Abstract

We investigate the dynamics of spatial optical solitons launched in a medium with a finite perturbation of the refractive index. For longitudinally short perturbations of super-Gaussian transverse profile, as the input power varies we observe a transition from a wave-like behavior where solitons break up into multiple fringes to a particle-like behavior where solitons acquire a transverse velocity retaining their shape. For longitudinally long perturbations with an attractive potential solitons get trapped inside the well and propagate with transverse periodic oscillations, resulting in an efficient power-dependent angular steering or deflection. Using the Ehrenfest theorem we derive analytical expressions for soliton trajectory, and achieve excellent agreement between theory and numerical simulations for large powers, that is, narrow solitons.

© 2013 OSA

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  1. A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
    [CrossRef] [PubMed]
  2. C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett.107, 183902 (2011).
    [CrossRef] [PubMed]
  3. I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys.85, 299–366 (2013).
    [CrossRef]
  4. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science286, 1518–1523 (1999).
    [CrossRef] [PubMed]
  5. A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. i. equivalent-particle theory for a single interface,” Phys. Rev. A39, 1809–1827 (1989).
    [CrossRef] [PubMed]
  6. A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. ii. multiple-particle and multiple-interface extensions,” Phys. Rev. A39, 1828–1840 (1989).
    [CrossRef] [PubMed]
  7. L. Friedrich, G. I. Stegeman, P. Millar, C. J. Hamilton, and J. S. Aitchison, “Dynamic, electronically controlled angle steering of spatial solitons in AlGaAs slab waveguides,” Opt. Lett.23, 1438–1440 (1998).
    [CrossRef]
  8. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
    [CrossRef]
  9. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett.98, 213901 (2007).
    [CrossRef] [PubMed]
  10. M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
    [CrossRef] [PubMed]
  11. A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
    [CrossRef]
  12. A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
    [CrossRef] [PubMed]
  13. Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
    [CrossRef] [PubMed]
  14. A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett.32, 2795–2797 (2007).
    [CrossRef] [PubMed]
  15. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
    [CrossRef] [PubMed]
  16. A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett.35, 390–392 (2010).
    [CrossRef] [PubMed]
  17. C. P. Jisha, A. Alberucci, R.-K. Lee, and G. Assanto, “Optical solitons and wave-particle duality,” Opt. Lett.36, 1848–1850 (2011).
    [CrossRef] [PubMed]
  18. A. Alberucci, G. Assanto, A. A. Minzoni, and N. F. Smyth, “Scattering of reorientational optical solitary waves at dielectric perturbations,” Phys. Rev. A85, 013804 (2012).
    [CrossRef]
  19. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
    [CrossRef]
  20. 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]
  21. V. A. Brazhnyi, C. P. Jisha, and A. S. Rodrigues, “Interaction of discrete nonlinear Schrodinger solitons with a ¨ linear lattice impurity,” Phys. Rev. A87, 013609 (2013).
    [CrossRef]
  22. R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett.28, 834–836 (2003).
    [CrossRef] [PubMed]
  23. A. Fratalocchi and G. Assanto, “Symmetry-breaking instabilities in perturbed optical lattices: Nonlinear nonreciprocity and macroscopic self-trapping,” Phys. Rev. A75, 063828 (2007).
    [CrossRef]
  24. V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
    [CrossRef]
  25. L. Morales-Molina and R. A. Vicencio, “Trapping of discrete solitons by defects in nonlinear waveguide arrays,” Opt. Lett.31, 966–968 (2006).
    [CrossRef] [PubMed]
  26. J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, “Motion of discrete solitons assisted by nonlinearity management,” Phys. Rev. E71, 066614 (2005).
    [CrossRef]
  27. G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
    [CrossRef] [PubMed]
  28. K. Forinash, M. Peyrard, and B. Malomed, “Interaction of discrete breathers with impurity modes,” Phys. Rev. E49, 3400–3411 (1994).
    [CrossRef]
  29. I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
    [CrossRef]
  30. A. Alberucci, C. P. Jisha, R.-K. Lee, and G. Assanto, “Soliton self-routing in a finite photonic potential,” Opt. Lett.38, 2071–2073 (2013).
    [CrossRef]
  31. X. D. Cao and B. A. Malomed, “Soliton-defect collisions in the nonlinear Schrödinger equation,” Phys. Lett. A206, 177–182 (1995).
    [CrossRef]
  32. P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping bragg solitons by a pair of defects,” Phys. Rev. E71, 066601 (2005).
    [CrossRef]
  33. S. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial solitons,” Opt. Comm.139, 193–198 (1997).
    [CrossRef]
  34. L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B84, 465–469 (2006).
    [CrossRef]
  35. Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).
  36. J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).
  37. Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
    [CrossRef]
  38. V. Serkin, A. Hasegawa, and T. Belyaeva, “Geiger–nuttall law for Schrödinger solitons,” J. Mod. Opt.60, 116–127 (2013).
    [CrossRef]
  39. G. Assanto, A. A. Minzoni, and N. F. Smyth, “Nematicons escaping a wide trapping potential: modulation theory,” Phys. Rev. A79, 033837 (2009).
    [CrossRef]
  40. M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep.516, 147–208 (2012).
    [CrossRef]

