Abstract

We report a self–accelerating wave packets eigenmode solution of a two-dimensional (2D) nonlocal nonlinear Schrödinger equation (NNLSE) with an Airy–beam time–dependence, and present their spatiotemporal profiles. The behaviours of such Airy–Laguerre–Gaussian light bullets, as propagated in a strongly nonlocal nonlinear medium (SNNM), are investigated both analytically and numerically. We found that the generation, control, and manipulation of the NL spatiotemporal light bullets are affected by the radial mode number and the azimuthal mode number, as well as the modulation depth. Our scheme is quite different from the linear light bullets, in which the wave propagates in a NL medium and is an eigenmode of NLSE.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [PubMed]
  4. 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).
    [PubMed]
  5. I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, “Self-accelerating beams in photonic crystals,” Opt. Express 21(7), 8886–8896 (2013).
    [PubMed]
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  7. H. Zhong, Y. Zhang, Z. Zhang, C. Li, D. Zhang, Y. Zhang, and M. R. Belić, “Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency,” Opt. Lett. 41(24), 5644–5647 (2016).
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  10. 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).
    [PubMed]
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    [PubMed]
  15. 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).
  16. T. J. Eichelkraut and G. A. Siviloglou, 1I. M. Besieris and D. N. Christodoulides, “Blique Airy wave packets in bidispersive optical media,” Opt. Lett. 35(21), 3655–3657 (2010).
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    [PubMed]
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    [PubMed]
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  24. Z. K. Wu and Y. Z. Gu, “Laguerre–Gaussian, Hermite–Gaussian, Bessel–Gaussian, and Finite-Energy Airy beams carrying orbital angular momentum in strongly nonlocal nonlinear media,” J. Phys. Soc. Jpn. 85(12), 124402 (2016).
  25. Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
    [PubMed]
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    [PubMed]
  27. W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
    [PubMed]
  28. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
    [PubMed]
  29. S. Chen and L. Yi, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016606 (2005).
    [PubMed]
  30. W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 1801 (2007).
  31. W. P. Zhong, L. Yi, and R. H. Xie, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. At. Mol. Opt. Phys. 41(2), 025402 (2008).
  32. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
    [PubMed]
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  34. Y. Zhang, M. R. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
    [PubMed]

2016 (5)

H. Zhong, Y. Zhang, Z. Zhang, C. Li, D. Zhang, Y. Zhang, and M. R. Belić, “Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency,” Opt. Lett. 41(24), 5644–5647 (2016).
[PubMed]

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

F. Deng and D. Deng, “Three-dimensional localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets in free space,” Opt. Express 24(5), 5478–5486 (2016).
[PubMed]

Y. Peng, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space,” Opt. Express 24(17), 18973–18985 (2016).
[PubMed]

Z. K. Wu and Y. Z. Gu, “Laguerre–Gaussian, Hermite–Gaussian, Bessel–Gaussian, and Finite-Energy Airy beams carrying orbital angular momentum in strongly nonlocal nonlinear media,” J. Phys. Soc. Jpn. 85(12), 124402 (2016).

2015 (3)

2014 (2)

G. Q. Zhou, R. P. Chen, and G. Y. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. W. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phy. 340(1), 171–178 (2014).

2013 (2)

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

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

2012 (1)

2011 (4)

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[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).
[PubMed]

N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36(15), 3006–3008 (2011).
[PubMed]

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
[PubMed]

2010 (5)

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

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).
[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).
[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).

T. J. Eichelkraut and G. A. Siviloglou, 1I. M. Besieris and D. N. Christodoulides, “Blique Airy wave packets in bidispersive optical media,” Opt. Lett. 35(21), 3655–3657 (2010).
[PubMed]

T. J. Eichelkraut and G. A. Siviloglou, 1I. M. Besieris and D. N. Christodoulides, “Blique Airy wave packets in bidispersive optical media,” Opt. Lett. 35(21), 3655–3657 (2010).
[PubMed]

2008 (1)

W. P. Zhong, L. Yi, and R. H. Xie, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. At. Mol. Opt. Phys. 41(2), 025402 (2008).

2007 (4)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[PubMed]

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 1801 (2007).

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

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

2005 (1)

S. Chen and L. Yi, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016606 (2005).
[PubMed]

2004 (1)

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[PubMed]

2002 (1)

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046619 (2002).
[PubMed]

2000 (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

1997 (1)

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).

1979 (1)

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

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).
[PubMed]

Balazs, N. L.

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

Bang, O.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046619 (2002).
[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).

Besieris, I. M.

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).
[PubMed]

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[PubMed]

Chen, B.

Chen, R. P.

G. Q. Zhou, R. P. Chen, and G. Y. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).

Chen, S.

S. Chen and L. Yi, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016606 (2005).
[PubMed]

Chen, Z.

Chi, S.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[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).

Christodoulides, D. N.

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).

T. J. Eichelkraut and G. A. Siviloglou, 1I. M. Besieris and D. N. Christodoulides, “Blique Airy wave packets in bidispersive optical media,” Opt. Lett. 35(21), 3655–3657 (2010).
[PubMed]

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

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

Deng, D.

