The Evolution of Lorentz–Gauss Breathers Induced by Off-Waist Incidence

  • Zhenfeng YangEmail author


We investigate the propagation of Lorentz–Gauss beams (LGBs) for the case of the off-waist incident condition in strongly nonlocal nonlinear media (SNNM) and derive the analytical expression describing the beam width evolution of LGBs. We found that the beam width of LGBs cannot remain invariant and always varies periodically like a breather for the off-waist incident condition, even when the input power of LGBs is equal to the critical input power, which is much different from that for the on-waist incident condition. Also we provide the evolution of the curvature radius of LGBs for the off-waist incident condition, and it is the cause of Lorentz–Gauss breather formation. Numerical simulations are performed to show the propagation characteristics.


spatial nonlocality nonlinear propagation Lorentz–Gauss beam breather 


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  1. 1.
    X. Ma, O. A. Egorov, and S. Schumacher, Phys. Rev. Lett., 118, 157401 (2017).ADSCrossRefGoogle Scholar
  2. 2.
    X. J. Zhao, R. Guo, and H. Q. Hao, Appl. Math. Lett., 75, 114 (2018).MathSciNetCrossRefGoogle Scholar
  3. 3.
    H. Q. Hao, R. Guo, and J. W. Zhang, Nonlin. Dyn., 88, 1615 (2017).CrossRefGoogle Scholar
  4. 4.
    J. Y. Song, H. Q. Hao, and X. M. Zhang, Appl. Math. Lett., 78, 126 (2018).MathSciNetCrossRefGoogle Scholar
  5. 5.
    A. W. Snyder and D. J. Mitchell, Science, 276, 1538 (1997).CrossRefGoogle Scholar
  6. 6.
    W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, Appl. Phys. Lett., 89, 071111 (2006).ADSCrossRefGoogle Scholar
  7. 7.
    Z. J. Yang, Z. F. Yang, J. X. Li, et al., Results Phys., 7, 1485 (2017).ADSCrossRefGoogle Scholar
  8. 8.
    Q. Guo, B. Luo, F. Yi, et al., Phys. Rev. E, 69, 016602 (2004).ADSCrossRefGoogle Scholar
  9. 9.
    C. Rotschild, M. Segev, Z. Xu, et al., Opt. Lett., 31, 3312 (2006).ADSCrossRefGoogle Scholar
  10. 10.
    Z. Dai, Z. Yang, X. Ling, et al., Sci. Rep., 7, 122 (2017).ADSCrossRefGoogle Scholar
  11. 11.
    Z. J. Yang, Z. P. Dai, S. M. Zhang, and Z. G. Pang, Nonlin. Dyn., 80, 1081 (2015).CrossRefGoogle Scholar
  12. 12.
    Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, Opt. Lett., 36, 184 (2011).ADSCrossRefGoogle Scholar
  13. 13.
    L. Song, Z. Yang, X. Li, and S. Zhang, Opt. Express, 26, 19182 (2018).ADSCrossRefGoogle Scholar
  14. 14.
    C. Rotschild, O. Cohen, O. Manela, and M. Segev, Phys. Rev. Lett., 95, 213904 (2005).ADSCrossRefGoogle Scholar
  15. 15.
    Q. Wang, J. Li, and W. Xie, IEEE Photon. J., 10, 6500611 (2018).Google Scholar
  16. 16.
    Q. Wang, J. Li, and W. Xie, Appl. Phys. B, 124, 104 (2018).ADSCrossRefGoogle Scholar
  17. 17.
    Y. V. Izdebskaya, A. S. Desyatnikov, and Y. S. Kivshar, Phys. Rev. Lett., 111, 123902 (2013).ADSCrossRefGoogle Scholar
  18. 18.
    L. M. Song, Z. J. Yang, Z. G. Pang, et al., Appl. Math. Lett., 90, 42 (2019).MathSciNetCrossRefGoogle Scholar
  19. 19.
    S. Chen, Z. Qi, J. Xie, et al., Opt. Commun., 429, 72 (2018).ADSCrossRefGoogle Scholar
  20. 20.
    G. Liang, Q. Guo, W. Cheng, e al., Opt. Express, 23, 24612 (2015).ADSCrossRefGoogle Scholar
  21. 21.
    Z. Dai, Z. Yang, S. Zhang, and Z. Pang, Opt. Commun., 350, 19 (2015).ADSCrossRefGoogle Scholar
  22. 22.
    Z. Dai, S. Tang, Z. Yang, et al., J. Russ. Laser Res., 38, 241 (2017).CrossRefGoogle Scholar
  23. 23.
    Y. V. Izdebskaya, V. G. Shvedov, P. S. Jung, and W. Krolikowski, Opt. Lett., 43, 66 (2018).ADSCrossRefGoogle Scholar
  24. 24.
    Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, Appl. Math. Lett., 82, 64 (2018).ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    R. Guo and H. Q. Hao, Commun. Nonlin. Sci. Numer. Simul., 18, 2426 (2013).CrossRefGoogle Scholar
  26. 26.
    R. Guo, Y. F. Liu, H. Q. Hao, and F. H. Qi, Nonlin. Dyn., 80, 1221 (2015).CrossRefGoogle Scholar
  27. 27.
    W. Du, J. Yang, Z. Yao, et al., J. Russ. Laser Res., 35, 416 (2014).CrossRefGoogle Scholar
  28. 28.
    Y. Yang, Y. Dong, C. Zhao, and Y. Cai, Opt. Lett., 38, 5418 (2013).ADSCrossRefGoogle Scholar
  29. 29.
    Z. Dai, Y. Xu, Q. Guo, and S. Chi, Phys. Rev. A, 87, (2013).Google Scholar
  30. 30.
    O. E. Gawhary and S. Severini, J. Opt. A: Pure Appl. Opt., 8, 409 (2006).ADSCrossRefGoogle Scholar
  31. 31.
    G. Zhou, Opt. Commun., 283, 1236 (2010).ADSCrossRefGoogle Scholar
  32. 32.
    G. Zhou and X. Chu, Appl. Phys. B, 100, 909 (2010).ADSCrossRefGoogle Scholar
  33. 33.
    W. Du, C. Zhao, and Y. Cai, Opt. Laser Eng., 49, 25 (2011).CrossRefGoogle Scholar
  34. 34.
    X. Wang, Z. Liu, and D. Zhao, J. Opt. Soc. Am. A, 31, 872 (2014).ADSCrossRefGoogle Scholar
  35. 35.
    A. Keshavarz and G. Honarasa, Commun. Theor. Phys., 61, 241 (2014).ADSCrossRefGoogle Scholar
  36. 36.
    D. Lu, W. Hu, Y. Zheng, et al., Phys. Rev. A, 78, 043815 (2008).ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Information ManagementHebei University of Science and TechnologyShijiazhuangChina

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