Abstract

We address (2+1)D surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium whose nonlinear contribution to the refractive index has an initial value at the interface. We find that there exist stable single and dipole surface solitons that do not exhibit a power threshold. The properties of the surface solitons can be affected by the initial value and the degree of nonlocality. When a laser beam is launched away from the interface, the beam will oscillate periodically.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

2011 (2)

Z. W. Shi, H. G. Li, and Qi Guo, “Surface-wave solitons between linear media and nonlocal nonlinear media,” Phys. Rev. A 83, 023817 (2011).
[CrossRef]

X. K. Ma, Z. J. Yang, D. Q. Lu, and W. Hu, “Interface solitons in thermal nonlinear media,” Phys. Rev. A 83, 053831 (2011).
[CrossRef]

2010 (3)

F. Ye, B. Hu, Y. V. Kartashov, and L. Torner, “Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media,” Phys. Rev. A 82, 023822 (2010).
[CrossRef]

A. A. Minzoni, N. F. Smyth, and Z. Xu, “Stability of an optical vortex in a circular nematic cell,” Phys. Rev. A 81, 033816(2010).
[CrossRef]

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

2009 (4)

2008 (3)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198–200 (2008).
[CrossRef] [PubMed]

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[CrossRef]

2007 (7)

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

V. M. Lashkin, “Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose-Einstein condensates,” Phys. Rev. A 75, 043607 (2007).
[CrossRef]

A. Fratalocchi, A. Piccardi, M. Peccianti, and G. Assanto, “Nonlinearly controlled angular momentum of soliton clusters,” Opt. Lett. 32, 1447–1449 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stability of vortex solitons in thermal nonlinear media with cylindrical symmetry,” Opt. Express 15, 9378–9384 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, F. Ye, V. A. Vysloukh, and L. Torner, “Surface waves in decofusing thermal media,” Opt. Lett. 32, 2260–2262(2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Ring surface waves in thermal nonlinear media,” Opt. Express 15, 16216–16221 (2007).
[CrossRef] [PubMed]

2006 (10)

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[CrossRef]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev. E 73, 066605 (2006).
[CrossRef]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

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]

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

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, “Multipole vector solitons in nonlocal nonlinear media,” Opt. Lett. 31, 1483–1485 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett. 31, 2595–2597 (2006).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006).
[CrossRef] [PubMed]

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

2005 (4)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

A. I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005).
[CrossRef] [PubMed]

2004 (2)

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

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

2003 (1)

W. Krolikowski, B. Luther-Davies, and C. Denz, “Photorefractive solitons,” Quantum Electron. 39, 3–12 (2003).
[CrossRef]

2002 (1)

2001 (1)

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[CrossRef]

1992 (2)

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39, 2277–2291 (1992).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[CrossRef] [PubMed]

1988 (1)

1987 (2)

D. Mihalache, G. Stegeman, C. T. Seaton, R. Zanoni, A. D. Boardman, and T. Twardowski, “Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface,” Opt. Lett. 12, 187–189 (1987).
[CrossRef] [PubMed]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164(1987).
[CrossRef] [PubMed]

1985 (1)

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985) [Zh. Eksp. Teor. Fiz. 88, 107–115 (1985), in Russian].

1980 (1)

Aceves, A.

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985) [Zh. Eksp. Teor. Fiz. 88, 107–115 (1985), in Russian].

Alberucci, A.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Alfassi, B.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

Assanto, G.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Fratalocchi, A. Piccardi, M. Peccianti, and G. Assanto, “Nonlinearly controlled angular momentum of soliton clusters,” Opt. Lett. 32, 1447–1449 (2007).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

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

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

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

Bang, O.

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[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]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Belic, M.

W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79, 023804 (2009).
[CrossRef]

Bludov, Yu. V.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Boardman, A. D.

D. Mihalache, G. Stegeman, C. T. Seaton, R. Zanoni, A. D. Boardman, and T. Twardowski, “Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface,” Opt. Lett. 12, 187–189 (1987).
[CrossRef] [PubMed]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164(1987).
[CrossRef] [PubMed]

Briedis, D.

Brzdkiewicz, K.