2013

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys.85, 299–366 (2013).
[CrossRef]

V. A. Brazhnyi, C. P. Jisha, and A. S. Rodrigues, “Interaction of discrete nonlinear Schrodinger solitons with a ¨ linear lattice impurity,” Phys. Rev. A87, 013609 (2013).
[CrossRef]

A. Alberucci, C. P. Jisha, R.-K. Lee, and G. Assanto, “Soliton self-routing in a finite photonic potential,” Opt. Lett.38, 2071–2073 (2013).
[CrossRef]

V. Serkin, A. Hasegawa, and T. Belyaeva, “Geiger–nuttall law for Schrödinger solitons,” J. Mod. Opt.60, 116–127 (2013).
[CrossRef]

2012

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
[CrossRef]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep.516, 147–208 (2012).
[CrossRef]

A. Alberucci, G. Assanto, A. A. Minzoni, and N. F. Smyth, “Scattering of reorientational optical solitary waves at dielectric perturbations,” Phys. Rev. A85, 013804 (2012).
[CrossRef]

2011

C. P. Jisha, A. Alberucci, R.-K. Lee, and G. Assanto, “Optical solitons and wave-particle duality,” Opt. Lett.36, 1848–1850 (2011).
[CrossRef] [PubMed]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett.107, 183902 (2011).
[CrossRef] [PubMed]

2010

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett.35, 390–392 (2010).
[CrossRef] [PubMed]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

2009

G. Assanto, A. A. Minzoni, and N. F. Smyth, “Nematicons escaping a wide trapping potential: modulation theory,” Phys. Rev. A79, 033837 (2009).
[CrossRef]

2008

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]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
[CrossRef] [PubMed]

A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
[CrossRef]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[CrossRef] [PubMed]

2007

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett.32, 2795–2797 (2007).
[CrossRef] [PubMed]

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

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
[CrossRef] [PubMed]

A. Fratalocchi and G. Assanto, “Symmetry-breaking instabilities in perturbed optical lattices: Nonlinear nonreciprocity and macroscopic self-trapping,” Phys. Rev. A75, 063828 (2007).
[CrossRef]

2006

L. Morales-Molina and R. A. Vicencio, “Trapping of discrete solitons by defects in nonlinear waveguide arrays,” Opt. Lett.31, 966–968 (2006).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
[CrossRef]

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B84, 465–469 (2006).
[CrossRef]

2005

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, “Motion of discrete solitons assisted by nonlinearity management,” Phys. Rev. E71, 066614 (2005).
[CrossRef]

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping bragg solitons by a pair of defects,” Phys. Rev. E71, 066601 (2005).
[CrossRef]

2003

1999

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science286, 1518–1523 (1999).
[CrossRef] [PubMed]

1998

1997

S. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial solitons,” Opt. Comm.139, 193–198 (1997).
[CrossRef]

1996

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

1995

X. D. Cao and B. A. Malomed, “Soliton-defect collisions in the nonlinear Schrödinger equation,” Phys. Lett. A206, 177–182 (1995).
[CrossRef]

1994

K. Forinash, M. Peyrard, and B. Malomed, “Interaction of discrete breathers with impurity modes,” Phys. Rev. E49, 3400–3411 (1994).
[CrossRef]

1989

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. i. equivalent-particle theory for a single interface,” Phys. Rev. A39, 1809–1827 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. ii. multiple-particle and multiple-interface extensions,” Phys. Rev. A39, 1828–1840 (1989).
[CrossRef] [PubMed]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. i. equivalent-particle theory for a single interface,” Phys. Rev. A39, 1809–1827 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. ii. multiple-particle and multiple-interface extensions,” Phys. Rev. A39, 1828–1840 (1989).
[CrossRef] [PubMed]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

Aimez, V.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

Aitchison, J. S.

Alberucci, A.

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]

Amo, A.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Ares, R.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

Assanto, G.

A. Alberucci, C. P. Jisha, R.-K. Lee, and G. Assanto, “Soliton self-routing in a finite photonic potential,” Opt. Lett.38, 2071–2073 (2013).
[CrossRef]

A. Alberucci, G. Assanto, A. A. Minzoni, and N. F. Smyth, “Scattering of reorientational optical solitary waves at dielectric perturbations,” Phys. Rev. A85, 013804 (2012).
[CrossRef]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep.516, 147–208 (2012).
[CrossRef]

C. P. Jisha, A. Alberucci, R.-K. Lee, and G. Assanto, “Optical solitons and wave-particle duality,” Opt. Lett.36, 1848–1850 (2011).
[CrossRef] [PubMed]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett.35, 390–392 (2010).
[CrossRef] [PubMed]

G. Assanto, A. A. Minzoni, and N. F. Smyth, “Nematicons escaping a wide trapping potential: modulation theory,” Phys. Rev. A79, 033837 (2009).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
[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]

A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
[CrossRef]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett.32, 2795–2797 (2007).
[CrossRef] [PubMed]

A. Fratalocchi and G. Assanto, “Symmetry-breaking instabilities in perturbed optical lattices: Nonlinear nonreciprocity and macroscopic self-trapping,” Phys. Rev. A75, 063828 (2007).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
[CrossRef]

Bar-Ad, S.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

Barak, A.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[CrossRef] [PubMed]

Belyaeva, T.

V. Serkin, A. Hasegawa, and T. Belyaeva, “Geiger–nuttall law for Schrödinger solitons,” J. Mod. Opt.60, 116–127 (2013).
[CrossRef]

Bertolotti, M.

S. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial solitons,” Opt. Comm.139, 193–198 (1997).
[CrossRef]

Bishop, A. R.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[CrossRef]

Bortolozzo, U.

Bramati, A.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Brazhnyi, V. A.

V. A. Brazhnyi, C. P. Jisha, and A. S. Rodrigues, “Interaction of discrete nonlinear Schrodinger solitons with a ¨ linear lattice impurity,” Phys. Rev. A87, 013609 (2013).
[CrossRef]

Cai, D.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[CrossRef]

Cao, X. D.

X. D. Cao and B. A. Malomed, “Soliton-defect collisions in the nonlinear Schrödinger equation,” Phys. Lett. A206, 177–182 (1995).
[CrossRef]

Carusotto, I.

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys.85, 299–366 (2013).
[CrossRef]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Chen, P. Y. P.

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping bragg solitons by a pair of defects,” Phys. Rev. E71, 066601 (2005).
[CrossRef]

Christodoulides, D. N.

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

Chu, P. L.

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping bragg solitons by a pair of defects,” Phys. Rev. E71, 066601 (2005).
[CrossRef]

Cisneros, L. A.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Ciuti, C.

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys.85, 299–366 (2013).
[CrossRef]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Cuevas, J.

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, “Motion of discrete solitons assisted by nonlinearity management,” Phys. Rev. E71, 066614 (2005).
[CrossRef]

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

Dong, L. W.

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B84, 465–469 (2006).
[CrossRef]

Dyadyusha, A.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
[CrossRef]

Eisenberg, H. S.

Forinash, K.

K. Forinash, M. Peyrard, and B. Malomed, “Interaction of discrete breathers with impurity modes,” Phys. Rev. E49, 3400–3411 (1994).
[CrossRef]

Fratalocchi, A.

