OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 7160–7171

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media

Yiqi Zhang, Milivoj R. Belić, Huaibin Zheng, Haixia Chen, Changbiao Li, Yuanyuan Li, and Yanpeng Zhang  »View Author Affiliations

Optics Express, Vol. 22, Issue 6, pp. 7160-7171 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (19997 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior.

© 2014 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(190.3270) Nonlinear optics : Kerr effect
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(350.5500) Other areas of optics : Propagation
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

Original Manuscript: December 27, 2013
Revised Manuscript: February 25, 2014
Manuscript Accepted: March 2, 2014
Published: March 19, 2014

Yiqi Zhang, Milivoj R. Belić, Huaibin Zheng, Haixia Chen, Changbiao Li, Yuanyuan Li, and Yanpeng Zhang, "Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media," Opt. Express 22, 7160-7171 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. A. Siviloglou, D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007). [CrossRef] [PubMed]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007). [CrossRef]
  3. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678–1680 (2008). [CrossRef] [PubMed]
  4. M. A. Bandres, “Accelerating beams,” Opt. Lett. 34, 3791–3793 (2009). [CrossRef] [PubMed]
  5. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009). [CrossRef]
  6. A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010). [CrossRef]
  7. N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010). [CrossRef] [PubMed]
  8. M. A. Alonso, M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37, 5175–5177 (2012). [CrossRef] [PubMed]
  9. I. Kaminer, J. Nemirovsky, M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012). [CrossRef] [PubMed]
  10. I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012). [CrossRef]
  11. P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012). [CrossRef] [PubMed]
  12. M. A. Bandres, M. A. Alonso, I. Kaminer, M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21, 13917–13929 (2013). [CrossRef] [PubMed]
  13. M. A. Bandres, B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013). [CrossRef]
  14. Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35, 3952–3954 (2010). [CrossRef] [PubMed]
  15. I. Kaminer, M. Segev, D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011). [CrossRef] [PubMed]
  16. N. K. Efremidis, V. Paltoglou, W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013). [CrossRef]
  17. A. Salandrino, D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35, 2082–2084 (2010). [CrossRef] [PubMed]
  18. P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011). [CrossRef] [PubMed]
  19. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011). [CrossRef] [PubMed]
  20. L. Li, T. Li, S. M. Wang, C. Zhang, S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011). [CrossRef] [PubMed]
  21. L. Li, T. Li, S. Wang, S. Zhu, X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11, 4357–4361 (2011). [CrossRef] [PubMed]
  22. F. Zhuang, J. Shen, X. Du, D. Zhao, “Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor,” Opt. Lett. 37, 3054–3056 (2012). [CrossRef] [PubMed]
  23. F. Zhuang, X. Du, Y. Ye, D. Zhao, “Evolution of Airy beams in a chiral medium,” Opt. Lett. 37, 1871–1873 (2012). [CrossRef] [PubMed]
  24. I. Kaminer, J. Nemirovsky, K. G. Makris, M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21, 8886–8896 (2013). [CrossRef] [PubMed]
  25. J. Durnin, “Exact solutions for nondiffracting beams. I. the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987). [CrossRef]
  26. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012). [CrossRef] [PubMed]
  27. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012). [CrossRef] [PubMed]
  28. S. Liu, M. Wang, P. Li, P. Zhang, J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013). [CrossRef] [PubMed]
  29. C. Ament, P. Polynkin, J. V. Moloney, “Supercontinuum generation with femtosecond self-healing airy pulses,” Phys. Rev. Lett. 107, 243901 (2011). [CrossRef]
  30. I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012). [CrossRef] [PubMed]
  31. Y. Fattal, A. Rudnick, D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express 19, 17298–17307 (2011). [CrossRef] [PubMed]
  32. R. Driben, B. A. Malomed, A. V. Yulin, D. V. Skryabin, “Newton’s cradles in optics: From 𝒩-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013). [CrossRef]
  33. Y. Q. Zhang, M. Belić, Z. K. Wu, H. B. Zheng, K. Q. Lu, Y. Y. Li, Y. P. Zhang, “Soliton pair generation in the interactions of airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4588 (2013). [CrossRef] [PubMed]
  34. M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979). [CrossRef]
  35. J. Yang, Nonlinear Waves in Integrable and Non-integrable Systems(SIAM, 2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited