Abstract

Based on a reduction of nonlocal nonlinear Schrödinger equation in strongly nonlocal regime, the linear Schrödinger equation with parabolic potential, analytical results describing the evolution of dual Airy beam are presented. The results show that the dual Airy beam in strongly nonlocal medium exhibits a periodic focusing and defocusing behavior, and forms the interference fringes between the focusing and defocusing positions. The analytical results are verified by numerically solving nonlocal nonlinear Schrödinger equation and shown to be reasonable when the characteristic response width is broader than the width of the dual Airy beam. Furthermore, the characteristics of the interference fringes induced by the dual Airy beam are also investigated in detail, and can be used for the measurement of the system parameters. In addition, we propose a scheme to generate dual Airy beam in strongly nonlocal medium.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Propagation dynamics of finite-energy Airy beams in competing nonlocal nonlinear media

Bing Liu, Kaiyun Zhan, and Zhendong Yang
J. Opt. Soc. Am. B 35(11) 2794-2798 (2018)

Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential

Yiqi Zhang, Milivoj R. Belić, Lei Zhang, Weiping Zhong, Dayu Zhu, Ruimin Wang, and Yanpeng Zhang
Opt. Express 23(8) 10467-10480 (2015)

Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays

Zheng Cao, Qinggui Tan, Xiaojun Li, and Xinyuan Qi
Appl. Opt. 55(24) 6601-6605 (2016)

References

  • View by:
  • |
  • |
  • |

  1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
    [Crossref]
  2. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–653 (1987).
    [Crossref]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  4. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [Crossref]
  5. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [Crossref] [PubMed]
  6. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
    [Crossref] [PubMed]
  7. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [Crossref] [PubMed]
  8. X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
    [Crossref]
  9. R. Cao, Y. Hua, C. J. Min, S. W. Zhu, and X. C. Yuan, “Self-healing optical pillar array,” Opt. Lett. 373540–3542 (2012).
    [Crossref] [PubMed]
  10. I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear medium,” Phys. Rev. Lett. 108, 113903 (2012).
    [Crossref]
  11. M. D. Cottrell, J. A. Davis, and T. M. Hazard, “Direct generation of accelerating Airy beams using a 3/2 phase-only pattern,” Opt. Lett. 34, 2634–2636 (2009).
    [Crossref] [PubMed]
  12. 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, 126804 (2011).
    [Crossref] [PubMed]
  13. N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36, 3006–3008 (2011).
    [Crossref] [PubMed]
  14. Y. Q. Zhang, M. R. Belić, H. B. Zheng, H. X. Chen, C. B. Li, Y. Y. Li, and Y. P. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear medium,” Opt. Express 22, 7160–7171 (2014).
    [Crossref] [PubMed]
  15. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
    [Crossref] [PubMed]
  16. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 363, 675–678 (2008).
    [Crossref]
  17. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
    [Crossref]
  18. C. Chen, H. M. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
    [Crossref]
  19. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
    [Crossref]
  20. B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
    [Crossref]
  21. Y. I. Salamin, “Approximate fields of an ultra-short, tightly-focused, radially-polarized laser pulse in an under-dense plasma: a Bessel-Bessel light bullet,” Opt. Express 25, 28990–28999 (2017).
    [Crossref]
  22. D. Mihalache, “Multidimensional localized structures in optical and matter-wave media: a topical survey of recent literature,” Romanian Reports in Physics 69, 403 (2017).
  23. Y. I. Salamin, “Fields of a Bessel-Bessel light bullet of arbitrary order in an under-dense plasma,” Sci. Reports 8, 11362 (2018).
    [Crossref]
  24. Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
    [Crossref]
  25. J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
    [Crossref]
  26. Y. Q. Zhang, M. R. Belić, L. Zhang, W. P. Zhong, D. Y. Zhu, R. M. Wang, and Y. P. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23, 10467–10480 (2015).
    [Crossref] [PubMed]
  27. Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
    [Crossref]
  28. N. Li, Y. F. Jiang, K. K. Huang, and X. H. Lu, “Abruptly autofocusing property of blocked circular Airy beams,” Opt. Express 22, 22847–22853 (2014).
    [Crossref] [PubMed]
  29. J. G. Zhang and J. He, “Dual abruptly focus of modulated circular Airy beams,” IEEE Photon. J. 96500510 (2017).
  30. G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
    [Crossref] [PubMed]
  31. J. G. Zhang and X. S. Yang, “Periodic abruptly autofocusing and autodefocusing behavior of circular Airy beams in parabolic optical potentials,” Opt. Commun. 420, 163–167 (2018).
    [Crossref]
  32. A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538 (1997).
    [Crossref]
  33. Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
    [Crossref]
  34. Q. Guo, B. Luo, and S. Chi, “Optical beams in sub-strongly non-local nonlinear medium: A variational solution,” Opt. Commun. 259, 336–341 (2006).
    [Crossref]
  35. H. Zhang, L. Li, and S. Jia, “Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal medium,” Phys. Rev. A 76, 043833 (2007).
    [Crossref]
  36. S. Longhi, “Fractional Schrödinger equation in optics,” Opt. Lett. 40, 1117–1120 (2015).
    [Crossref] [PubMed]
  37. J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).
  38. C. Bernardini, F. Gori, and M. Santarsiero, “Converting states of a particle under uniform or elastic forces into free particle states,” Eur. J. Phys. 16, 58–62 (1995).
    [Crossref]
  39. O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial University, 2004).
    [Crossref]
  40. T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
    [Crossref]
  41. C. Conti, M. Peccianti, and G. Assanto, “Observation of Optical Spatial Solitons in a Highly Nonlocal Medium,” Phys. Rev. Lett. 92, 113902 (2004).
    [Crossref] [PubMed]
  42. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
    [Crossref] [PubMed]
  43. C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312–3314 (2006).
    [Crossref] [PubMed]

