Abstract

We investigate controllable spatial modulation of circular autofocusing Airy beams, under action of different dynamic linear potentials, both theoretically and numerically. We introduce a novel treatment method in which the circular Airy beam is represented as a superposition of narrow azimuthally-modulated one-dimensional Airy beams that can be analytically treated. The dynamic linear potentials are appropriately designed, so that the autofocusing effect can either be weakened or even eliminated when the linear potential exerts a “pulling” effect on the beam, or if the linear potential exerts a “pushing” effect, the autofocusing effect can be greatly strengthened. Numerical simulations agree with the theoretical results very well.

© 2016 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  29. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
    [Crossref] [PubMed]
  30. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
    [Crossref] [PubMed]
  31. I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  33. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  36. P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  39. Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, F. Wen, and Y. P. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40, 3786–3789 (2015).
    [Crossref] [PubMed]
  40. Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, Y. P. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).
    [Crossref]
  41. Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).
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    [Crossref] [PubMed]

2016 (1)

2015 (8)

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, 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,” Ann. Phys. 363, 305–315 (2015).
[Crossref]

L. Zhang, K. Liu, H. Zhong, J. Zhang, Y. Li, and D. Fan, “Effect of initial frequency chirp on Airy pulse propagation in an optical fiber,” Opt. Express 23, 2566–2576 (2015).
[Crossref] [PubMed]

Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
[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, 9814 (2015).
[Crossref] [PubMed]

F. Diebel, B. M. Bokić, D. V. Timotijević, D. M. J. Savić, and C. Denz, “Soliton formation by decelerating interacting Airy beams,” Opt. Express 23, 24351–24361 (2015).
[Crossref] [PubMed]

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, F. Wen, and Y. P. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40, 3786–3789 (2015).
[Crossref] [PubMed]

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, Y. P. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).
[Crossref]

2014 (2)

2013 (8)

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

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

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, “Spectrum to distance mapping via nonlinear Airy pulses,” Opt. Lett. 38, 380–382 (2013).
[Crossref] [PubMed]

R. Driben, Y. Hu, Z. Chen, B. A. Malomed, and R. Morandotti, “Inversion and tight focusing of Airy pulses under the action of third-order dispersion,” Opt. Lett. 38, 2499–2501 (2013).
[Crossref] [PubMed]

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

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

2012 (3)

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, 113903 (2012).
[Crossref] [PubMed]

C.-Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4, 174–180 (2012).
[Crossref]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

2011 (12)

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref] [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, 1164–1166 (2011).
[Crossref] [PubMed]

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

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

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011).
[Crossref] [PubMed]

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

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

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19, 7356–7364 (2011).
[Crossref] [PubMed]

2010 (2)

2008 (1)

2007 (3)

1979 (1)

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

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

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, 113903 (2012).
[Crossref] [PubMed]

Azaña, J.

Balazs, N. L.

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

Bandres, M. A.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15, 16719–16728 (2007).
[Crossref] [PubMed]

Belic, M.

Belic, M. R.

Berry, M. V.

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

Bokic, B. M.

Bongiovanni, D.

Broky, J.

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]

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

Chen, H. X.

Chen, Z.

Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
[Crossref] [PubMed]

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, “Spectrum to distance mapping via nonlinear Airy pulses,” Opt. Lett. 38, 380–382 (2013).
[Crossref] [PubMed]

R. Driben, Y. Hu, Z. Chen, B. A. Malomed, and R. Morandotti, “Inversion and tight focusing of Airy pulses under the action of third-order dispersion,” Opt. Lett. 38, 2499–2501 (2013).
[Crossref] [PubMed]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011).
[Crossref] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
[Crossref] [PubMed]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

Chen, Z. G.

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

Chen, Z.-G.

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Chremmos, I.

Chremmos, I. D.

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

Christodoulides, D.

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

Christodoulides, D. N.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref] [PubMed]

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

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
[Crossref] [PubMed]

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

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

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]

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

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

Clerici, M.

Couairon, A.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

Denz, C.

Diebel, F.

Dogariu, A.

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]

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

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, 113903 (2012).
[Crossref] [PubMed]

Driben, R.

Efremidis, N. K.