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198–200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Carretero-González, R.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Christodoulides, D. N.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

Cohen, O.

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

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

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Conti, C.

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

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[CrossRef] [PubMed]

De Luca, A.

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

Denz, C.

W. Krolikowski, B. Luther-Davies, and C. Denz, “Photorefractive solitons,” Quantum Electron. 39, 3–12 (2003).
[CrossRef]

Desyatnikov, A. S.

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]

Dyadyusha, A.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Edmundson, D.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[CrossRef]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005).
[CrossRef] [PubMed]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Fratalocchi, A.

Guo, Qi

Z. W. Shi, H. G. Li, and Qi Guo, “Surface-wave solitons between linear media and nonlocal nonlinear media,” Phys. Rev. A 83, 023817 (2011).
[CrossRef]

Heatley, D. R.

Hoq, Q. E.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Hu, B.

F. Ye, B. Hu, Y. V. Kartashov, and L. Torner, “Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media,” Phys. Rev. A 82, 023822 (2010).
[CrossRef]

Hu, W.

X. K. Ma, Z. J. Yang, D. Q. Lu, and W. Hu, “Interface solitons in thermal nonlinear media,” Phys. Rev. A 83, 053831 (2011).
[CrossRef]

Kaczmarek, M.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Kang, H. Z.

Kartashov, Y. V.

F. Ye, B. Hu, Y. V. Kartashov, and L. Torner, “Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media,” Phys. Rev. A 82, 023822 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Multipole surface solitons in thermal media,” Opt. Lett. 34, 283–285(2009).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stability of vortex solitons in thermal nonlinear media with cylindrical symmetry,” Opt. Express 15, 9378–9384 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, F. Ye, V. A. Vysloukh, and L. Torner, “Surface waves in decofusing thermal media,” Opt. Lett. 32, 2260–2262(2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Ring surface waves in thermal nonlinear media,” Opt. Express 15, 16216–16221 (2007).
[CrossRef] [PubMed]

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

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, “Multipole vector solitons in nonlocal nonlinear media,” Opt. Lett. 31, 1483–1485 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett. 31, 2595–2597 (2006).
[CrossRef] [PubMed]

Kevrekidis, P. G.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Kivshar, Yu. S.

Konotop, V. V.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985) [Zh. Eksp. Teor. Fiz. 88, 107–115 (1985), in Russian].

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198–200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

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]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[CrossRef]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005).
[CrossRef] [PubMed]

W. Krolikowski, B. Luther-Davies, and C. Denz, “Photorefractive solitons,” Quantum Electron. 39, 3–12 (2003).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Kruglov, V. I.

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39, 2277–2291 (1992).
[CrossRef]

Kuzmenko, Y. V.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985) [Zh. Eksp. Teor. Fiz. 88, 107–115 (1985), in Russian].

Lashkin, V. M.

V. M. Lashkin, “Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose-Einstein condensates,” Phys. Rev. A 75, 043607 (2007).
[CrossRef]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Li, H. G.

Z. W. Shi, H. G. Li, and Qi Guo, “Surface-wave solitons between linear media and nonlocal nonlinear media,” Phys. Rev. A 83, 023817 (2011).
[CrossRef]

Liu, S. M.

Logvin, Y. A.

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39, 2277–2291 (1992).
[CrossRef]

Lopez-Aguayo, S.

Lou, C. B.

Lu, D. Q.

X. K. Ma, Z. J. Yang, D. Q. Lu, and W. Hu, “Interface solitons in thermal nonlinear media,” Phys. Rev. A 83, 053831 (2011).
[CrossRef]

Luther-Davies, B.

W. Krolikowski, B. Luther-Davies, and C. Denz, “Photorefractive solitons,” Quantum Electron. 39, 3–12 (2003).
[CrossRef]

Ma, H. H.

Ma, X. K.

X. K. Ma, Z. J. Yang, D. Q. Lu, and W. Hu, “Interface solitons in thermal nonlinear media,” Phys. Rev. A 83, 053831 (2011).
[CrossRef]

Malomed, B. A.

