Abstract

We investigate interactions between in-phase or out-of-phase Airy beams and nonlinear accelerating beams in photorefractive crystals by means of direct numerical simulations. Since self-accelerating beams possess infinite energy, we evaluated the propagation of two shifted counter beams by truncating the oscillating tails. The numerical results show that the external bias electric field has a profound effect on the propagation dynamics and the solitons shed from the Airy beam. We also found that during interactions between two nonlinear accelerating beams, single solitons, soliton pairs, and bound breathing solitons were produced. When the nonlinear accelerating beam collides with a soliton beam, the main lobe continues accelerating while the soliton intensity fluctuates with the lobes.

© 2017 Optical Society of America

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    [Crossref] [PubMed]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [Crossref] [PubMed]
  3. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33(15), 1678–1680 (2008).
    [Crossref] [PubMed]
  4. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [Crossref]
  5. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
    [Crossref] [PubMed]
  6. M. A. Alonso and M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37(24), 5175–5177 (2012).
    [Crossref] [PubMed]
  7. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
    [Crossref] [PubMed]
  8. P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
    [Crossref] [PubMed]
  9. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
    [Crossref] [PubMed]
  10. M. A. Bandres, M. A. Alonso, I. Kaminer, and M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21(12), 13917–13929 (2013).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  13. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
    [Crossref] [PubMed]
  14. N. K. Efremidis, V. Paltoglou, and W. V. Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
    [Crossref]
  15. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
    [Crossref] [PubMed]
  16. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
    [Crossref] [PubMed]
  17. L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
    [Crossref] [PubMed]
  18. I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21(7), 8886–8896 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  21. C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 243901 (2011).
    [Crossref] [PubMed]
  22. R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(3), 1406 (2013).
    [Crossref] [PubMed]
  23. R. Driben, V. V. Konotop, and T. Meier, “Coupled Airy breathers,” Opt. Lett. 39(19), 5523–5526 (2014).
    [Crossref] [PubMed]
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    [Crossref]
  25. N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
    [Crossref] [PubMed]
  26. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [Crossref]
  27. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
    [Crossref] [PubMed]
  28. I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
    [Crossref] [PubMed]
  29. Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
    [Crossref] [PubMed]
  30. Y. Zhang, M. R. Belić, H. Zheng, H. Chen, C. Li, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express 22(6), 7160–7171 (2014).
    [Crossref] [PubMed]
  31. M. Shen, W. Li, and R. K. Lee, “Control on the anomalous interactions of Airy beams in nematic liquid crystals,” Opt. Express 24(8), 8501–8511 (2016).
    [Crossref] [PubMed]
  32. M. Shen, J. Gao, and L. Ge, “Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media,” Sci. Rep. 5(1), 9814 (2015).
    [Crossref] [PubMed]
  33. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
    [Crossref] [PubMed]
  34. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [Crossref]
  35. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [Crossref] [PubMed]
  36. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995).
    [Crossref]

2016 (2)

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
[Crossref] [PubMed]

M. Shen, W. Li, and R. K. Lee, “Control on the anomalous interactions of Airy beams in nematic liquid crystals,” Opt. Express 24(8), 8501–8511 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (3)

2013 (5)

2012 (6)

M. A. Alonso and M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37(24), 5175–5177 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

F. Zhuang, J. Shen, X. Du, and D. Zhao, “Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor,” Opt. Lett. 37(15), 3054–3056 (2012).
[Crossref] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

2011 (4)

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 243901 (2011).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

2010 (5)

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[Crossref] [PubMed]

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35(23), 3952–3954 (2010).
[Crossref] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

2009 (1)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

2008 (2)

M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33(15), 1678–1680 (2008).
[Crossref] [PubMed]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

2007 (3)

1995 (1)

1994 (1)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Aleahmad, P.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

Allayarov, I. M.