A. Fratalocchi and G. Assanto, “Symmetry-breaking instabilities in perturbed optical lattices: Nonlinear nonreciprocity and macroscopic self-trapping,” Phys. Rev. A75, 063828 (2007).
[CrossRef]

Friedrich, L.

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
[CrossRef]

Garzia, S.

S. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial solitons,” Opt. Comm.139, 193–198 (1997).
[CrossRef]

Giacobino, E.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Grønbech-Jensen, N.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[CrossRef]

Hamilton, C. J.

Hasegawa, A.

V. Serkin, A. Hasegawa, and T. Belyaeva, “Geiger–nuttall law for Schrödinger solitons,” J. Mod. Opt.60, 116–127 (2013).
[CrossRef]

Hivet, R.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Houdr, R.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Jisha, C. P.

A. Alberucci, C. P. Jisha, R.-K. Lee, and G. Assanto, “Soliton self-routing in a finite photonic potential,” Opt. Lett.38, 2071–2073 (2013).
[CrossRef]

V. A. Brazhnyi, C. P. Jisha, and A. S. Rodrigues, “Interaction of discrete nonlinear Schrodinger solitons with a ¨ linear lattice impurity,” Phys. Rev. A87, 013609 (2013).
[CrossRef]

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett.107, 183902 (2011).
[CrossRef] [PubMed]

C. P. Jisha, A. Alberucci, R.-K. Lee, and G. Assanto, “Optical solitons and wave-particle duality,” Opt. Lett.36, 1848–1850 (2011).
[CrossRef] [PubMed]

Kaczmarek, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
[CrossRef]

Kevrekidis, P. G.

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, “Motion of discrete solitons assisted by nonlinearity management,” Phys. Rev. E71, 066614 (2005).
[CrossRef]

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

Konotop, V. V.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[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]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

Lee, R.-K.

Lee, T.-D.

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett.107, 183902 (2011).
[CrossRef] [PubMed]

Lemnager, G.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Lin, Y.

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett.107, 183902 (2011).
[CrossRef] [PubMed]

Linzon, Y.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
[CrossRef]

Lucchetti, L.

A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
[CrossRef]

Malomed, B.

K. Forinash, M. Peyrard, and B. Malomed, “Interaction of discrete breathers with impurity modes,” Phys. Rev. E49, 3400–3411 (1994).
[CrossRef]

Malomed, B. A.

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, “Motion of discrete solitons assisted by nonlinearity management,” Phys. Rev. E71, 066614 (2005).
[CrossRef]

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping bragg solitons by a pair of defects,” Phys. Rev. E71, 066601 (2005).
[CrossRef]

X. D. Cao and B. A. Malomed, “Soliton-defect collisions in the nonlinear Schrödinger equation,” Phys. Lett. A206, 177–182 (1995).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

Mandelik, D.

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]

Millar, P.

Minzoni, A. A.

A. Alberucci, G. Assanto, A. A. Minzoni, and N. F. Smyth, “Scattering of reorientational optical solitary waves at dielectric perturbations,” Phys. Rev. A85, 013804 (2012).
[CrossRef]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

G. Assanto, A. A. Minzoni, and N. F. Smyth, “Nematicons escaping a wide trapping potential: modulation theory,” Phys. Rev. A79, 033837 (2009).
[CrossRef]

Modotto, D.

Moloney, J. V.

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. ii. multiple-particle and multiple-interface extensions,” Phys. Rev. A39, 1828–1840 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. i. equivalent-particle theory for a single interface,” Phys. Rev. A39, 1809–1827 (1989).
[CrossRef] [PubMed]

Morales-Molina, L.

Morandotti, R.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett.28, 834–836 (2003).
[CrossRef] [PubMed]

Muschall, R.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. i. equivalent-particle theory for a single interface,” Phys. Rev. A39, 1809–1827 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. ii. multiple-particle and multiple-interface extensions,” Phys. Rev. A39, 1828–1840 (1989).
[CrossRef] [PubMed]

Peccianti, M.

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep.516, 147–208 (2012).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett.32, 2795–2797 (2007).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
[CrossRef]

Peleg, O.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[CrossRef] [PubMed]

Peschel, T.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

Peyrard, M.

K. Forinash, M. Peyrard, and B. Malomed, “Interaction of discrete breathers with impurity modes,” Phys. Rev. E49, 3400–3411 (1994).
[CrossRef]

Piccardi, A.

