Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]

2013 (7)

2012 (9)

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]

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]

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]

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]

F. Zhuang, X. Du, Y. Ye, D. Zhao, “Evolution of Airy beams in a chiral medium,” Opt. Lett. 37, 1871–1873 (2012).
[CrossRef] [PubMed]

M. A. Alonso, M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37, 5175–5177 (2012).
[CrossRef] [PubMed]

I. Kaminer, J. Nemirovsky, M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

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]

2011 (7)

I. Kaminer, M. Segev, D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef] [PubMed]

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]

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]

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]

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]

C. Ament, P. Polynkin, J. V. Moloney, “Supercontinuum generation with femtosecond self-healing airy pulses,” Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Y. Fattal, A. Rudnick, D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express 19, 17298–17307 (2011).
[CrossRef] [PubMed]

2010 (4)

2009 (2)

M. A. Bandres, “Accelerating beams,” Opt. Lett. 34, 3791–3793 (2009).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

2008 (1)

2007 (2)

G. A. Siviloglou, D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

1987 (1)

1979 (1)

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Aleahmad, P.

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]

Alonso, M. A.

Ament, C.

C. Ament, P. Polynkin, J. V. Moloney, “Supercontinuum generation with femtosecond self-healing airy pulses,” Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Arie, A.

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]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Balazs, N. L.

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Bandres, M. A.

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Belic, M.

Berry, M. V.

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cannan, D.

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]

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]

Chen, Z.

Chong, A.

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]

Christodoulides, D. N.

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]

I. Kaminer, M. Segev, D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef] [PubMed]

A. Salandrino, D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35, 2082–2084 (2010).
[CrossRef] [PubMed]

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]

N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[CrossRef] [PubMed]

G. A. Siviloglou, D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

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]

Driben, R.

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]

Du, X.

Durnin, J.

Efremidis, N. K.

N. K. Efremidis, V. Paltoglou, W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[CrossRef]

N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[CrossRef] [PubMed]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Fattal, Y.

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Hu, Y.

Huang, S.

Janunts, N.

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]

Kaminer, I.

M. A. Bandres, M. A. Alonso, I. Kaminer, M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21, 13917–13929 (2013).
[CrossRef] [PubMed]

I. Kaminer, J. Nemirovsky, K. G. Makris, M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21, 8886–8896 (2013).
[CrossRef] [PubMed]

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]

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

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]

I. Kaminer, J. Nemirovsky, M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef] [PubMed]

Kivshar, Y. S.

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]

Klein, A. E.

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]

Li, L.

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]

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]

Li, P.

Li, T.

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]

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]

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]

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]

Li, Y. Y.

Liu, S.

Liu, Y.

Lou, C.

Lu, C.

Lu, K. Q.

Makris, K. G.

Malomed, B. A.

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]

Marom, D. M.

Mills, M. S.

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]

Minovich, A.

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]

Miri, M.-A.

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]

Moloney, J. V.

C. Ament, P. Polynkin, J. V. Moloney, “Supercontinuum generation with femtosecond self-healing airy pulses,” Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Morandotti, R.

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]

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]

Nemirovsky, J.

Neshev, D. N.

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]

Paltoglou, V.

N. K. Efremidis, V. Paltoglou, W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[CrossRef]

Pertsch, T.

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]

Polynkin, P.

C. Ament, P. Polynkin, J. V. Moloney, “Supercontinuum generation with femtosecond self-healing airy pulses,” Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Renninger, W. H.

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]

Rodríguez-Lara, B. M.

M. A. Bandres, B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013).
[CrossRef]

Rudnick, A.

Salandrino, A.

Segev, M.

M. A. Bandres, M. A. Alonso, I. Kaminer, M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21, 13917–13929 (2013).
[CrossRef] [PubMed]

I. Kaminer, J. Nemirovsky, K. G. Makris, M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21, 8886–8896 (2013).
[CrossRef] [PubMed]

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]

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]

I. Kaminer, J. Nemirovsky, M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, M. Segev, D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef] [PubMed]

Shapira, A.

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]

Shen, J.

Siviloglou, G. A.

G. A. Siviloglou, D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Skryabin, D. V.

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]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

von Klitzing, W.

N. K. Efremidis, V. Paltoglou, W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[CrossRef]

Wang, M.

Wang, S.

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]

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]

Wang, S. M.

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]

Wise, F. W.

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]

Wu, Z. K.

Xu, J.

Yang, J.

J. Yang, Nonlinear Waves in Integrable and Non-integrable Systems(SIAM, 2010).
[CrossRef]

Ye, Y.

