Abstract

Existence and stability of the fundamental and higher-order solitons, which exist in nonlinear media with asymmetric response and periodic linear refractive index modulation, are presented. It is found that the existence of solitons results in the balance between linear refractive index modulation (optical lattices) and nonlinear refractive index induced by incident optical field. In addition, Dynamical properties of fundamental mode solitons are also investigated in detail, and may be applied in the fields of soliton controlling and steering.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  40. W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–850 (2006).
    [Crossref]
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    [Crossref]

2013 (2)

2012 (4)

2010 (1)

2009 (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5–6), 221–267 (2009).
[Crossref]

2008 (2)

Z. Birnbaum and B. A. Malomed, “Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity,” Physica D 237, 3252–3262 (2008).
[Crossref]

R. Yang and X. Wu, “Spatial soliton tunneling, compression and splitting,” Opt. Express 16, 17759–17767 (2008)
[Crossref] [PubMed]

2007 (1)

2006 (2)

Z. Xu, Y. V. Kartashov, and L. Torner, “Gap solitons supported by optical lattices in photorefractive crystals with asymmetric nonlocality,” Opt. Lett. 31, 2027–2029 (2006).
[Crossref] [PubMed]

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–850 (2006).
[Crossref]

2005 (3)

Z. Xu, Y. V. Kartashov, and L. Torner, “Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media,” Opt. Lett. 30, 3171–3173 (2005).
[Crossref] [PubMed]

D. Briedis, D. Edmundson, O. Bang, and W. Krolikowski, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (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, 3904–3907 (2005).
[Crossref]

2004 (6)

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

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

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

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

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

Y. V. Kartashov, V. A. Vusloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[Crossref] [PubMed]

2003 (1)

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

2002 (2)

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable nonlocality of thermal nonlinearity in dye-doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

2001 (2)

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

E. DelRe, A. Ciattoni, and A. J. Agranat, “Anisotropic charge displacement supporting isolated photorefractive optical needles,” Opt. Lett. 26, 908–910 (2001).
[Crossref]

2000 (2)

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).
[Crossref]

M. L. Chiofalo, S. Succi, and M. P. Tosi, “Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm,” Phys. Rev. E 62, 7438–7444 (2000).
[Crossref]

1999 (2)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[Crossref]

1997 (2)

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

1996 (1)

1993 (2)

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

1980 (1)

H. L. Pecseli and J. J. Rasmussen, “Nonlinear electron waves in strongly magnetized plasmas,” Plasma Phys. 22, 421–438 (1980).
[Crossref]

1968 (1)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[Crossref]

Adamski, A.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

Agranat, A. J.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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

Anderson, D. Z.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

Assanto, G.

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

M. Peccianti, C. Conti, G. Assanto, A. De 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]

Bang, O.

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

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

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[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]

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).
[Crossref]

Bao, W.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–850 (2006).
[Crossref]

Birnbaum, Z.

Z. Birnbaum and B. A. Malomed, “Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity,” Physica D 237, 3252–3262 (2008).
[Crossref]

Blasberg, T.

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[Crossref] [PubMed]

Briedis, D.

Cai, C.

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 3904–3907 (2005).
[Crossref]

Chapra, S. C.

S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd ed. (McGraw-Hill, 2012), pp. 621–628.

Chen, L.

Chen, X.

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

Chern, I.-L.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–850 (2006).
[Crossref]

Chi, S.

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

Chiofalo, M. L.

M. L. Chiofalo, S. Succi, and M. P. Tosi, “Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm,” Phys. Rev. E 62, 7438–7444 (2000).
[Crossref]

Christiansen, P. L.

Ciattoni, A.

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 3904–3907 (2005).
[Crossref]

Conti, C.

V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
[Crossref] [PubMed]

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, “Shock wave far-field in ordered and disordered nonlocal media,” Opt. Express 20, 27369–27375 (2012).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De 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, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (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]

Crosignani, B.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Dabby, F. W.

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[Crossref]

Dalfovo, F.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

De Luca, A.

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

Debailleul, M.

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable nonlocality of thermal nonlinearity in dye-doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

DelRe, E.

Di Porto, P.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Dreischuh, A.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[Crossref]

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Edmundson, D.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Relaxation methods,” in Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University, 2001), pp. 753–763.

