Abstract

We reveal a controllable manipulation of anomalous interactions between Airy beams in nonlocal nematic liquid crystals numerically. With the help of an in-phase fundamental Gaussian beam, attraction between in-phase Airy beams can be suppressed or become a repulsive one to each other; whereas the attraction can be strengthened when the Gaussian beam is out-of-phase. In contrast to the repulsive interaction in local media, stationary bound states of breathing Airy soliton pairs are found in nematic liquid crystals.

© 2016 Optical Society of America

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2016 (1)

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
[Crossref]

2015 (5)

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Spatiotemporal dynamics of counterpropagating Airy beams,” Sci. Rep. 5, 13463 (2015).
[Crossref] [PubMed]

G. Assanto, A. A. Minzonib, and N. F. Smyth, “On optical Airy beams in integrable and non-integrable systems,” Wave Motion 52, 183–193 (2015).
[Crossref]

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]

R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, “Optical simulations of gravitational effects in the Newton-Schrodinger system,” Nat. Phys. 11, 872–878 (2015).
[Crossref]

R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
[Crossref] [PubMed]

2014 (9)

R. Driben and T. Meier, “Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves,” Opt. Lett. 39, 5539–5542 (2014).
[Crossref] [PubMed]

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

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

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

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39, 1764–1767 (2014).
[Crossref] [PubMed]

Chao Hang and Guoxiang Huang, “Guiding ultraslow weak-light bullets with Airy beams in a coherent atomic system,” Phys. Rev. A 89, 013821 (2014).
[Crossref]

N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “All-optical interconnects using Airy beams,” Opt. Lett. 39, 5997–6000 (2014).
[Crossref] [PubMed]

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11105001 (2014).
[Crossref]

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

2013 (4)

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4587 (2013).
[Crossref] [PubMed]

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]

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

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

2012 (7)

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012)
[Crossref] [PubMed]

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

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

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

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

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

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

2011 (8)

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213903 (2011).
[Crossref]

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

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(R) (2011).
[Crossref]

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

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

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express 19, 23706–23715 (2011).
[Crossref] [PubMed]

A. Rudnick and D. M. Marom, “Airy-soliton interactions in Kerr media,” Opt. Express 19, 25570–25582 (2011).
[Crossref]

2010 (8)

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, “Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality,” Phys. Rev. A 82, 013826 (2010).
[Crossref]

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref] [PubMed]

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

R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82, 043832 (2010).
[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]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35, 2260–2262 (2010).
[Crossref] [PubMed]

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

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

2009 (4)

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

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]

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

Z. Xu, N. F. Smyth, A. A. Minzoni, and Y. S. Kivshar, “Vector vortex solitons in nematic liquid crystals,” Opt. Lett. 34, 1414–1416 (2009).
[Crossref] [PubMed]

2008 (4)

G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78, 013832 (2008).
[Crossref]

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

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, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
[PubMed]

2007 (3)

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

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Y. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[Crossref]

2006 (3)

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[Crossref]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
[Crossref]

2005 (1)

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 (2005).
[Crossref]

2004 (3)

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Attraction of nonlocal dark optical solitons,” Opt. Lett. 29, 286–288 (2004).
[Crossref] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclass. Opt. 6, S288–S294 (2004).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733–737 (2004).
[Crossref] [PubMed]

2003 (2)

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003)
[Crossref]

2002 (1)

1999 (1)

G. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

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(R) (2011).
[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]

Aleahmad, P.

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

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
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Allayarov, I. M.

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

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

R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
[Crossref] [PubMed]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012)
[Crossref] [PubMed]

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

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

Assanto, G.

G. Assanto, A. A. Minzonib, and N. F. Smyth, “On optical Airy beams in integrable and non-integrable systems,” Wave Motion 52, 183–193 (2015).
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G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78, 013832 (2008).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733–737 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002).
[Crossref]

Bandres, M. A.

Bang, O.

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, “Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality,” Phys. Rev. A 82, 013826 (2010).
[Crossref]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 (2005).
[Crossref]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Attraction of nonlocal dark optical solitons,” Opt. Lett. 29, 286–288 (2004).
[Crossref] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclass. Opt. 6, S288–S294 (2004).
[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003)
[Crossref]

Baumgartl, J.