Q. E. Hoq, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, Yu. V. Bludov, and V. V. Konotop, “Surface solitons in three dimensions,” Phys. Rev. E 78, 036605 (2008).
[CrossRef]

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Maradudin, A. A.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164(1987).
[CrossRef] [PubMed]

Mihalache, D.

Minzoni, A. A.

A. A. Minzoni, N. F. Smyth, and Z. Xu, “Stability of an optical vortex in a circular nematic cell,” Phys. Rev. A 81, 033816(2010).
[CrossRef]

Moloney, J. V.

Neshev, D. N.

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]

Peccianti, M.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Fratalocchi, A. Piccardi, M. Peccianti, and G. Assanto, “Nonlinearly controlled angular momentum of soliton clusters,” Opt. Lett. 32, 1447–1449 (2007).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

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

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

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

Petersen, D.

Petersen, D. E.

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]

Piccardi, A.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Fratalocchi, A. Piccardi, M. Peccianti, and G. Assanto, “Nonlinearly controlled angular momentum of soliton clusters,” Opt. Lett. 32, 1447–1449 (2007).
[CrossRef] [PubMed]

Prikhodko, O. O.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Rasmussen, J. J.

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Rotschild, C.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

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

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Seaton, C. T.

Segev, M.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

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

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[CrossRef] [PubMed]

Shi, Z. W.

Z. W. Shi, H. G. Li, and Qi Guo, “Surface-wave solitons between linear media and nonlocal nonlinear media,” Phys. Rev. A 83, 023817 (2011).
[CrossRef]

Skupin, S.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

Smyth, N. F.

A. A. Minzoni, N. F. Smyth, and Z. Xu, “Stability of an optical vortex in a circular nematic cell,” Phys. Rev. A 81, 033816(2010).
[CrossRef]

Stegeman, G.

Stegeman, G. I.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164(1987).
[CrossRef] [PubMed]

Tian, J. G.

Tomlinson, W. J.

Torner, L.

F. Ye, B. Hu, Y. V. Kartashov, and L. Torner, “Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media,” Phys. Rev. A 82, 023822 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Multipole surface solitons in thermal media,” Opt. Lett. 34, 283–285(2009).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stability of vortex solitons in thermal nonlinear media with cylindrical symmetry,” Opt. Express 15, 9378–9384 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Ring surface waves in thermal nonlinear media,” Opt. Express 15, 16216–16221 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, F. Ye, V. A. Vysloukh, and L. Torner, “Surface waves in decofusing thermal media,” Opt. Lett. 32, 2260–2262(2007).
[CrossRef] [PubMed]

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

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett. 31, 2595–2597 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, “Multipole vector solitons in nonlocal nonlinear media,” Opt. Lett. 31, 1483–1485 (2006).
[CrossRef] [PubMed]

Twardowski, T.

D. Mihalache, G. Stegeman, C. T. Seaton, R. Zanoni, A. D. Boardman, and T. Twardowski, “Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface,” Opt. Lett. 12, 187–189 (1987).
[CrossRef] [PubMed]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164(1987).
[CrossRef] [PubMed]

Umeton, C.

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

Varatharajah, P.

Volkov, V. M.

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39, 2277–2291 (1992).
[CrossRef]

Vysloukh, V. A.

Wang, B. H.

Wright, E. M.

P. Varatharajah, A. Aceves, J. V. Moloney, D. R. Heatley, and E. M. Wright, “Stationary nonlinear surface waves and their stability in diffusive Kerr media,” Opt. Lett. 13, 690–692(1988).
[CrossRef] [PubMed]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164(1987).
[CrossRef] [PubMed]

Wyller, J.

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Xu, J. J.

Xu, Z.

Xu, Z. Y.

Z. Y. Xu, “Multipole-mode interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 053827 (2009).
[CrossRef]

Yakimenko, A. I.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev. E 73, 066605 (2006).
[CrossRef]

A. I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Yang, Z. J.

X. K. Ma, Z. J. Yang, D. Q. Lu, and W. Hu, “Interface solitons in thermal nonlinear media,” Phys. Rev. A 83, 053831 (2011).
[CrossRef]

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[CrossRef] [PubMed]

Ye, F.

