy beams. Opt. Express 16, 12880 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    M.A. Bandres, B.M. Rodríguez-Lara, Nondiffracting accelerating waves: weber waves and parabolic momentum. New J. Phys. 15, 13054 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    J. Baumgartl, M. Mazilu, K. Dholakia, Optically mediated particle clearing using Airy wavepackets. Nat. Photon. 2, 675 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    I. Dolev, T. Ellenbogen, A. Arie, Switching the acceleration direction of Airy beams by a nonlinear optical process. Opt. Lett. 35, 1581 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    P. Polynkin, M. Kolesik, J.V. Moloney et al., Curved plasma channel generation using ultraintense Airy beams. Science 324, 229 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Fattal, A. Rudnick, D.M. Marom, Soliton shedding from Airy pulses in Kerr media. Opt. Express 19, 17298 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Y.Q. Zhang, M.R. Belic, Z.K. Wu et al., Soliton pair generation in the interactions of Airy and nonlinear accelerating beams. Opt. Lett. 38, 4585 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    Y.Q. Zhang, M.R. Belic, H.B. Zheng et al., Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media. Opt. Express 22, 7160 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    L.F. Zhang, K. Liu, H.Z. Zhong et al., Effect of initial frequency chirp on Airy pulse propagation in an optical fiber. Opt. Express 23, 2566 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    Y.Q. Zhang, M.R. Belic, L. Zhang et al., Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential. Opt. Express 23, 10467 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    Z.K. Wu, P. Li, Y.Z. Gu, Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media. Front. Phys. 12, 124203 (2017)CrossRefGoogle Scholar
  16. 16.
    Y.Q. Zhang, H. Zhong, M.R. Belic et al., Diffraction-free beams in fractional Schrödinger equation. Sci Rep 6, 23645 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    C.M. Huang, L.W. Dong, Beam propagation management in a fractional Schrödinger equation. Sci. Rep. 7, 5442 (2017)ADSCrossRefGoogle Scholar
  18. 18.
    X.W. Huang, X.H. Shi, Z.X. Deng et al., Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation. Opt. Express 25, 32560 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    D. Deng, H. Li, Propagation properties of Airy-Gaussian beams. Appl. Phys. B. 106, 677 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Y.L. Peng, X. Peng, B. Chen et al., Interaction of Airy-Gaussian beams in Kerr media. Opt. Commun. 359, 116 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    M.L. Zhou, Y.L. Peng, C.D. Chen et al., Interaction of Airy-Gaussian beams in saturable media. Chin. Phys. B 25, 084102 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    L.P. Zhang, F. Deng, Y.L. Peng et al., Chirped Airy-Gaussian beam in a medium with a parabolic potential. Laser Phys. 27, 015404 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    M.J. Ablowitz, B. Prinari, A.D. Trubatch, Discrete and continuous nonlinear schrödinger systems (Cambridge University Press, Cambridge, 2004)zbMATHGoogle Scholar
  24. 24.
    G.P. Agrawal, Nonlinear fiber optics, 3rd edn. (Academic Press, San Diego, 2001)zbMATHGoogle Scholar
  25. 25.
    L. Zhang, X.Q. Bai, Y.H. Wang et al., Interaction of Airy beams in a medium with parabolic potential. Optik 161, 106 (2018)ADSCrossRefGoogle Scholar
  26. 26.
    S.M. Wang, Q. Lin, Non-diffracting properties of airy beams. Appl. Laser 14, 1 (1994)Google Scholar
  27. 27.
    M.A. Bandres, J.C. Gutiérrez-Vega, Airy-Gauss beams and their transformation by paraxial optical systems. Opt. Express 15, 16719 (2007)ADSCrossRefGoogle Scholar
  28. 28.
    Y.L. Wu, J.S. Nie, L. Shao, Complete solutions of finite Airy beams in free space and graded index media with fourier analysis. Optik 138, 377 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    A.M. Ruiz, J.M. Heredia, L.A. Ruiz-Ochoa et al., Propagation of optical beams in two transverse gradient index media. Euro. Phys. J. D 70, 110 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    T.R. Taha, M.I. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation. J. Comput. Phys. 55, 203 (1984)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Physics and Electronics EngineeringShanxi UniversityTaiyuanChina

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