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Airy-Tricomi-Gaussian compressed light bullets

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Abstract.

Exact solution of the (3+1)D Schrödinger-type equation without external potential is obtained in cylindrical coordinates by using the method of separation of variables. Linear compressed light bullets are constructed with the help of a superposition of two counter-accelerating finite Airy wave functions and the Tricomi-Gaussian polynomials. We present some typical examples of the obtained solutions on the basis of four parameters: radial nodes, azimuthal nodes, the decay factor and the modulation depth. We find that the wave packets display different patterns and demonstrate that such linear light bullets can retain their shape over several Rayleigh lengths during propagation.

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References

  1. M.V. Berry, N.L. Balazs, Am. J. Phys. 47, 264 (1979)

    Article  ADS  Google Scholar 

  2. Z. Ye, S. Liu, C. Lou, P. Zhang, T. Hu, D. Song, J. Zhao, Z. Chen, Opt. Lett. 36, 3230 (2011)

    Article  ADS  Google Scholar 

  3. I. Kaminer, M. Segev, D.N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011)

    Article  ADS  Google Scholar 

  4. V.G. Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, Nature 419, 145 (2002)

    Article  ADS  Google Scholar 

  5. A. Salandrino, D.N. Christodoulides, Opt. Lett. 35, 2082 (2010)

    Article  ADS  Google Scholar 

  6. C. Hang, Z.Y. Bai, G.X. Huang, Phys. Rev. A 90, 023822 (2014)

    Article  ADS  Google Scholar 

  7. G.A. Siviloglou, J. Broky, A. Dogariu, D.N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007)

    Article  ADS  Google Scholar 

  8. G.A. Siviloglou, D.N. Christodoulides, Opt. Lett. 32, 979 (2007)

    Article  ADS  Google Scholar 

  9. G.A. Siviloglou, J. Broky, A. Dogariu, D.N. Christodoulides, Opt. Lett. 33, 207 (2008)

    Article  ADS  Google Scholar 

  10. W.P. Zhong, M. Belić, Y.Q. Zhang, J. Phys. B: At. Mol. Opt. Phys. 48, 175401 (2015)

    Article  ADS  Google Scholar 

  11. Y.Q. Zhang, M.R. Belić, J. Sun, H.B. Zheng, Z.K. Wu, Y.P. Zhang, Rom. Rep. Phys. 67, 1099 (2015)

    Google Scholar 

  12. F. Diebel, B.M. Bokić, D.V. Timotijević, D.M. Jović Savić, C. Denz, Opt. Express 23, 24351 (2015)

    Article  ADS  Google Scholar 

  13. W.P. Zhong, M. Belić, Eur. Phys. J. Plus 129, 234 (2014)

    Article  Google Scholar 

  14. W.P. Zhong, M. Belić, Y.Q. Zhang, Opt. Express 23, 23867 (2015)

    Article  ADS  Google Scholar 

  15. W.P. Zhong, M. Belić, Eur. Phys. J. D 59, 301 (2010)

    Article  ADS  Google Scholar 

  16. B.A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005)

    Article  ADS  Google Scholar 

  17. Y. Silberberg, Opt. Lett. 15, 1282 (1990)

    Article  ADS  Google Scholar 

  18. S. Minardi, F. Eilenberger, Y.V. Kartashov, A. Szameit, U. Ropke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tunnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010)

    Article  ADS  Google Scholar 

  19. D. Abdollahpour, S. Suntsov, D.G. Papazoglou, S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010)

    Article  ADS  Google Scholar 

  20. A. Chong, W. Renninger, D.N. Christodoulides, F.W. Wise, Nat. Photon. 4, 103 (2010)

    Article  ADS  Google Scholar 

  21. V.S. Bagnato, D.J. Frantzeskakis, P.G. Kevrekidis, B.A. Malomed, D. Mihalache, Rom. Rep. Phys. 67, 5 (2015)

    Google Scholar 

  22. D. Mihalache, Rom. J. Phys. 59, 295 (2014)

    Google Scholar 

  23. D. Mihalache, Rom. J. Phys. 57, 352 (2012)

    Google Scholar 

  24. W.P. Zhong, M. Belić, Y.Q. Zhang, Opt. Express 23, 23867 (2015)

    Article  ADS  Google Scholar 

  25. G.A. Siviloglou, D.N. Christodoulides, Opt. Lett. 32, 979 (2007)

    Article  ADS  Google Scholar 

  26. M.S. Mill, G.A. Siviloglou, N. Efremidis, T. Graf, E.M. Wright, J.V. Moloney, D.N. Christodoulides, Phys. Rev. A 86, 063811 (2012)