I. M. Allayarov and E. N. Tsoy, “Dynamics of Airy beams in nonlinear media,” Phys. Rev. A 90(2), 023852 (2014).
[Crossref]

Alonso, M. A.

Ament, C.

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 243901 (2011).
[Crossref] [PubMed]

Arie, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Bandres, M. A.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

Belic, M.

Belic, M. R.

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Cannan, D.

Carvalho, M. I.

Chen, H.

Chen, R. P.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(3), 1406 (2013).
[Crossref] [PubMed]

Chen, Z.

Chew, K. H.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(3), 1406 (2013).
[Crossref] [PubMed]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Christodoulides, D. N.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[Crossref] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995).
[Crossref]

Crosignani, B.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

Driben, R.

Du, X.

Efremidis, N. K.

N. K. Efremidis, V. Paltoglou, and W. V. Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Gao, J.

M. Shen, J. Gao, and L. Ge, “Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media,” Sci. Rep. 5(1), 9814 (2015).
[Crossref] [PubMed]

Ge, L.

M. Shen, J. Gao, and L. Ge, “Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media,” Sci. Rep. 5(1), 9814 (2015).
[Crossref] [PubMed]

He, S.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(3), 1406 (2013).
[Crossref] [PubMed]

Hu, Y.

Huang, S.

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Kaminer, I.

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21(7), 8886–8896 (2013).
[Crossref] [PubMed]

M. A. Bandres, M. A. Alonso, I. Kaminer, and M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21(12), 13917–13929 (2013).
[Crossref] [PubMed]

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

Kivshar, Y. S.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Klitzing, W. V.

N. K. Efremidis, V. Paltoglou, and W. V. Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

Konotop, V. V.

Lee, R. K.

Li, C.

Li, L.

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

Li, T.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

Li, W.

Li, Y.

Lou, C.

Lu, K.

Makris, K. G.

Marsal, N.

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
[Crossref] [PubMed]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Meier, T.

Mills, M. S.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Miri, M. A.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

Moloney, J. V.

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 243901 (2011).
[Crossref] [PubMed]

Morandotti, R.

Nemirovsky, J.

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21(7), 8886–8896 (2013).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Paltoglou, V.

N. K. Efremidis, V. Paltoglou, and W. V. Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Polynkin, P.

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 243901 (2011).
[Crossref] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Salandrino, A.

Sciamanna, M.

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
[Crossref] [PubMed]

Segev, M.

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21(7), 8886–8896 (2013).
[Crossref] [PubMed]

M. A. Bandres, M. A. Alonso, I. Kaminer, and M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21(12), 13917–13929 (2013).
[Crossref] [PubMed]

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Shapira, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

Shen, J.

Shen, M.

M. Shen, W. Li, and R. K. Lee, “Control on the anomalous interactions of Airy beams in nematic liquid crystals,” Opt. Express 24(8), 8501–8511 (2016).
[Crossref] [PubMed]

M. Shen, J. Gao, and L. Ge, “Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media,” Sci. Rep. 5(1), 9814 (2015).
[Crossref] [PubMed]

Siviloglou, G. A.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Tsoy, E. N.

I. M. Allayarov and E. N. Tsoy, “Dynamics of Airy beams in nonlinear media,” Phys. Rev. A 90(2), 023852 (2014).
[Crossref]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Wang, R.

Wang, S.

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

Wiersma, N.

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
[Crossref] [PubMed]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Wolfersberger, D.

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
[Crossref] [PubMed]

Wu, Z.

Xu, J.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Zhang, L.

Zhang, P.

Zhang, X.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

Zhang, Y.

Zhao, D.

Zheng, H.

Zhong, W.

Zhu, D.

Zhu, S.