Folli, V.

Gentilini, S.

Ghofraniha, N.

Giorgini, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

Grasbon, F.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[Crossref]

Guo, Q.

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

Haelterman, M.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

Henninot, J. F.

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable nonlocality of thermal nonlinearity in dye-doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Hu, B.

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

Iturbe Castillo, M. D.

Jeng, C.-C.

Kartashov, Y. V.

Khoo, I. C.

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5–6), 221–267 (2009).
[Crossref]

Kivshar, Y. S.

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

Krolikowski, W.

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

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[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]

Królikowski, W.

Lee, R.-K.

Lin, Y.-Y.

Lobanov, V. E.

Luo, B.

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

Malomed, B. A.

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

Z. Birnbaum and B. A. Malomed, “Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity,” Physica D 237, 3252–3262 (2008).
[Crossref]

Mamaev, A. V.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 3904–3907 (2005).
[Crossref]

Mezentsev, V. K.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Neshev, D.

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Neyts, K.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

Nikolov, N. I.

Paulus, G. G.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[Crossref]

Peccianti, M.

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

M. Peccianti, C. Conti, G. Assanto, A. De 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]

Pecseli, H. L.

H. L. Pecseli and J. J. Rasmussen, “Nonlinear electron waves in strongly magnetized plasmas,” Plasma Phys. 22, 421–438 (1980).
[Crossref]

Pitaevskii, L. P.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Relaxation methods,” in Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University, 2001), pp. 753–763.

Rasmussen, J. J.

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

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[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]

H. L. Pecseli and J. J. Rasmussen, “Nonlinear electron waves in strongly magnetized plasmas,” Plasma Phys. 22, 421–438 (1980).
[Crossref]

Rotschild, C.

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, 3904–3907 (2005).
[Crossref]

Sáchez-Mondragó, J. J.

Saffman, M.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Segev, M.

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, 3904–3907 (2005).
[Crossref]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Shen, M.

Shi, X.

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Stepanov, S.

Stringari, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

Succi, S.

M. L. Chiofalo, S. Succi, and M. P. Tosi, “Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm,” Phys. Rev. E 62, 7438–7444 (2000).
[Crossref]

Suter, D.

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[Crossref] [PubMed]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Relaxation methods,” in Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University, 2001), pp. 753–763.

Tian, Y.

Torner, L.

Tosi, M. P.

M. L. Chiofalo, S. Succi, and M. P. Tosi, “Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm,” Phys. Rev. E 62, 7438–7444 (2000).
[Crossref]

Umeton, C.

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

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Relaxation methods,” in Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University, 2001), pp. 753–763.

Vusloukh, V. A.

Y. V. Kartashov, V. A. Vusloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[Crossref] [PubMed]

Vysloukh, V. A.

Walther, H.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[Crossref]

Wang, Q.

Warenghem, M.

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable nonlocality of thermal nonlinearity in dye-doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Whinnery, J. R.

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[Crossref]

Wu, X.

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[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]

Xie, Y.

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

Xu, D.

Xu, Z.

Yang, R.

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Ye, F.

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Twin-vortex solitons in nonlocal nonlinear media,” Opt. Lett. 35, 628–630 (2010).
[Crossref] [PubMed]

Yi, F.

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

Yin Lim, F.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–850 (2006).
[Crossref]

Zacher, F.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[Crossref]

Zeng, H.

Zhang, H.

Zhao, H.

Zhu, D.

Zozulya, A. A.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

Appl. Phys. Lett. (1)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[Crossref]

J. Comput. Phys. (1)

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–850 (2006).
[Crossref]

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

Mol. Cryst. Liq. Cryst. (1)

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable nonlocality of thermal nonlinearity in dye-doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Nature (1)

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

Opt. Commun. (1)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 233, 211–217 (2004).
[Crossref]

Opt. Express (4)

Opt. Lett. (9)