2019 (2)

Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
[Crossref]

J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
[Crossref]

2018 (3)

Y. I. Salamin, “Fields of a Bessel-Bessel light bullet of arbitrary order in an under-dense plasma,” Sci. Reports 8, 11362 (2018).
[Crossref]

T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
[Crossref]

J. G. Zhang and X. S. Yang, “Periodic abruptly autofocusing and autodefocusing behavior of circular Airy beams in parabolic optical potentials,” Opt. Commun. 420, 163–167 (2018).
[Crossref]

2017 (5)

J. G. Zhang and J. He, “Dual abruptly focus of modulated circular Airy beams,” IEEE Photon. J. 96500510 (2017).

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
[Crossref] [PubMed]

D. Mihalache, “Multidimensional localized structures in optical and matter-wave media: a topical survey of recent literature,” Romanian Reports in Physics 69, 403 (2017).

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Y. I. Salamin, “Approximate fields of an ultra-short, tightly-focused, radially-polarized laser pulse in an under-dense plasma: a Bessel-Bessel light bullet,” Opt. Express 25, 28990–28999 (2017).
[Crossref]

2016 (1)

B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
[Crossref]

2015 (3)

2014 (3)

2012 (3)

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[Crossref]

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

R. Cao, Y. Hua, C. J. Min, S. W. Zhu, and X. C. Yuan, “Self-healing optical pillar array,” Opt. Lett. 373540–3542 (2012).
[Crossref] [PubMed]

2011 (2)

N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36, 3006–3008 (2011).
[Crossref] [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, 126804 (2011).
[Crossref] [PubMed]

2010 (1)

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

2009 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

M. D. Cottrell, J. A. Davis, and T. M. Hazard, “Direct generation of accelerating Airy beams using a 3/2 phase-only pattern,” Opt. Lett. 34, 2634–2636 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (3)

H. Zhang, L. Li, and S. Jia, “Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal medium,” Phys. Rev. A 76, 043833 (2007).
[Crossref]

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

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

2006 (2)

Q. Guo, B. Luo, and S. Chi, “Optical beams in sub-strongly non-local nonlinear medium: A variational solution,” Opt. Commun. 259, 336–341 (2006).
[Crossref]

C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312–3314 (2006).
[Crossref] [PubMed]

2005 (2)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
[Crossref]

2004 (2)

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of Optical Spatial Solitons in a Highly Nonlocal Medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

1997 (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538 (1997).
[Crossref]

1995 (1)

C. Bernardini, F. Gori, and M. Santarsiero, “Converting states of a particle under uniform or elastic forces into free particle states,” Eur. J. Phys. 16, 58–62 (1995).
[Crossref]

1987 (2)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–653 (1987).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 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, 253901 (2010).
[Crossref]

Arie, A.