Deng, D. M.

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

Deng, F.

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

F. Deng and D. Deng, “Three-dimensional localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets in free space,” Opt. Express 24(5), 5478–5486 (2016).
[PubMed]

Desyatnikov, A. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[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).
[PubMed]

Du, X.

Dudley, J. M.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

Efremidis, N. K.

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

N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36(15), 3006–3008 (2011).
[PubMed]

Eichelkraut, T. J.

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

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, 9814 (2015).
[PubMed]

Gao, X. H.

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

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, 9814 (2015).
[PubMed]

Gu, Y. Z.

Z. K. Wu and Y. Z. Gu, “Laguerre–Gaussian, Hermite–Gaussian, Bessel–Gaussian, and Finite-Energy Airy beams carrying orbital angular momentum in strongly nonlocal nonlinear media,” J. Phys. Soc. Jpn. 85(12), 124402 (2016).

Guan, J.

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

Guo, Q.

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[PubMed]

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

Hu, W.

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

Hu, Y.

Huang, J. W.

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

Huang, S.

Huang, T. W.

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. W. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phy. 340(1), 171–178 (2014).

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).
[PubMed]

Kaminer, I.

Kivshar, Y. S.

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
[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).
[PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[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).
[PubMed]

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046619 (2002).
[PubMed]

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

Li, C.

Li, D.

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[PubMed]

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[PubMed]

Liu, W.

Lou, C.

Lu, D. Q.

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

Luo, B.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[PubMed]

Makris, K. G.

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).
[PubMed]

Miroshnichenko, A. E.

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).

Nemirovsky, J.

Neshev, D. N.

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
[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).
[PubMed]

Paltoglou, V.

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

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).
[PubMed]

Peng, X.

Peng, Y.

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).
[PubMed]

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046619 (2002).
[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).

Ru, G. Y.

G. Q. Zhou, R. P. Chen, and G. Y. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).

Segev, M.

Shadrivov, I. V.

Shen, J.

Shen, M.

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, 9814 (2015).
[PubMed]

Siviloglou, G. A.

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).

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).
[PubMed]

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

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).
[PubMed]

von Klitzing, W.

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

Wang, R.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[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).

Wu, Z. K.

Z. K. Wu and Y. Z. Gu, “Laguerre–Gaussian, Hermite–Gaussian, Bessel–Gaussian, and Finite-Energy Airy beams carrying orbital angular momentum in strongly nonlocal nonlinear media,” J. Phys. Soc. Jpn. 85(12), 124402 (2016).

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046619 (2002).
[PubMed]

Xie, R. H.

W. P. Zhong, L. Yi, and R. H. Xie, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. At. Mol. Opt. Phys. 41(2), 025402 (2008).

Xie, Y.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[PubMed]

Xu, J.

Yang, Z. J.

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

Yi, F.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[PubMed]

Yi, L.

W. P. Zhong, L. Yi, and R. H. Xie, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. At. Mol. Opt. Phys. 41(2), 025402 (2008).

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 1801 (2007).

S. Chen and L. Yi, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016606 (2005).
[PubMed]

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[PubMed]

Zhang, D.

Zhang, L.

Zhang, P.

Zhang, Y.

Zhang, Y. Q.

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. W. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phy. 340(1), 171–178 (2014).

Zhang, Z.

Zhao, D.

Zheng, Y. Z.

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

Zhong, H.

Zhong, W.

Zhong, W. P.

W. P. Zhong, M. Belić, and Y. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[PubMed]

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. W. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phy. 340(1), 171–178 (2014).

W. P. Zhong, L. Yi, and R. H. Xie, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. At. Mol. Opt. Phys. 41(2), 025402 (2008).

Zhou, G. Q.

G. Q. Zhou, R. P. Chen, and G. Y. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).

Zhou, M.

Zhu, D.

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[PubMed]

Zhu, W.

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

Zhuang, F.

Am. J. Phys. (1)

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

Ann. Phy. (1)

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. W. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phy. 340(1), 171–178 (2014).

J. Phys. At. Mol. Opt. Phys. (1)

W. P. Zhong, L. Yi, and R. H. Xie, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. At. Mol. Opt. Phys. 41(2), 025402 (2008).

J. Phys. Soc. Jpn. (1)

Z. K. Wu and Y. Z. Gu, “Laguerre–Gaussian, Hermite–Gaussian, Bessel–Gaussian, and Finite-Energy Airy beams carrying orbital angular momentum in strongly nonlocal nonlinear media,” J. Phys. Soc. Jpn. 85(12), 124402 (2016).

Laser Phys. Lett. (1)

G. Q. Zhou, R. P. Chen, and G. Y. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).

Nat. Photonics (1)

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).

Opt. Commun. (1)

W. Zhu, J. Guan, F. Deng, D. M. Deng, and J. W. Huang, “The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium,” Opt. Commun. 380, 434–441 (2016).