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

Bekenstein, R.

R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, “Optical simulations of gravitational effects in the Newton-Schrodinger system,” Nat. Phys. 11, 872–878 (2015).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
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R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express 19, 23706–23715 (2011).
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Belic, M.

Belic, M. R.

Broky, J.

Brzdakiewicz, K. A.

Cai, W.

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

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

Chen, B.

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
[Crossref]

Chen, C.

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
[Crossref]

Chen, H.

Chen, R

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

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11105001 (2014).
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R. Chen, K. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
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R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82, 043832 (2010).
[Crossref]

Chen, W.

Chen, Z.

Chew, K.

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

Chong, A.

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

Christiansen, P. L.

Christodoulides, D. N.

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

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

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
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N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
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A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[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]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
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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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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Chu, X.

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

R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82, 043832 (2010).
[Crossref]

Cohen, O.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
[Crossref]

Conti, C.

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733–737 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

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(R) (2011).
[Crossref]

Deng, D.

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
[Crossref]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 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 media,” Phys. Rev. Lett. 108, 113903 (2012).
[Crossref] [PubMed]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012)
[Crossref] [PubMed]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Driben, R.

Edmundson, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclass. Opt. 6, S288–S294 (2004).
[Crossref]

Efremidis, N. K.

Ellenbogen, T.

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

Epstein, I.

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012)
[Crossref] [PubMed]

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(R) (2011).
[Crossref]

Fattal, Y.

Fleischer, J. W.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref] [PubMed]

Ganany-Padowicz, A.

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

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Greenfield, E.

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213903 (2011).
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Guo, Q.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[Crossref]

Hang, Chao

Chao Hang and Guoxiang Huang, “Guiding ultraslow weak-light bullets with Airy beams in a coherent atomic system,” Phys. Rev. A 89, 013821 (2014).
[Crossref]

He, S.

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

Hnatovsky, C.

R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
[Crossref] [PubMed]

Hu, W.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[Crossref]

Hu, Y.

Huang, Guoxiang

Chao Hang and Guoxiang Huang, “Guiding ultraslow weak-light bullets with Airy beams in a coherent atomic system,” Phys. Rev. A 89, 013821 (2014).
[Crossref]

Huang, S.

Janunts, N.

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

Jia, S.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref] [PubMed]

Kaminer, 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]

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

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

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

Kivshar, Y. S.

Z. Xu, N. F. Smyth, A. A. Minzoni, and Y. S. Kivshar, “Vector vortex solitons in nematic liquid crystals,” Opt. Lett. 34, 1414–1416 (2009).
[Crossref] [PubMed]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Y. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[Crossref]

Kivshar, Yuri S.

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

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]

Kong, Q.

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39, 1764–1767 (2014).
[Crossref] [PubMed]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, “Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality,” Phys. Rev. A 82, 013826 (2010).
[Crossref]

Konotop, V. V.

Krolikowski, W.

R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
[Crossref] [PubMed]

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39, 1764–1767 (2014).
[Crossref] [PubMed]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, “Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality,” Phys. Rev. A 82, 013826 (2010).
[Crossref]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 (2005).
[Crossref]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Attraction of nonlocal dark optical solitons,” Opt. Lett. 29, 286–288 (2004).
[Crossref] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclass. Opt. 6, S288–S294 (2004).
[Crossref]

Krolikowski, W. Z.

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003)
[Crossref]

Lan, S.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[Crossref]

Lee, J.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref] [PubMed]

Lereah, Y.

R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
[Crossref] [PubMed]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Li, C.

Li, T.

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

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Li, Y.

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
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Lotti, A.

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733–737 (2004).
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Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
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A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006).
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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).
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N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Attraction of nonlocal dark optical solitons,” Opt. Lett. 29, 286–288 (2004).
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W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclass. Opt. 6, S288–S294 (2004).
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E. Greenfield, M. Segev, W. Wallasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213903 (2011).
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R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
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G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11105001 (2014).
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Salandrino, A.