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

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, “Observation of Optical Spatial Solitons in a Highly Nonlocal Medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Astrakharchik, G. E.

Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
[Crossref]

Balazs, N. L.

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

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 363, 675–678 (2008).
[Crossref]

Belic, M. R.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Y. Q. Zhang, M. R. Belić, L. Zhang, W. P. Zhong, D. Y. Zhu, R. M. Wang, and Y. P. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23, 10467–10480 (2015).
[Crossref] [PubMed]

Y. Q. Zhang, M. R. Belić, H. B. Zheng, H. X. Chen, C. B. Li, Y. Y. Li, and Y. P. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear medium,” Opt. Express 22, 7160–7171 (2014).
[Crossref] [PubMed]

Bernardini, C.

C. Bernardini, F. Gori, and M. Santarsiero, “Converting states of a particle under uniform or elastic forces into free particle states,” Eur. J. Phys. 16, 58–62 (1995).
[Crossref]

Berry, M. V.

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

Bland, T.

T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
[Crossref]

Broky, J.

Cao, R.

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Chen, C.

C. Chen, H. M. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Chen, H. X.

Chen, R. P.

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[Crossref]

Chi, S.

Q. Guo, B. Luo, and S. Chi, “Optical beams in sub-strongly non-local nonlinear medium: A variational solution,” Opt. Commun. 259, 336–341 (2006).
[Crossref]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Christodoulides, D. N.

Chu, X. X.

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[Crossref]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, “Observation of Optical Spatial Solitons in a Highly Nonlocal Medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Cottrell, M. D.

Davis, J. A.

Deng, X. Q.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
[Crossref] [PubMed]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 363, 675–678 (2008).
[Crossref]

Dogariu, A.

Dolev, I.

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

Dong, G. J.

J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
[Crossref]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–653 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Efremidis, N. K.

Gori, F.

C. Bernardini, F. Gori, and M. Santarsiero, “Converting states of a particle under uniform or elastic forces into free particle states,” Eur. J. Phys. 16, 58–62 (1995).
[Crossref]

Guo, Q.

Q. Guo, B. Luo, and S. Chi, “Optical beams in sub-strongly non-local nonlinear medium: A variational solution,” Opt. Commun. 259, 336–341 (2006).
[Crossref]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Hazard, T. M.

He, J.

J. G. Zhang and J. He, “Dual abruptly focus of modulated circular Airy beams,” IEEE Photon. J. 96500510 (2017).

Hua, Y.

Huang, K. K.

Jia, S.

H. Zhang, L. Li, and S. Jia, “Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal medium,” Phys. Rev. A 76, 043833 (2007).
[Crossref]

Jiang, Y. F.

Kaminer, I.

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

Kartashov, Y. V.

Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
[Crossref]

C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312–3314 (2006).
[Crossref] [PubMed]

Kavehrad, M.

C. Chen, H. M. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Li, C. B.

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, 126804 (2011).
[Crossref] [PubMed]

H. Zhang, L. Li, and S. Jia, “Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal medium,” Phys. Rev. A 76, 043833 (2007).
[Crossref]

Li, N.

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, 126804 (2011).
[Crossref] [PubMed]

Li, Y. Y.

Liang, Z. X.

J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
[Crossref]

Liu, J. F.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Liu, X.

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Longhi, S.

Lu, X. H.

Luo, B.

Q. Guo, B. Luo, and S. Chi, “Optical beams in sub-strongly non-local nonlinear medium: A variational solution,” Opt. Commun. 259, 336–341 (2006).
[Crossref]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Malomed, B. A.

J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
[Crossref]

Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
[Crossref]

T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
[Crossref]

B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 363, 675–678 (2008).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Mihalache, D.

D. Mihalache, “Multidimensional localized structures in optical and matter-wave media: a topical survey of recent literature,” Romanian Reports in Physics 69, 403 (2017).

B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
[Crossref]

Min, C. J.

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538 (1997).
[Crossref]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

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, 253901 (2010).
[Crossref]

Parker, N. G.

T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
[Crossref]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, “Observation of Optical Spatial Solitons in a Highly Nonlocal Medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Petrovic, M. S.

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Proukakis, N. P.

T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
[Crossref]

Qin, J. L.

J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
[Crossref]

Rotschild, C.

C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312–3314 (2006).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Salamin, Y. I.

Santarsiero, M.