Opt. Express (5)

Opt. Lett. (7)

Phys. Lett. A (1)

Z. J. Yang, D. Q. Lu, W. Hu, Y. Z. Zheng, X. H. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).

Phys. Rev. A (2)

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 1801 (2007).

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

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

S. Chen and L. Yi, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016606 (2005).
[PubMed]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1 Pt 2), 016602 (2004).
[PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046619 (2002).
[PubMed]

Phys. Rev. Lett. (6)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000).
[PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[PubMed]

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

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[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).
[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).
[PubMed]

Sci. Rep. (1)

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, 9814 (2015).
[PubMed]

Science (1)

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1 (a1) and (b1) Contour-plots of accelerating finite-energy Airy pulse intensity distribution, as functions of the propagation distance with σ = + 1 and σ = 1 , respectively. (a2) and (b2) Intensity profiles of the pulse along the positive and negative T direction corresponding to (a1) and (b1). The parameters are r 0 = 100 μ m , λ = 530 n m and a = 0 . 1 . Not that Z = 5 when z = 59 c m .
Fig. 2
Fig. 2 Transverse intensity distribution of M n m for different values of radial mode number n , azimuthal mode number m : (a1)-(c1) n = 1 , (a2)-(c2) n = 2 and (a3)-(c3) n = 3 corresponding to m = 0 , 1 and 2 with q = 0 , respectively. (d)-(f) m = 2 corresponding to n = 0 , 1 and 2 with q = 1 , respectively. The insets present phase profile.
Fig. 3
Fig. 3 Snapshots describing the evolution of Airy–Laguerre–Gaussian light bullets with zero-vorticity ( m = 0 ) at Z = 0 (the first column) and Z = 5 Z R (the second and third column) with n = 1 (top row) and n = 2 (bottom row). Note that the second and third columns are obtained by analytically and numerically, respectively. Other parameters as chosen as follows: a = 0.1 , γ = 2 and P 0 = 1 .
Fig. 4
Fig. 4 Necklace Airy–Laguerre–Gaussian light bullets. Setup is the same as in Fig. 3, except for m = 1 (top row) and m = 2 (bottom row).
Fig. 5
Fig. 5 (a1)-(c1) Vortex Airy–Laguerre–Gaussian light bullets with n = 1 , m = 1 and q = 1 at Z = 0 (the first column) and Z = 5 Z R (the second and third column). (b1) and (c1) are obtained by analytically and numerically, respectively. (a2)-(c2) The transverse phase distribution correspond to (a1)-(c1). The singularity is placed in white ellipse.

Equations (12)

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

i ψ Z + 1 2 ( 2 r 2 + 1 r r + 1 r 2 2 φ 2 + 2 T 2 ) ψ + n [ I ( r , φ ) ] ψ = 0
n [ I ( r , φ ) ] = + 0 2 π R ( r r ) | ψ ( r , φ , Z ) | 2 r d r d φ
i ψ Z + 1 2 ( 2 r 2 + 1 r r + 1 r 2 2 φ 2 + 2 T 2 ) ψ 1 2 γ 2 P 0 r 2 ψ = 0
i N ( Z , T ) Z + 1 2 ( 2 T 2 ) N ( Z , T ) = 0
i M ( Z , r , φ ) Z + 1 2 ( 2 r 2 + 1 r r + 1 r 2 2 φ 2 ) M ( Z , r , φ ) r 2 M ( Z , r , φ ) = 0
N + ( Z , T ) = A i ( T Z 2 4 + i a Z ) e a T 1 4 a Z 2 + i ( Z 1 24 Z 3 + 1 2 a 2 Z + 1 2 T Z )
N ( Z , T ) = A i ( T Z 2 4 + i a Z ) e a T 1 4 a Z 2 + i ( Z 1 24 Z 3 + 1 2 a 2 Z 1 2 T Z )
B Z + 1 2 ( 1 A 2 A r 2 + ( B r ) 2 + 1 r A A r + 1 r 2 A 2 A φ 2 ) r 2 = 0
1 A A Z + 1 2 ( 2 A A r B r + 2 B r 2 + 1 r B r ) = 0
M n m s o l ( Z , r , φ ) = η ξ [ cos ( m φ ) + i q sin ( m φ ) ] ( r ξ ) m V n ( m ) ( r 2 ξ 2 ) e r 2 2 ξ 2 + i b ( z )
{ η = n ! / Γ ( n + m + 1 ) V n ( m ) ( θ ) = [ Γ ( m + 1 + n ) / ( n ! Γ ( m + 1 + n ) ) ] F ( n , m + 1 , θ )
ψ n m ( Z , R , φ , T ) = η ξ A i ( T Z 2 4 + i a Z ) e a T 1 4 a Z 2 + i ( Z 1 24 Z 3 + 1 2 a 2 Z + 1 2 T Z ) × [ cos ( m φ ) + i q sin ( m φ ) ] ( r ξ ) m V n ( m ) ( r 2 ξ 2 ) e r 2 2 ξ 2 i b ( Z )

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