Yin, X.

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]

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]

Yulin, A. V.

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]

Zhang, C.

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]

Zhang, P.

Zhang, X.

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]

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]

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]

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]

Zhang, Y. P.

Zhang, Y. Q.

Zhao, D.

Zhao, J.

Zheng, H. B.

Zhu, S.

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]

Zhu, S. N.

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]

Zhuang, F.

Am. J. Phys. (1)

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

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]

Nat. Photonics (2)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

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]

New J. Phys. (1)

M. A. Bandres, B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013).
[CrossRef]

Opt. Express (4)

Opt. Lett. (13)

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]

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]

F. Zhuang, X. Du, Y. Ye, D. Zhao, “Evolution of Airy beams in a chiral medium,” Opt. Lett. 37, 1871–1873 (2012).
[CrossRef] [PubMed]

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]

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]

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]

A. Salandrino, D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35, 2082–2084 (2010).
[CrossRef] [PubMed]

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]

N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[CrossRef] [PubMed]

M. A. Alonso, M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37, 5175–5177 (2012).
[CrossRef] [PubMed]

G. A. Siviloglou, D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678–1680 (2008).
[CrossRef] [PubMed]

M. A. Bandres, “Accelerating beams,” Opt. Lett. 34, 3791–3793 (2009).
[CrossRef] [PubMed]

Phys. Rev. A (2)

N. K. Efremidis, V. Paltoglou, W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[CrossRef]

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]

Phys. Rev. Lett. (9)

C. Ament, P. Polynkin, J. V. Moloney, “Supercontinuum generation with femtosecond self-healing airy pulses,” Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

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]

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]

G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

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]

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]

I. Kaminer, M. Segev, D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

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]

Other (1)

J. Yang, Nonlinear Waves in Integrable and Non-integrable Systems(SIAM, 2010).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) Intensities of an Airy beam and nonlinear accelerating solutions at z = 0. (b)–(e) Propagations of the strong Kerr, the Kerr, the saturable accelerating solution, and the Airy beam as shown in (a), respectively. (f)–(h) Propagation of the truncated nonlinear accelerating solutions that correspond to (b)–(d). Note the tendency of the shed radiation to move along the straight lines. (i) Propagation of a finite Airy beam that corresponds to (e).

Fig. 2
Fig. 2

Interference of two incident Airy beams in the linear medium, with A1 = A2 = 4 and different B. (a1)–(g1) In-phase case. (a2)–(g2) Out-of-phase case.

Fig. 3
Fig. 3

Soliton formation in the interaction of two in-phase ((a1)–(h1)) and out-of-phase ((a2)–(h2)) incident Airy beams with A1 = A2 = 3, in the Kerr medium. (a3)–(h3) The same as (a1)–(h1), but with A1 = A2 = 4.

Fig. 4
Fig. 4

Same as Fig. 3, but for shorter propagation distance. The black solid and dashed curves present the ideal accelerating trajectories of the main lobes of the input Airy beams.

Fig. 5
Fig. 5

Interactions of two in-phase ((a1)–(g1)) and out-of-phase ((a2)–(g2)) Airy beams with A1 = A2 = 3 in the saturable medium.

Fig. 6
Fig. 6

Interactions of two in-phase (top panels) and out-of-phase (bottom panels) nonlinear Kerr accelerating beams with α = 30, respectively.

Fig. 7
Fig. 7

Interactions of in-phase (top row) and out-of-phase (bottom row) soliton and truncated Kerr accelerating beams. Black curves show the accelerating trajectories of the main lobe.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

i ψ z + 1 2 2 ψ x 2 + δ n ψ = 0 ,
ψ ( x , z ) = Ai ( x z 2 4 ) exp [ i ( x z 2 z 3 12 ) ] ,
ψ ( x , z ) = Ai ( x z 2 4 + i a z ) exp [ i 12 ( 6 a 2 z 12 a i x + 6 i a z 2 + 6 x z z 3 ) ] ,
i ψ z i z 2 ψ x + 1 2 2 ψ x 2 + δ n ψ = 0 .
2 u x 2 + 2 δ n u x u = 0 .
ψ ( x ) = A 1 Ai [ ( x B ) ] exp [ a ( x B ) ] + exp ( i l π ) A 2 Ai [ ( x + B ) ] exp [ a ( x + B ) ] .
ψ ( x ) = ψ 1 [ ( x B ) ] + exp ( i l π ) ψ 2 [ ( x + B ) ] ,
ψ ( x , z ) = sech ( x ) exp ( i z / 2 ) ,

Metrics