C. Bernardini, F. Gori, and M. Santarsiero, “Converting states of a particle under uniform or elastic forces into free particle states,” Eur. J. Phys. 16, 58–62 (1995).
[Crossref]

Segev, M.

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

C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312–3314 (2006).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Shapira, A.

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

Siviloglou, G. A.

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538 (1997).
[Crossref]

Soares, M.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial University, 2004).
[Crossref]

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, 253901 (2010).
[Crossref]

Torner, L.

Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
[Crossref]

B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
[Crossref]

C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312–3314 (2006).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
[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, 253901 (2010).
[Crossref]

Vallée, O.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial University, 2004).
[Crossref]

Wang, R.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Wang, R. M.

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, 126804 (2011).
[Crossref] [PubMed]

Wise, F.

B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
[Crossref]

Wu, Q. Y.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
[Crossref] [PubMed]

Xie, Y.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Xu, S. X.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
[Crossref] [PubMed]

Xu, Z. Y.

Yang, H. M.

C. Chen, H. M. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Yang, X. S.

J. G. Zhang and X. S. Yang, “Periodic abruptly autofocusing and autodefocusing behavior of circular Airy beams in parabolic optical potentials,” Opt. Commun. 420, 163–167 (2018).
[Crossref]

Yi, F.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Yuan, X. C.

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, 126804 (2011).
[Crossref] [PubMed]

Zhang, H.

H. Zhang, L. Li, and S. Jia, “Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal medium,” Phys. Rev. A 76, 043833 (2007).
[Crossref]

Zhang, J. G.

J. G. Zhang and X. S. Yang, “Periodic abruptly autofocusing and autodefocusing behavior of circular Airy beams in parabolic optical potentials,” Opt. Commun. 420, 163–167 (2018).
[Crossref]

J. G. Zhang and J. He, “Dual abruptly focus of modulated circular Airy beams,” IEEE Photon. J. 96500510 (2017).

Zhang, J. W.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Zhang, L.

Zhang, Y. P.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Y. Q. Zhang, M. R. Belić, L. Zhang, W. P. Zhong, D. Y. Zhu, R. M. Wang, and Y. P. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23, 10467–10480 (2015).
[Crossref] [PubMed]

Y. Q. Zhang, M. R. Belić, H. B. Zheng, H. X. Chen, C. B. Li, Y. Y. Li, and Y. P. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear medium,” Opt. Express 22, 7160–7171 (2014).
[Crossref] [PubMed]

Zhang, Y. Q.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Y. Q. Zhang, M. R. Belić, L. Zhang, W. P. Zhong, D. Y. Zhu, R. M. Wang, and Y. P. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23, 10467–10480 (2015).
[Crossref] [PubMed]

Y. Q. Zhang, M. R. Belić, H. B. Zheng, H. X. Chen, C. B. Li, Y. Y. Li, and Y. P. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear medium,” Opt. Express 22, 7160–7171 (2014).
[Crossref] [PubMed]

Zheng, G. L.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
[Crossref] [PubMed]

Zheng, H. B.

Zhong, H.

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Zhong, W. P

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Zhong, W. P.

Zhou, G. Q.

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[Crossref]

Zhou, Z.

C. Chen, H. M. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Zhu, D. Y.

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, 126804 (2011).
[Crossref] [PubMed]

Zhu, S. W.

Am. J. Phys. (1)

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

Ann. Phys. (Berlin) (1)

J. F. Liu, Y. Q. Zhang, H. Zhong, J. W. Zhang, R. Wang, M. R. Belić, and Y. P. Zhang, “Optical Bloch oscillations of a dual Airy Beam,” Ann. Phys. (Berlin) 2017, 1700307 (2017).

Annals of Physics (1)

Y. Q. Zhang, X. Liu, M. R. Belić, W. P Zhong, M. S. Petrović, and Y. P. Zhang, “Automatic Fourier transform and self-Fourier beams due to parabolic potential,” Annals of Physics 363, 305–315 (2015).
[Crossref]

Applied Optics (1)

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Applied Optics 56, 2444–2448 (2017).
[Crossref] [PubMed]

Eur. J. Phys. (1)

C. Bernardini, F. Gori, and M. Santarsiero, “Converting states of a particle under uniform or elastic forces into free particle states,” Eur. J. Phys. 16, 58–62 (1995).
[Crossref]

IEEE Photon. J. (1)