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R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, “Optical simulations of gravitational effects in the Newton-Schrodinger system,” Nat. Phys. 11, 872–878 (2015).
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N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Spatiotemporal dynamics of counterpropagating Airy beams,” Sci. Rep. 5, 13463 (2015).
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N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “All-optical interconnects using Airy beams,” Opt. Lett. 39, 5997–6000 (2014).
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R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, “Optical simulations of gravitational effects in the Newton-Schrodinger system,” Nat. Phys. 11, 872–878 (2015).
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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).
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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).
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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).
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M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733–737 (2004).
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W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
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N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Spatiotemporal dynamics of counterpropagating Airy beams,” Sci. Rep. 5, 13463 (2015).
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A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
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N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Spatiotemporal dynamics of counterpropagating Airy beams,” Sci. Rep. 5, 13463 (2015).
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G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78, 013832 (2008).
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Xu, Z.

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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Appl. Phys. Lett. (1)

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
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J. Opt. B: Quantum Semiclass. Opt. (1)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclass. Opt. 6, S288–S294 (2004).
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G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11105001 (2014).
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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).
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Nat. Photonics (3)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
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A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
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T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
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Nat. Phys. (2)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
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R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, “Optical simulations of gravitational effects in the Newton-Schrodinger system,” Nat. Phys. 11, 872–878 (2015).
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Nature (2)

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733–737 (2004).
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N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
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Opt. Commun. (2)

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
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W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
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Opt. Express (5)

Opt. Lett. (15)

R. Driben, V. V. Konotop, and T. Meier, “Coupled Airy breathers,” Opt. Lett. 39, 5523–5526 (2014).
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R. Driben and T. Meier, “Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves,” Opt. Lett. 39, 5539–5542 (2014).
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N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “All-optical interconnects using Airy beams,” Opt. Lett. 39, 5997–6000 (2014).
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P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
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Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4587 (2013).
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W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39, 1764–1767 (2014).
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Z. Xu, N. F. Smyth, A. A. Minzoni, and Y. S. Kivshar, “Vector vortex solitons in nematic liquid crystals,” Opt. Lett. 34, 1414–1416 (2009).
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M. A. Bandres, “Accelerating beams,” Opt. Lett. 34, 3791–3793 (2009).
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Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35, 2260–2262 (2010).
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Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35, 3952–3954 (2010).
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N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
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M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002).
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N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, “Attraction of nonlocal dark optical solitons,” Opt. Lett. 29, 286–288 (2004).
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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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Phys. Rev. A (8)

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Y. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
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G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78, 013832 (2008).
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Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, “Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality,” Phys. Rev. A 82, 013826 (2010).
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Chao Hang and Guoxiang Huang, “Guiding ultraslow weak-light bullets with Airy beams in a coherent atomic system,” Phys. Rev. A 89, 013821 (2014).
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X. Chu, G. Zhou, and R Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012)
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R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82, 043832 (2010).
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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(R) (2011).
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I. M. Allayarov and E. N. Tsoy, “Dynamics of Airy beams in nonlinear media,” Phys. Rev. A 90, 023852 (2014).
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Phys. Rev. E (2)

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N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003)
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C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
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A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006).
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S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
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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).
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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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I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Yuri S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011)
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I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012)
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R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, “Unveiling the orbital angular momentum and acceleration of electron beams,” Phys. Rev. Lett. 114, 096102 (2015).
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E. Greenfield, M. Segev, W. Wallasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213903 (2011).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
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P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
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C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107, 243901 (2011).
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Sci. Rep. (3)

R. Chen, K. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
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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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N. Wiersma, N. Marsal, M. Sciamanna, and D. Wolfersberger, “Spatiotemporal dynamics of counterpropagating Airy beams,” Sci. Rep. 5, 13463 (2015).
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Science (2)

G. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
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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).
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Wave Motion (1)

G. Assanto, A. A. Minzonib, and N. F. Smyth, “On optical Airy beams in integrable and non-integrable systems,” Wave Motion 52, 183–193 (2015).
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Figures (10)