R.-S. Penciu, K. G. Makris, and N. K. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
[Crossref] [PubMed]

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

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref] [PubMed]

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

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
[Crossref] [PubMed]

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

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

Fan, D.

Gan, X.

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).
[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, 9814 (2015).
[Crossref] [PubMed]

Greenfield, E.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

Gutiérrez-Vega, J. C.

Hu, Y.

Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
[Crossref] [PubMed]

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, “Spectrum to distance mapping via nonlinear Airy pulses,” Opt. Lett. 38, 380–382 (2013).
[Crossref] [PubMed]

R. Driben, Y. Hu, Z. Chen, B. A. Malomed, and R. Morandotti, “Inversion and tight focusing of Airy pulses under the action of third-order dispersion,” Opt. Lett. 38, 2499–2501 (2013).
[Crossref] [PubMed]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

Hwang, C.-Y.

C.-Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4, 174–180 (2012).
[Crossref]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19, 7356–7364 (2011).
[Crossref] [PubMed]

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, 116802 (2011).
[Crossref] [PubMed]

Jiang, D.-S.

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Kaminer, I.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

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, 113903 (2012).
[Crossref] [PubMed]

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

Kashyap, R.

Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
[Crossref] [PubMed]

Kim, K. Y.

C.-Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4, 174–180 (2012).
[Crossref]

Kim, K.-Y.

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, 1164–1166 (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, 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, 116802 (2011).
[Crossref] [PubMed]

Lee, B.

C.-Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4, 174–180 (2012).
[Crossref]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19, 7356–7364 (2011).
[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]

Li, M.

Li, P.

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.

Li, Y. Y.

Liu, J.-J.

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Liu, K.

Liu, S.

Liu, W.

Liu, X.

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, Y. P. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).
[Crossref]

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,” Ann. Phys. 363, 305–315 (2015).
[Crossref]

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, F. Wen, and Y. P. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40, 3786–3789 (2015).
[Crossref] [PubMed]

Liu, Y.

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

Lu, C.

Lu, K. Q.

Makris, K. G.

Malomed, B. A.

Mills, M.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

Mills, M. S.

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, 116802 (2011).
[Crossref] [PubMed]

Miroshnichenko, A. E.

Morandotti, R.

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, 116802 (2011).
[Crossref] [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, 1164–1166 (2011).
[Crossref] [PubMed]

Ni, P.-G.

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Paltoglou, V.

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

Panagiotopoulos, P.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

Papazoglou, D. G.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

Penciu, R.-S.

Peng, T.

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, 116802 (2011).
[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,” Ann. Phys. 363, 305–315 (2015).
[Crossref]

Prakash, J.

Rodriguez-Lara, B. M.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

Salandrino, A.

Savic, D. M. J.

Segev, M.

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

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, 113903 (2012).
[Crossref] [PubMed]

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

Shadrivov, I. V.

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, 113903 (2012).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Siviloglou, G.

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

Siviloglou, G. A.

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]

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

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

Tehranchi, A.

Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
[Crossref] [PubMed]

Timotijevic, D. V.

Tzortzakis, S.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

von Klitzing, W.

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

Wabnitz, S.

Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
[Crossref] [PubMed]

Wang, R. M.

Wang, S.

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]

Wen, F.

Wu, Z. K.

Xiao, M.

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, Y. P. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).
[Crossref]

Xie, G.

Yao, J.

Yin, X.

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, J.

Zhang, L.

Zhang, P.

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011).
[Crossref] [PubMed]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

Zhang, X.

Zhang, Y. P.

Zhang, Y. Q.

Zhang, Z.

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

Zhao, J.

Zhao, J. Y.

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

Zheng, H. B.

Zhong, H.

Zhong, W. P.

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, X. Liu, M. R. Belić, W. P. Zhong, F. Wen, and Y. P. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40, 3786–3789 (2015).
[Crossref] [PubMed]

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,” Ann. Phys. 363, 305–315 (2015).
[Crossref]

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, Y. P. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).
[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]

Acta Phys. Sin. (1)

Z. Zhang, J.-J. Liu, P. Zhang, P.-G. Ni, J. Prakash, Y. Hu, D.-S. Jiang, D. N. Christodoulides, and Z.-G. Chen, “Generation of autofocusing beams with multi-Airy beams,” Acta Phys. Sin. 62, 034209 (2013).