L. Chen, Q. Wang, M. Shen, H. Zhao, Y.-Y. Lin, C.-C. Jeng, R.-K. Lee, and W. Królikowski, “Nonlocal dark solitons under competing cubic–quintic nonlinearities,” Opt. Lett. 38, 13–15 (2013).
[Crossref] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, “Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media,” Opt. Lett. 30, 3171–3173 (2005).
[Crossref] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, “Gap solitons supported by optical lattices in photorefractive crystals with asymmetric nonlocality,” Opt. Lett. 31, 2027–2029 (2006).
[Crossref] [PubMed]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Twin-vortex solitons in nonlocal nonlinear media,” Opt. Lett. 35, 628–630 (2010).
[Crossref] [PubMed]

V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
[Crossref] [PubMed]

V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton generation by counteracting gain-guiding and self-bending,” Opt. Lett. 37, 4540–4542 (2012).
[Crossref] [PubMed]

M. D. Iturbe Castillo, J. J. Sáchez-Mondragó, and S. Stepanov, “Formation of steady-state cylindrical thermal lenses in dark stripes,” Opt. Lett. 21, 1622–1624 (1996).
[Crossref]

E. DelRe, A. Ciattoni, and A. J. Agranat, “Anisotropic charge displacement supporting isolated photorefractive optical needles,” Opt. Lett. 26, 908–910 (2001).
[Crossref]

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

Phys, Rev. Lett. (1)

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

Phys. Rep. (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5–6), 221–267 (2009).
[Crossref]

Phys. Rev. A (3)

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[Crossref] [PubMed]

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[Crossref]

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

Phys. Rev. E (6)

M. L. Chiofalo, S. Succi, and M. P. Tosi, “Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm,” Phys. Rev. E 62, 7438–7444 (2000).
[Crossref]

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, “Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium,” Phys. Rev. E 60, 6111–6117 (1999).
[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]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

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

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).
[Crossref]

Phys. Rev. Lett. (4)

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, 3904–3907 (2005).
[Crossref]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[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]

Y. V. Kartashov, V. A. Vusloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[Crossref] [PubMed]

Physica D (1)

Z. Birnbaum and B. A. Malomed, “Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity,” Physica D 237, 3252–3262 (2008).
[Crossref]

Plasma Phys. (1)

H. L. Pecseli and J. J. Rasmussen, “Nonlinear electron waves in strongly magnetized plasmas,” Plasma Phys. 22, 421–438 (1980).
[Crossref]

Rev. Mod. Phys. (1)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

Science (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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

S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd ed. (McGraw-Hill, 2012), pp. 621–628.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Relaxation methods,” in Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University, 2001), pp. 753–763.

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Figures (11)