J. G. Zhang and J. He, “Dual abruptly focus of modulated circular Airy beams,” IEEE Photon. J. 96500510 (2017).

J. Opt. B: Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7, R53–R72 (2005).
[Crossref]

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

J. Phys. B (1)

T. Bland, N. G. Parker, N. P. Proukakis, and B. A. Malomed, “Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential,” J. Phys. B 51, 205303 (2018).
[Crossref]

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

B. A. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. B: At. Mol. Opt. Phys. 49, 170502 (2016).
[Crossref]

Nat. Photon. (1)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 363, 675–678 (2008).
[Crossref]

Nature Reviews Physics (1)

Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-traping of nonlinear fields and matter,” Nature Reviews Physics 1, 185–197 (2019).
[Crossref]

Opt. Commun. (2)

J. G. Zhang and X. S. Yang, “Periodic abruptly autofocusing and autodefocusing behavior of circular Airy beams in parabolic optical potentials,” Opt. Commun. 420, 163–167 (2018).
[Crossref]

Q. Guo, B. Luo, and S. Chi, “Optical beams in sub-strongly non-local nonlinear medium: A variational solution,” Opt. Commun. 259, 336–341 (2006).
[Crossref]

Opt. Express (5)

Opt. Lasers Eng. (1)

C. Chen, H. M. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Opt. Lett. (7)

Phys. Rev. A (3)

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[Crossref]

J. L. Qin, Z. X. Liang, B. A. Malomed, and G. J. Dong, “Tail-free self-accelerating solitons and vortices,” Phys. Rev. A 99, 023610 (2019).
[Crossref]

H. Zhang, L. Li, and S. Jia, “Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal medium,” Phys. Rev. A 76, 043833 (2007).
[Crossref]

Phys. Rev. E (1)

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Phys. Rev. Lett. (7)

C. Conti, M. Peccianti, and G. Assanto, “Observation of Optical Spatial Solitons in a Highly Nonlocal Medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

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

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, 126804 (2011).
[Crossref] [PubMed]

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

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

Romanian Reports in Physics (1)

D. Mihalache, “Multidimensional localized structures in optical and matter-wave media: a topical survey of recent literature,” Romanian Reports in Physics 69, 403 (2017).

Sci. Reports (1)

Y. I. Salamin, “Fields of a Bessel-Bessel light bullet of arbitrary order in an under-dense plasma,” Sci. Reports 8, 11362 (2018).
[Crossref]

Science (2)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538 (1997).
[Crossref]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Other (1)

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial University, 2004).
[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 The self-induced periodic interfering behavior of the dual Airy beam governed by Eq. (4). (a) α = 0.1, x0 = 5; (b) α = 0.2, x0 = 5; (c) α = 0.2, x0 = 8, where the white and yellow dashed lines are the focusing position and the defocusing position, respectively. As comparison, the green curves show the trajectories of two main lobes given by Eq. (11).
Fig. 2
Fig. 2 Intensity distribution of the dual Airy beam (5) and ϕ1(x, 0) + ϕ2(x, 0) for different x0. (a) x0 = 1, (b) x0 = 5, (c) x0 = 8. (d) Powers of the dual Airy beam and ϕ1(x, 0) + ϕ2(x, 0) versus x0. The black curve and red points correspond to the dual Airy beam and ϕ1(x, 0) + ϕ2(x, 0), respectively.
Fig. 3
Fig. 3 (a, b) The first focusing position z f 1, (c, d) the first defocusing position z d 1, and (e, f) the range of interference fringes r versus the parameters α and x0, respectively. Here, x0 = 5 in (a, c, e) and α = 0.1 in (b, d, f).
Fig. 4
Fig. 4 Intensity distribution at z0 = T/4. (a) α = 0.1, x0 = 5, (b) α = 0.2, x0 = 5, and (c) α = 0.2, x0 = 8.
Fig. 5
Fig. 5 The numerical evolution of the dual Airy beam governed by Eq. (16). (a) Δ = 5, (b) Δ = 10, (c) Δ = 15, where the green curves are the trajectories of the two main lobes of the dual Airy beams given by Eq. (11). (d) The intensity distribution at z = T/4, where the red, yellow and green dashed curves correspond to Δ = 5, 10, and 15, respectively. As comparison, the analytical result given by Eq. (15) is shown by the black curve. Here, the other parameters are α = 0.3 and x0 = 5.
Fig. 6
Fig. 6 (a, b) The spacing between the central fringe and its adjacent fringe d, (c, d) the central peak pc, and (e, f) the width of the envelope W versus α and x0, respectively. Here, x0 = 5 in (a, c, e); α = 0.1 in (b, d, f). The black curves and red points correspond to the analytical results and the numerical results, respectively.
Fig. 7
Fig. 7 The intensity distribution at z = 0 and z = 3T/4, where the black dashed curve is the profile of the dual Airy beam given by Eq. (5). The parameters are x0 = 5 and α = 0.3.