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

Zhuang, F.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

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

Nano Lett. (1)

L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[Crossref] [PubMed]

Nat. Photonics (3)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (11)

F. Zhuang, J. Shen, X. Du, and D. Zhao, “Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor,” Opt. Lett. 37(15), 3054–3056 (2012).
[Crossref] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[Crossref] [PubMed]

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35(23), 3952–3954 (2010).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

M. A. Alonso and M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37(24), 5175–5177 (2012).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33(15), 1678–1680 (2008).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

R. Driben, V. V. Konotop, and T. Meier, “Coupled Airy breathers,” Opt. Lett. 39(19), 5523–5526 (2014).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref] [PubMed]

Phys. Rev. A (2)

I. M. Allayarov and E. N. Tsoy, “Dynamics of Airy beams in nonlinear media,” Phys. Rev. A 90(2), 023852 (2014).
[Crossref]

N. K. Efremidis, V. Paltoglou, and W. V. Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

Phys. Rev. Lett. (9)

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 203902 (2012).
[Crossref] [PubMed]

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 243901 (2011).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108(11), 113903 (2012).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Sci. Rep. (3)

M. Shen, J. Gao, and L. Ge, “Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media,” Sci. Rep. 5(1), 9814 (2015).
[Crossref] [PubMed]

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(3), 1406 (2013).
[Crossref] [PubMed]

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Airy beam self-focusing in a photorefractive medium,” Sci. Rep. 6(1), 35078 (2016), doi:.
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) Intensities of self-accelerating beams at ξ=0. (b), (c) Propagations of the Pockels accelerating solution and its shed radiation. (d), (e) Propagations of an airy beam with infinite and finite energy, as shown in (a). (f) Propagation of a bright solitary beam for E 0 =4000V/m and r=10.
Fig. 2
Fig. 2 Interactions between two Airy beams in SBN with A 1 = A 2 =4, E 0 =4000V/m and various values of B. (a1)–(g1) In-phase case; (a2)–(g2) Out-of-phase case.
Fig. 3
Fig. 3 Same as Fig. 2, but for E 0 = 4000V/m .
Fig. 4
Fig. 4 Interactions of two Airy beams in SBN, with A 1 = A 2 =4, B=2and different E 0 . (a1)–(f1) In-phase case; (a2)–(f2) Out-of-phase case.
Fig. 5
Fig. 5 Interactions of two nonlinear accelerating beams with a=10 and E 0 = 4000V/m . (a1)–(f1) In-phase case; (a2)–(f2) Out-of-phase case.
Fig. 6
Fig. 6 Interactions of in-phase (top row) and out-of-phase (bottom row) soliton and truncated nonlinear accelerating beams in PR SBN crystal with a=30and E 0 = 4000V/m .

Equations (10)

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

i A z + 1 2k 2 A x 2 + k 0 ΔnA=0 ,
E sc = E 0 I + I d I+ I d ,
i ψ ξ + 1 2 2 ψ s 2 1 2 n e 4 r 33 ( k 0 x 0 ) 2 E 0 1 1+|ψ | 2 ψ=0 .
ψ( s,ξ )=Ai( s ξ 2 4 )exp( i 1 2 sξi 1 12 ξ 3 ) .
ψ( s,ξ )=Ai( s ξ 2 4 +iαξ )exp( αs 1 2 α ξ 2 1 12 i ξ 3 + 1 2 i α 2 ξ+ 1 2 isξ ) .
i ψ ξ i ξ 2 ψ s + 1 2 2 ψ s 2 1 2 n e 4 r 33 ( k 0 x 0 ) 2 E 0 1 1+|ψ | 2 ψ=0 .
2 u s 2 su n e 4 r 33 ( k 0 x 0 ) 2 E 0 1 1+|u | 2 u=0 .
2 u s 2 2νu n e 4 r 33 ( k 0 x 0 ) 2 E 0 u 1+r|u | 2 =0 .
ψ(s)= ψ 1 ( sB )+exp( iφ ) ψ 2 [ ( s+B ) ] ,
ψ(s)= A 1 Ai( sB )exp[ α( sB ) ]+ A 2 exp( iφ )Ai[ ( s+B ) ]exp[ α( s+B ) ] ,

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