Am. J. Phys. (1)

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

Ann. Phys. (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,” Ann. Phys. 363, 305–315 (2015).
[Crossref]

Chin. Sci. Bull. (1)

Z. Zhang, Y. Hu, J. Y. Zhao, P. Zhang, and Z. G. Chen, “Research progress and application prospect of Airy beams,” Chin. Sci. Bull. 58, 3513–3520 (2013).
[Crossref]

IEEE Photonics J. (1)

C.-Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4, 174–180 (2012).
[Crossref]

Nat. Commun. (1)

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Opt. Express (8)

F. Diebel, B. M. Bokić, D. V. Timotijević, D. M. J. Savić, and C. Denz, “Soliton formation by decelerating interacting Airy beams,” Opt. Express 23, 24351–24361 (2015).
[Crossref] [PubMed]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19, 7356–7364 (2011).
[Crossref] [PubMed]

M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15, 16719–16728 (2007).
[Crossref] [PubMed]

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]

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 media,” Opt. Express 22, 7160–7171 (2014).
[Crossref] [PubMed]

P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22, 7598–7606 (2014).
[Crossref] [PubMed]

L. Zhang, K. Liu, H. Zhong, J. Zhang, Y. Li, and D. Fan, “Effect of initial frequency chirp on Airy pulse propagation in an optical fiber,” Opt. Express 23, 2566–2576 (2015).
[Crossref] [PubMed]

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]

Opt. Lett. (15)

Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, F. Wen, and Y. P. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40, 3786–3789 (2015).
[Crossref] [PubMed]

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

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[Crossref] [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, 1164–1166 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

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

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011).
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I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
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Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, “Spectrum to distance mapping via nonlinear Airy pulses,” Opt. Lett. 38, 380–382 (2013).
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R. Driben, Y. Hu, Z. Chen, B. A. Malomed, and R. Morandotti, “Inversion and tight focusing of Airy pulses under the action of third-order dispersion,” Opt. Lett. 38, 2499–2501 (2013).
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Y. Q. Zhang, M. Belić, Z. K. Wu, H. B. Zheng, K. Q. Lu, Y. Y. Li, and Y. P. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4588 (2013).
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G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
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R.-S. Penciu, K. G. Makris, and N. K. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
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Opt. Photonics News (1)

M. A. Bandres, I. Kaminer, M. Mills, B. M. Rodriguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

Phys. Rev. A (3)

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807 (2011).
[Crossref]

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

Phys. Rev. Lett. (7)

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, 116802 (2011).
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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).
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Y. Hu, A. Tehranchi, S. Wabnitz, R. Kashyap, Z. Chen, and R. Morandotti, “Improved intrapulse Raman scattering control via asymmetric Airy pulses,” Phys. Rev. Lett. 114, 073901 (2015).
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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, 113903 (2012).
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G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
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Y. Q. Zhang, X. Liu, M. R. Belić, W. P. Zhong, Y. P. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).
[Crossref]

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).
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Other (1)

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Input beam intensities. (a) An example of finite-energy circular Airy beam. (b) An azimuthally-modulated circular Airy beam, with w0 = 1.5. (c) Same as (b), but with w0 = 0.05. (d) A combination of 40 azimuthally modulated circular Airy beams along different azimuthal directions, according to Eq. (6). Other parameters: r0 = 5 and a = 0.1. All the panels share the same variables and dimensions.

Fig. 2
Fig. 2

(a) Analytical intensity distribution of a CAi beam during propagation in the xz plane at y = 0, according to Eq. (9), for d = 1. (b) Same as (a), but for numerical simulation. (c) Intensity profiles of CAi beam at different propagation distances (noted in each panel). Other parameters: r0 = 5 and a = 0.1. All the panels in (c) share the same variables, dimensions, and color scales.

Fig. 3
Fig. 3

Same as Fig. 2, but for d(z) = 1 + 4π2 cos(πz).

Fig. 4
Fig. 4

(a) Maximum of the beam intensity during propagation for d(z) = 13 − 12z and r0 = 5. The maximum of the beam intensity at z = 0 is 1. Inset shows the propagation of the components corresponding to θ0 = 0 and θ0 = π, and the corresponding theoretical trajectories. (b) The maximum of the beam intensity as a function of r0 and z. The white dashed line corresponds to the curve in (a). The decay parameter is a = 0.05.