Equations (24)

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

i 2 k ψ z + 2 ψ x 2 + 2 k 2 η Δ n ( x , z ) ψ = 0 ,
Δ n ( x , z ) = + R ( x x ) I ( x , z ) d x ,
i 2 k ψ z + 2 ψ x 2 k 2 γ 2 P x 2 ψ = 0 ,
i ϕ z + 1 2 2 ϕ x 2 1 2 α 2 x 2 ϕ = 0
ϕ ( x , 0 ) = Ai [ ( | x | x 0 ) ] exp [ a ( | x | x 0 ) ] ,
ϕ ( x , z ) = f ( x , z ) + [ ϕ ( ξ , 0 ) e i b ξ 2 ] e i K ξ d ξ ,
f ( x , z ) = e i b x 2 i 2 π K x .
ϕ ^ 1 , 2 ( k , 0 ) = exp ( ± i k x 0 ) exp [ a k 2 ] exp [ a 3 3 ± i 3 ( k 3 3 a 2 k ) ] ,
G ^ ( k ) = i π b exp ( i 4 b k 2 ) ,
ϕ 1 , 2 ( x , z ) = f ( x , z ) + [ ϕ 1 , 2 ( ξ , 0 ) e i b ξ 2 ] e i K ξ d ξ = f ( x , z ) 1 2 π + ϕ ^ 1 , 2 ( k , 0 ) G ^ ( K k ) d k .
ϕ 1 , 2 ( x , z ) = f ( x , z ) i π b exp ( a 3 3 ) Ai ( ± K 2 b 1 16 b 2 + x 0 + i a 2 b ) × exp [ ( a + i 4 b ) ( ± K 2 b 1 16 b 2 + x 0 + i a 2 b ) ] × exp [ i 4 b K 2 1 3 ( a + i 4 b ) 3 ] .
x ± ( z ) = ± sin 2 ( α z ) 4 α 2 cos ( α z ) x 0 cos ( α z ) .
z f n = arctan ( 2 α x 0 ) α + ( n 1 ) π α , z d n = arctan ( 2 α x 0 ) α + n α π ,
r = z d n z f n = π α 2 arctan ( 2 α x 0 ) α ,
ϕ 1 , 2 ( x , z m ) = i s α 2 π exp ( a 3 3 ) exp ( a α 2 x 2 ) × exp { ± i s [ 1 3 α 3 x 3 ( a 2 x 0 ) α x ] } ,
| ϕ ( x , z m ) | 2 | ϕ 1 ( x , z m ) + ϕ 2 ( x , z m ) | 2 = α π exp ( 2 a 3 3 ) exp ( 2 a α 2 x 2 ) × { 1 + cos [ 2 α 3 3 x 3 2 α ( a 2 x 0 ) x ] } ,
R ( x ) = 1 2 π ρ m exp ( x 2 2 ρ m 2 ) ,
i ϕ z + 1 2 2 ϕ x 2 + α 2 δ 2 + e ( x x ) 2 2 δ 2 | ϕ ( x , z ) | 2 d x ϕ = 0 ,
d = x 2 x 1 = ( 3 π + X 0 ) / ( 2 α 3 ) 3 + ( 3 π X 0 ) / ( 2 α 3 ) 3 .
p c = 2 α π e 2 a 3 / 3 ,
W = 1 2 a α .
ϕ ( x , 0 ) = ϕ 1 ( x , z 0 ) + ϕ 2 ( x , z 0 ) .
ϕ ( x , 3 T / 4 ) = Ai ( x + x 0 ) exp [ a ( x + x 0 ) ] + Ai [ ( x x 0 ) ] exp [ a ( x x 0 ) ] ,
ϕ ( x / 3 T / 4 ) Ai [ ( | x | x 0 ) ] exp [ a ( | x | x 0 ) ] .

Metrics