F. Ye, B. Hu, Y. V. Kartashov, and L. Torner, “Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media,” Phys. Rev. A 82, 023822 (2010).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[CrossRef]

Y. V. Kartashov, F. Ye, V. A. Vysloukh, and L. Torner, “Surface waves in decofusing thermal media,” Opt. Lett. 32, 2260–2262(2007).
[CrossRef] [PubMed]

Zaliznyak, Y. A.

A. I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Zanoni, R.

Zhang, T. H.

Zhong, W. P.

W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79, 023804 (2009).
[CrossRef]

Zhu, B. G.

J. Mod. Opt. (1)

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39, 2277–2291 (1992).
[CrossRef]

Nat. Phys. (1)

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

Nature (1)

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

Opt. Express (4)

Opt. Lett. (13)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198–200 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Multipole surface solitons in thermal media,” Opt. Lett. 34, 283–285(2009).
[CrossRef] [PubMed]

H. Z. Kang, T. H. Zhang, B. H. Wang, C. B. Lou, B. G. Zhu, H. H. Ma, S. M. Liu, J. G. Tian, and J. J. Xu, “(2+1)D surface solitons in virtue of the cooperation of nonlocal and local nonlinearities,” Opt. Lett. 34, 3298–3300 (2009).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Sketches of 2D single surface solitons at the edge of the interface with (a)  ϕ d = 1 , d = 20 , (b)  ϕ d = 7 , d = 20 , and (c)  ϕ d = 7 , d = 5 ; the normalized nonlinear contribution to the refractive index with (d)  ϕ d = 7 , d = 1 , (e)  ϕ d = 7 , d = 20 , and (f)  ϕ d = 7 , d = 5 ; the positions of the peak values y max and FWHM versus (g) the boundary value ϕ d and (h) the nonlocal degree d.

Fig. 2
Fig. 2

(a) Energy flow U versus the propagation constant b with d = 20 and ϕ d = 7 , (b) stable propagation of surface solitons in Fig. 1b with noise σ noise 2 = 0.05 for a distance of 15 diffraction lengths, (c) trajectories of the incident beam with the beam center coordinates y = 1.99 μm . White dashed line indicates interface position. All quantities are plotted in arbitrary dimensionless units.

Fig. 3
Fig. 3

Sketches of 2D single surface solitons at the corner of the interface with (a)  ϕ d = 5 , d = 20 , (b)  ϕ d = 10 , d = 20 , and (c)  ϕ d = 10 , d = 10 ; the positions of the peak values y max and FWHM versus (d) the boundary value ϕ d and (e) the nonlocal degree d.

Fig. 4
Fig. 4

(a) Energy flow U versus the propagation constant b with d = 20 and ϕ d = 10 , (b) stable propagation of surface solitons in Fig. 3b with noise σ noise 2 = 0.05 for a distance of 15 diffraction lengths.

Fig. 5
Fig. 5

Sketch of 2D dipole surface solitons with (a)  ϕ d = 1 , d = 20 , (b)  ϕ d = 10 , d = 20 , and (c)  ϕ d = 10 , d = 10 ; the positions of the peak values y max and FWHM versus (d) the boundary value ϕ d and (e) the nonlocal degree d.

Fig. 6
Fig. 6

(a) Energy flow U versus the propagation constant b with d = 20 and ϕ d = 10 , (b) stable propagation of surface solitons in Fig. 5b with noise σ noise 2 = 0.05 for a distance of 15 diffraction lengths, (c) trajectories of the incident beam with the beam center coordinates y = 1.91 μm .

Equations (8)

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X Y 2 E + 2 E Z 2 + k 0 2 n 2 E = 0 ,
w m 2 X Y 2 Δ n Δ n + n 2 | E | 2 = 0 ,
1 2 2 a + i z a + β 1 a + ϕ a = 0   in a nonlocal medium ,
d 2 2 ϕ ϕ + | a | 2 = 0   in a nonlocal medium ,
1 2 2 a + i z a + β 2 a = 0   in a linear medium ,
1 2 2 u b u + β 1 u + ϕ u = 0   in a nonlocal medium ,
d 2 2 ϕ ϕ + | u | 2 = 0   in a nonlocal medium ,
1 2 2 u b u + β 2 u = 0   in a linear medium .

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