Fig. 1
Fig. 1 Distribution of nonlinear refractive index n induced by light field (red curves) whose amplitude is |q| = ex2 at different nonlocality parameter μ. Blue solid, dotted and dashed curves correspond to (a) μ = 0, −0.2, and 0.2; and (b) μ = 0, 0.1 and 0.2.
Fig. 2
Fig. 2 Profiles (column 1 in rows 1 and 2) and corresponding propagation (column 2 in rows 1 and 2) of fundamental mode solitons at p = 0.5 ((a) and (b) in row 1) and p = 5 ((c) and (d) in row 2). Dependence of (e) peak amplitude and (f) center deviation of the fundamental mode soliton on lattice depth p. Other parameters are U = 2, Ω = 1 and μ = 0.2.
Fig. 3
Fig. 3 Critical lattice depth pcr versus (a) nonlocality parameter μ at U = 2 and (b) energy flow U at μ = 0.2; critical nonlocality parameter μcr versus (c) energy flow U at p = 1 and (d) lattice depth p at U = 2; critical energy flow Ucr versus (e) nonlocality parameter μ at p = 1 and (f) lattice depth p at μ = 0.2. The other parameter is Ω = 1.
Fig. 4
Fig. 4 Profiles (column 1 in rows 1 and 2) and corresponding propagation (column 2 in rows 1 and 2) of fundamental mode solitons at μ = 0.1 ((a) and (b) in row 1) and μ = 0.3 ((c) and (d) in row 2). Dependence of (e) peak amplitude and (f) center deviation of the fundamental mode soliton on lattice depth μ. Other parameters are U = 2, Ω = 1 and p = 2.
Fig. 5
Fig. 5 Profiles (column 1 in rows 1 and 2) and corresponding propagation (column 2 in rows 1 and 2) of fundamental mode solitons at U = 1 ((a) and (b) in row 1) and U = 3 ((c) and (d) in row 2). Dependence of (e) peak amplitude and (f) center deviation of the fundamental mode soliton on energy flow U. Other parameters are μ = 0.2, Ω = 1 and p = 2.
Fig. 6
Fig. 6 Propagation against white noise whose maximal value is 0.01 of fundamental solitons at (a) μ = 0.1 and (b) μ = 0.3 for p = 1 and U = 2; (c) p = 0.38 and (d) p = 5 for μ = 0.2 and U = 2; (e) U = 1 and (f) U = 2.5 for μ = 0.2 and p = 1. The other parameter is Ω = 1.
Fig. 7
Fig. 7 Profiles of two-pole mode solitons (red lines) and optical lattices R(x) (blue lines) in the system (4) at (a) μ = 0.1, (b) μ = 0.35 for b = 1 and p = 1; (c) b = 0.7, (d) b = 2.1 for μ = 0.1 and p = 1; (e) p = 1, (f) p = 2.9 for μ = 0.1 and b = 2. The other parameter is Ω = 1.
Fig. 8
Fig. 8 Critical lattice depth pcr for the dipole-mode soliton versus (a) propagation constant b at μ = 0.1 and (b) nonlocality parameter μ at b = 1; critical nonlocality parameter μcr for the dipole-mode soliton versus (c) propagation constant b at p = 1 and (d) lattice depth p at b = 1; critical propagation constant bcr for the dipole-mode soliton versus (e) lattice depth p at μ = 0.1 and (f) nonlocality parameter μ at p = 1. The other parameter is Ω = 1.
Fig. 9
Fig. 9 Energy flow U and (b) imaginary part of the perturbation growth rate for the dipole-mode soliton versus nonlocality parameter μ at b = 1 and p = 1. (c) Energy flow U and (d) imaginary part of the perturbation growth rate for the dipole-mode soliton versus a propagation constant b at μ = 0.1 and p = 1. (e) Energy flow U and (f) imaginary part of the perturbation growth rate for the dipole-mode soliton versus lattice depth p at b = 2 and μ = 0.1. The other parameter is Ω = 1.
Fig. 10
Fig. 10 Typical evolvement diagrams of the fundamental mode soliton in the system described by Eqs. (7) and (8) for different lattice depthes (a) p0 = 1 and (b) p0 = 2 at U = 2 and μ = 0.2; Typical evolvement diagrams of the fundamental mode soliton in the system described by Eqs. (7) and (8) for different nonlocality parameters (c) μ = 0.05 and (d) μ = 0.15 at U = 2 and p0 = 1; Typical evolvement diagrams of the fundamental mode soliton in the system described by Eqs. (7) and (8) for different energy flows (e) U = 1.8 and (f) U = 2.1 at μ = 0.2 and p0 = 1; Other parameter is Ω = 1. Dashed line, border between p = p0 and p = 0.
Fig. 11
Fig. 11 (a) Center shift Δ and (b) escape angle α versus lattice depth p at μ = 0.2 and U = 2; (c) center shift Δ and (d) escape angle α versus nonlocality parameter μ at p = 1 and U = 2; (e) center shift Δ and (f) escape angle α versus energy flow U at p = 1 and μ = 0.2. Other parameters is Ω = 1.

Equations (8)

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i q z + 1 2 2 q x 2 + n q + p R ( x ) q = 0 .
n ( x , z ) = G ( x x ) I ( x , z ) d x .
n ( x , z ) = | q ( x , z ) | 2 μ x | q ( x , z ) | 2 .
i q z + 1 2 2 q x 2 + | q | 2 q μ q x | q | 2 + p R ( x ) q = 0 ,
λ u = 1 2 2 u x 2 + w 2 ( 2 u + v ) 2 μ w u w x + p R u b u ,
λ v = 1 2 2 v x 2 w 2 ( 2 v + u ) + 2 μ w v w x p R v + b v .
i q z + 1 2 2 q x 2 + | q | 2 q μ q x | q | 2 + p ( z ) R ( x ) q = 0 ,
p ( z ) = p 0 , for z 20 ; p ( z ) = 0 , for z > 20 .

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