Fig. 5
Fig. 5

Figure setup is as in Fig. 4.

Fig. 6
Fig. 6

Same as Fig. 2(b), but for Gaussian apodization with (a) w = 10, and (b) w = 5. The dashed curves represent the analytical trajectories. The panels share the same variables and dimensions.

Equations (24)

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i d ψ d z + 1 2 ( 2 ψ x 2 + 2 ψ y 2 ) V ( x , y , z ) ψ = 0 ,
i d ψ d z + 1 2 ( 2 ψ r 2 + 1 r ψ r ) d ( z ) 2 r ψ = 0 .
i ψ z + 1 2 2 ψ x 2 d ( z ) 2 | x | ψ = 0 ,
ψ ( x , y ) = Ai ( r 0 r ) exp [ a ( r 0 r ) ] ,
ψ az ( x , y ) = Ai ( r 0 r ) exp [ a ( r 0 r ) ] exp ( ( θ θ 0 ) 2 w 0 2 ) ,
δ ( θ θ 0 ) = lim w 0 0 exp ( ( θ θ 0 ) 2 w 0 2 ) = { 1 , θ = θ 0 0 , θ θ 0
[ x p y p ] = [ cos θ 0 sin θ 0 sin θ 0 cos θ 0 ] [ x y ] ,
tan θ p = y p x p = x sin θ 0 + y cos θ 0 x cos θ 0 y sin θ 0 = tan ( θ + θ 0 ) .
ψ ( x , y ) = θ 0 = π + π Ai ( r 0 x p ) exp [ a ( r 0 x p ) ] .
ψ ( x , y , z ) = C θ 0 = π + π Ai [ i a z + ( 1 2 f 1 1 4 z 2 + ( r 0 x p ) ) ] × exp [ a ( 1 2 f 1 1 2 z 2 + ( r 0 x p ) ) ] × exp [ i ( 1 2 a 2 z + 1 4 z f 1 1 8 f 2 1 12 z 3 1 2 ( r 0 x p ) g + 1 2 ( r 0 x p ) z ) ] ,
g ( z ) = 0 z d ( t ) d t ,
f 1 ( z ) = f 0 + 0 z g ( t ) d t ,
f 2 ( z ) = 0 z g 2 ( t ) d t ,
x p = r 0 + 1 2 f 1 1 4 z 2 ,
ψ ( x , y , z ) = Ai [ i a z + ( 1 2 f 1 1 4 z 2 + ( r 0 r ) ) ] × exp [ a ( 1 2 f 1 1 2 z 2 + ( r 0 r ) ) ] × exp [ i ( 1 2 a 2 z + 1 4 z f 1 1 8 f 2 1 12 z 3 1 2 ( r 0 r ) g + 1 2 ( r 0 r ) z ) ] ,
x p = r 0 ,
x p = r 0 2 cos ( π z ) + 2 ,
x p = r 0 z 3 + 3 z 2 ,
H ( z 2 ) = { 0 , for ( z 2 ) , 1 , for ( z > 2 ) .
x p = { r 0 , for ( z 2 ) , r 0 + 2 2 ( z 4 ) z + 5 , for ( z > 2 ) .
ψ = Ai ( r 0 r ) exp ( ( r 0 r ) 2 w 2 ) ,
ψ ( x , y , z ) = 1 σ θ 0 = π + π Ai [ 1 σ ( r 0 x p ) + f 1 2 z 2 4 σ 2 ] exp [ 1 σ w 2 ( ( r 0 x p ) + f 1 2 ) ] × exp { i [ f 2 8 D 2 ( r 0 x p ) + z 2 σ 2 ( r 0 x p + f 1 2 z 2 6 σ ) ] } ,
ψ ( x , y , z ) = 1 σ Ai [ 1 σ ( ( r 0 r ) + f 1 2 ) z 2 4 σ 2 ] exp [ 1 σ w 2 ( ( r 0 r ) + f 1 2 ) ] × exp { i [ f 2 8 D 2 ( r 0 r ) + z 2 σ 2 ( r 0 r + f 1 2 z 2 6 σ ) ] } .
x p = r 0 z 2 w 4 4 ( w 4 + 4 z 2 ) + f 1 2 ,

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