Abstract

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  4. 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]
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    [Crossref]
  6. M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating Optical Beams,” Opt. Photonics News 24, 30–37 (2013).
    [Crossref]
  7. A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
    [Crossref]
  8. 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]
  9. 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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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  23. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  26. Y. Zhang, M. R. 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, 4585–4588 (2013).
    [Crossref] [PubMed]
  27. 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]
  28. I. M. Allayarov and E. N. Tsoy, “Dynamics of Airy beams in nonlinear media,” Phys. Rev. A 90, 023852 (2014).
    [Crossref]
  29. A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
    [Crossref] [PubMed]
  30. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding Amplitude Information onto Phase-Only Filters,” Appl. Opt. 38, 5004–5013 (1999).
    [Crossref]
  31. U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
    [Crossref]
  32. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
    [Crossref] [PubMed]
  33. 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]
  34. W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
    [Crossref]

2014 (7)

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

N. K. Efremidis, “Accelerating beam propagation in refractive-index potentials,” Phys. Rev. A 89, 023841 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

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]

K. G. Makris, I. Kaminer, R. El-Ganainy, N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39, 2129–2132 (2014).
[Crossref] [PubMed]

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

2013 (4)

Y. Zhang, M. R. 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, 4585–4588 (2013).
[Crossref] [PubMed]

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

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

2012 (1)

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

2011 (4)

2010 (3)

2009 (1)

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]

2008 (4)

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

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[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]

2007 (2)

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]

1999 (2)

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding Amplitude Information onto Phase-Only Filters,” Appl. Opt. 38, 5004–5013 (1999).
[Crossref]

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

1998 (1)

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

1995 (1)

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

1979 (1)

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

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

Allayarov, I. M.

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

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Arrizón, V.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Balazs, N. L.

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

Bandres, M. A.

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

Belic, M. R.

Berry, M. V.

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

Boguslawski, M.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

Bohatý, L.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Bokic, B. M.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

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

Campos, J.

Chávez-Cerda, S.

Chen, H.

Chen, Z.

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]

Christodoulides, D. N.

K. G. Makris, I. Kaminer, R. El-Ganainy, N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39, 2129–2132 (2014).
[Crossref] [PubMed]

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

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]

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]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (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 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]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Nonlinear Photonics and Novel Optical Phenomena, vol. 170 of Springer Series in Optical Sciences (Springer New York, New York, NY, 2012).

Cottrell, D. M.

Courvoisier, F.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Davis, J. A.

Denz, C.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, vol. 188 of Springer Tracts in Modern Physics (Springer, Berlin, 2003).
[Crossref]

Desyatnikov, A. S.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Dholakia, K.

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

Diebel, F.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

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

Dörfler, U. B.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Driben, R.

Dudley, J. M.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Efremidis, N. K.

El-Ganainy, R.

Froehly, L.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Furfaro, L.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Greenfield, E.

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

Grujic, D. Z.

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Hu, Y.

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]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Nonlinear Photonics and Novel Optical Phenomena, vol. 170 of Springer Series in Optical Sciences (Springer New York, New York, NY, 2012).

Huang, S.

Imlau, M. K.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Jacquot, M.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Jelenkovic, B. M.

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Jovic, D. M.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Kaiser, F.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Kaminer, I.

K. G. Makris, I. Kaminer, R. El-Ganainy, N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39, 2129–2132 (2014).
[Crossref] [PubMed]

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

Kivshar, Y. S.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

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]

Konotop, V. V.

Królikowski, W.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

Lacourt, P. A.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Leykam, D.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

Li, C.

Li, Y.

Lou, C.

Lu, K.

Lucic, N. M.

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Luther-Davies, B.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

Makris, K. G.

Mathis, A.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Mazilu, M.

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

Meier, T.

Mills, M.

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

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy Beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Moreno, I.

Moya-Cessa, H. M.

Neshev, D. N.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Pankrath, R.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Pantelic, D. V.

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Papazoglou, D. G.

Piechatzek, R.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Piper, A.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy Beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Renninger, W. H.

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

Richter, T.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Rodríguez-Lara, B.

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

Rose, P.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

Ruiz, U.

Saffman, M.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

Schwab, M.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, vol. 188 of Springer Tracts in Modern Physics (Springer, Berlin, 2003).
[Crossref]

Segev, M.

K. G. Makris, I. Kaminer, R. El-Ganainy, N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39, 2129–2132 (2014).
[Crossref] [PubMed]

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

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

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Siviloglou, G. A.

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).
[Crossref] [PubMed]

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]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Nonlinear Photonics and Novel Optical Phenomena, vol. 170 of Springer Series in Optical Sciences (Springer New York, New York, NY, 2012).

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Stepken, A.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

Terhalle, B.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Timotijevic, D. V.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

Tsoy, E. N.

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

Tzortzakis, S.

Volk, T.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Weilnau, C.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, vol. 188 of Springer Tracts in Modern Physics (Springer, Berlin, 2003).
[Crossref]

Wirth, V.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Wise, F. W.