Fig. 1
Fig. 1 Trajectories of in-phase interacting Airy beams and Gaussian beam in nematic liquid crystals with the degree of nonlocality σ = 0 (local case). The amplitude is A = 3 in all the plots, and C = 0 for (a–c) and C = 0.3, 0.8, 1 for (d–f), respectively. The beam intervals are: (a,d) B = 1, (b,e) B = 2, and (c,f) B = 3.
Fig. 2
Fig. 2 Amplitude and intensity of the in-phase input beam. The amplitude is A = 3 in all the plots. All the solid lines represent C = 0, and dashed lines in (a,d), (b,e), and (c,f) represent C = 0.3, 0.8, 1, respectively. The beam intervals are: (a,d) B = 1, (b,e) B = 2, and (c,f) B = 3, respectively.
Fig. 3
Fig. 3 Trajectories of in-phase interacting Airy beams and Gaussian beam in nematic liquid crystals with the degree of nonlocality σ = 0 (local case). The amplitude is A = 3 and the interval is B = 3. The amplitude for the Gaussian beams are C = 0.9, 1.5, 1.6, 1.7 for (a–d), respectively.
Fig. 4
Fig. 4 Intensity distribution of the in-phase input beam with A = 3 and B = 3. The dotted, solid, dashed, and dash-dotted lines represent the amplitude in the Gaussian beams for C = 0, 0.8, 1.3, and 2, respectively.
Fig. 5
Fig. 5 Trajectories of in-phase interacting Airy beams and Gaussian beam in nematic liquid crystals. The degrees of nonlocality are σ = 0 (local case) for (a–c), and σ = 0.1, 0.15, 0.42 for (d–f). The amplitudes are A = 3 in all the plots and C = 0.4, 1.62, and 2.41 for (a,d), (b,e), and (c,f), respectively. The beam intervals are: (a,d) B = 1, (b,e) B = 2, and (c,f) B = 3.
Fig. 6
Fig. 6 Amplitudes and intensity of the in-phase input beam. The amplitudes are A = 3 for all the plots. All the solid lines represent C = 0, and dashed lines in (a,d), (b,e), and (c,f) represent C = 0.4, 1.62, 2.41, respectively. The beam intervals are: (a,d) B = 1, (b,e) B = 2, and (c,f) B = 3.
Fig. 7
Fig. 7 Trajectories of out-of-phase interacting Airy beams and an Gaussian beam in nematic liquid crystals with the degree of nonlocality σ = 0 (local case). The amplitude is A = 3 in all the plots, and C = 0.8, 0.3, 0.2, 2.4, 1.1, 0.7 for (a–f), respectively. The beam intervals are: (a,d) B = 1, (b,e) B = 2, and (c,f) B = 3, respectively.
Fig. 8
Fig. 8 Amplitudes and intensity of the out-of-phase input beam. The amplitude is A = 3 in all the plots. All the solid lines represent C = 0, dashed lines in (a,d), (b,e), and (c,f) represent C = 0.8, 0.3, 0.2, and dotted lines in (a,d), (b,e), and (c,f) represent C = 2.4, 1.1, and 0.7, respectively. The beam intervals are: (a,d) B = 1, (b,e) B = 2, and (c,f) B = 3.
Fig. 9
Fig. 9 Trajectories of out-of-phase interacting Airy beams and Gaussian beam in nematic liquid crystals. The degrees of nonlocality are σ = 0 (local case) for (a), and σ = 0.8 for (b). The amplitudes are A = 4.7 and C = 3; while the beam interval is B = 3.
Fig. 10
Fig. 10 The intensity distribution of Fig. 9(b) at the propagation distance z = 0 (a) and z = 30 (b).

Equations (6)

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i ψ z + 1 2 2 ψ x 2 + 2 θ ψ = 0 ,
σ 2 2 θ x 2 θ + 1 2 | ψ | 2 = 0 ,
θ = 1 2 R ( x x ) | ψ ( x ) | 2 d x ,
R ( x ) = 1 2 σ exp ( | x | σ ) .
ψ ( x ) = A { Ai [ ( x B ) ] exp [ a ( x B ) ] + exp ( i ρ π ) Ai [ ( x + B ) ] exp [ a ( x + B ) ] } ,
ψ ( x ) = A { Ai [ ( x B ) ] exp [ a ( x B ) ] + Ai [ ( x + B ) ] exp [ a ( x + B ) ] } + exp ( i ρ π ) C exp ( x 2 / 2 ) ,

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