    Article  ADS  Google Scholar 

  27. D.N. Christodoulides, N.K. Efremidis, P.D. Trapani, B.A. Malomed, Opt. Lett. 39, 1446 (2004)

    Article  ADS  Google Scholar 

  28. M.V. Berry, J. Opt. A: Pure Appl. Opt. 6, 259 (2004)

    Article  ADS  Google Scholar 

  29. W.P. Zhong, M. Belić, R.H. Xie, T. Huang, Y. Lu, Opt. Commun. 283, 5213 (2010)

    Article  ADS  Google Scholar 

  30. W.P. Zhong, M. Belić, R.H. Xie, G. Chen, Phys. Rev. A 78, 013826 (2008)

    Article  ADS  Google Scholar 

  31. W.M. Lee, X.C. Yuan, K. Dholakia, Opt. Commun. 239, 129 (2004)

    Article  ADS  Google Scholar 

  32. J. Leach, E. Yao, M.J. Padget, New J. Phys. 6, 71 (2004)

    Article  ADS  Google Scholar 

  33. S.H. Tao, X.C. Yuan, J. Liu, X. Peng, H.B. Niu, Opt. Express 13, 7726 (2005)

    Article  ADS  Google Scholar 

  34. M.R. Belić, W.P. Zhong, Eur. Phys. J. D 53, 97 (2009)

    Article  ADS  Google Scholar 

  35. W.P. Zhong, M. Belić, Phys. Lett. A 373, 296 (2009)

    Article  ADS  MATH  Google Scholar 

  36. W.P. Zhong, L. Yi, Phys. Rev. A 75, 061801 (2007)

    Article  ADS  Google Scholar 

  37. W.P. Zhong, M. Belić, Phys. Rev. A 79, 023804 (2009)

    Article  ADS  Google Scholar 

  38. L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, Phys. Rev. A 45, 8185 (1992)

    Article  ADS  Google Scholar 

  39. V. Garcez-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, Nature 419, 145 (2002)

    Article  ADS  Google Scholar 

  40. D. Zwillinger, Handbook of Differential Equations, 3rd edition (Academic, Boston, 1997)

  41. M.J. Padgett, J. Molloy, D. McGloin, Optical Tweezers (Chapman and Hall, London, 2010)

  42. W.P. Zhong, M. Belić, G. Assanto, Boris. A. Malomed, T. Huang, Phys. Rev. A 83, 043833 (2011)

    Article  ADS  Google Scholar 

  43. W.P. Zhong, M. Belić, Y. Xia, Phys. Rev. E 83, 036603 (2011)

    Article  ADS  Google Scholar 

  44. W.P. Zhong, M. Belić, G. Assanto, Boris. A. Malomed, T. Huang, Phys. Rev. A 84, 043801 (2011)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, 528300, Shunde, China

    Wei-Ping Zhong

  2. Science Program, Texas A&M Univsersity at Qatar, P.O. Box 23874, Doha, Qatar

    Milivoj R. Belić

  3. Department of Electronic Science and Technology, Xi’an Jiaotong University, 710049, Xi’an, China

    Yiqi Zhang

Authors
  1. Wei-Ping Zhong
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  2. Milivoj R. Belić
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  3. Yiqi Zhang
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Correspondence to Wei-Ping Zhong.

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Zhong, WP., Belić, M. & Zhang, Y. Airy-Tricomi-Gaussian compressed light bullets. Eur. Phys. J. Plus 131, 42 (2016). https://doi.org/10.1140/epjp/i2016-16042-6

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  • DOI: https://doi.org/10.1140/epjp/i2016-16042-6

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