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

Wöhlecke, M.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Woike, T.

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Wu, Z.

Xu, J.

Yzuel, M. J.

Zhang, P.

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]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Nonlinear Photonics and Novel Optical Phenomena, vol. 170 of Springer Series in Optical Sciences (Springer New York, New York, NY, 2012).

Zhang, Y.

Zheng, H.

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Am. J. Phys. (1)

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

Appl. Opt. (1)

Appl. Phys. B Lasers Opt. (1)

U. B. Dörfler, R. Piechatzek, T. Woike, M. K. Imlau, V. Wirth, L. Bohatý, T. Volk, R. Pankrath, and M. Wöhlecke, “A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate,” Appl. Phys. B Lasers Opt. 68, 843–848 (1999).
[Crossref]

Appl. Phys. Lett. (3)

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

Nat. Photonics (2)

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]

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

Opt. Express (4)

Opt. Lett. (8)

Opt. Photonics News (1)

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

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Phys. Rev. A (5)

N. K. Efremidis, “Accelerating beam propagation in refractive-index potentials,” Phys. Rev. A 89, 023841 (2014).
[Crossref]

N. M. Lučić, B. M. Bokić, D. Z. Grujić, D. V. Pantelić, B. M. Jelenković, A. Piper, D. M. Jović, and D. V. Timotijević, “Defect-guided Airy beams in optically induced waveguide arrays,” Phys. Rev. A 88, 063815 (2013).
[Crossref]

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

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

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Królikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of Multivortex Solitons in Photonic Lattices,” Phys. Rev. Lett. 101, 013903 (2008).
[Crossref] [PubMed]

Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B (1)

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 10, 823 (1998).
[Crossref]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy Beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Other (3)

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Nonlinear Photonics and Novel Optical Phenomena, vol. 170 of Springer Series in Optical Sciences (Springer New York, New York, NY, 2012).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, vol. 188 of Springer Tracts in Modern Physics (Springer, Berlin, 2003).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Experimental setup and single Airy beam characteristics. (a) Experimental setup (SLM: Spatial light modulator, BS: beam splitter, FM: Fourier mask, SBN: strontium barium niobate crystal, MO: microscope objective). (b–d) Linear propagation of a single two-dimensional Airy beam through the homogeneous crystal. (b),(d): Intensity at the input and output face of the crystal, (c) cross-section during propagation.
Fig. 2
Fig. 2 Interference of multiple Airy beams in homogeneous linear medium. (a–d) Evolution of two Airy beams in experiment and numerics. (a,b) in phase, (c,d) with π phase difference. (e–h) Evolution of four Airy beams in experiment and numerics. (e,f) in phase, (g,h) with π phase difference. Each panel is normalized individually.
Fig. 3
Fig. 3 Formation of solitary states from the interaction of two in-phase Airy beams. (a) Experimental results for different probe beam power. Each panel shows the intensity pattern at the output face of the SBN crystal (individually normalized). (b) Results from corresponding numerical simulations. (c) Volumetric plot of the numerically calculated three-dimensional intensity distribution (three times longer crystal) for strong nonlinearity. The position of the marked plane corresponds to the length of the used SBN crystal, L = 20mm and to Figs. (a4),(b4).
Fig. 4
Fig. 4 Formation of solitary states from the interaction of two out-of-phase Airy beams. (a) Experimental results for different probe beam power. Each panel shows the intensity pattern at the output face of the SBN crystal (individually normalized). (b) Results from corresponding numerical simulations. (c) Volumetric plot of the numerically calculated three-dimensional intensity distribution (three times longer crystal) for strong nonlinearity. The position of the marked plane corresponds to the length of the used SBN crystal, L = 20mm and to Figs. (a4),(b4).
Fig. 5
Fig. 5 Interaction of four Airy beams. (left) Formation of solitary state for the case where the beams are in phase. (right) Nonlinear propagation for π phase difference. (a),(d) Experimental results for different probe beam power. Each panel shows the intensity pattern at the output face of the SBN crystal (individually normalized). (b,e) Results from corresponding numerical simulations. (c,f) Volumetric plot of the three-dimensional intensity distribution (from numerics) for strong nonlinearity.

Equations (4)

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i A ζ + 1 2 ( 2 A χ 2 + 2 A ν 2 ) + 1 2 k 0 2 w 0 2 Δ n 2 ( I ) A = 0.
2 ϕ + ln ( 1 + I ) ϕ = E ext x ln ( 1 + I ) + k B T e ( 2 ln ( 1 + I ) + ( ln ( 1 + I ) ) 2 ) ,
ψ ( χ , ν , ζ ) = A 0 φ ( χ , ζ ) φ ( ν , ζ ) ,
φ ( X , ζ ) = A i [ X ζ 2 4 + i a X ζ ] exp [ i 12 ( 6 a X 2 ζ 12 i a X X + 6 i a X ζ 2 + 6 X ζ ζ 3 ) ] , with X = { χ , ν }

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