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett.35, 390–392 (2010).
[CrossRef] [PubMed]

A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
[CrossRef]

Pigeon, S.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Pisanello, F.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Residori, S.

Rodrigues, A. S.

V. A. Brazhnyi, C. P. Jisha, and A. S. Rodrigues, “Interaction of discrete nonlinear Schrodinger solitons with a ¨ linear lattice impurity,” Phys. Rev. A87, 013609 (2013).
[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]

Sakurai, J. J.

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).

Sala, V. G.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Salerno, M.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[CrossRef]

Sanvitto, D.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Segev, M.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[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]

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

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science286, 1518–1523 (1999).
[CrossRef] [PubMed]

Serkin, V.

V. Serkin, A. Hasegawa, and T. Belyaeva, “Geiger–nuttall law for Schrödinger solitons,” J. Mod. Opt.60, 116–127 (2013).
[CrossRef]

Sibilia, C.

S. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial solitons,” Opt. Comm.139, 193–198 (1997).
[CrossRef]

Silberberg, Y.

Simoni, F.

A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
[CrossRef]

Skuse, B. D.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Smyth, N. F.

A. Alberucci, G. Assanto, A. A. Minzoni, and N. F. Smyth, “Scattering of reorientational optical solitary waves at dielectric perturbations,” Phys. Rev. A85, 013804 (2012).
[CrossRef]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

G. Assanto, A. A. Minzoni, and N. F. Smyth, “Nematicons escaping a wide trapping potential: modulation theory,” Phys. Rev. A79, 033837 (2009).
[CrossRef]

Soffer, A.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[CrossRef] [PubMed]

Sorel, M.

Stanley, C. R.

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]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science286, 1518–1523 (1999).
[CrossRef] [PubMed]

L. Friedrich, G. I. Stegeman, P. Millar, C. J. Hamilton, and J. S. Aitchison, “Dynamic, electronically controlled angle steering of spatial solitons in AlGaAs slab waveguides,” Opt. Lett.23, 1438–1440 (1998).
[CrossRef]

Stucchio, C.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[CrossRef] [PubMed]

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
[CrossRef]

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

Vicencio, R. A.

Volatier, M.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

Wang, H.

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B84, 465–469 (2006).
[CrossRef]

Worthy, A. L.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Appl. Phys. B

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B84, 465–469 (2006).
[CrossRef]

Appl. Phys. Lett.

A. Piccardi, G. Assanto, L. Lucchetti, and F. Simoni, “All-optical steering of soliton waveguides in dye-doped liquid crystals,” Appl. Phys. Lett.93, 171104 (2008).
[CrossRef]

J. Mod. Opt.

V. Serkin, A. Hasegawa, and T. Belyaeva, “Geiger–nuttall law for Schrödinger solitons,” J. Mod. Opt.60, 116–127 (2013).
[CrossRef]

Nat. Phys.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys.2, 737–742 (2006).
[CrossRef]

Opt. Comm.

S. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial solitons,” Opt. Comm.139, 193–198 (1997).
[CrossRef]

Opt. Lett.

Phys. Lett. A

X. D. Cao and B. A. Malomed, “Soliton-defect collisions in the nonlinear Schrödinger equation,” Phys. Lett. A206, 177–182 (1995).
[CrossRef]

Phys. Rep.

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]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep.516, 147–208 (2012).
[CrossRef]

Phys. Rev. A

V. A. Brazhnyi, C. P. Jisha, and A. S. Rodrigues, “Interaction of discrete nonlinear Schrodinger solitons with a ¨ linear lattice impurity,” Phys. Rev. A87, 013609 (2013).
[CrossRef]

A. Fratalocchi and G. Assanto, “Symmetry-breaking instabilities in perturbed optical lattices: Nonlinear nonreciprocity and macroscopic self-trapping,” Phys. Rev. A75, 063828 (2007).
[CrossRef]

G. Assanto, A. A. Minzoni, and N. F. Smyth, “Nematicons escaping a wide trapping potential: modulation theory,” Phys. Rev. A79, 033837 (2009).
[CrossRef]

A. Alberucci, G. Assanto, A. A. Minzoni, and N. F. Smyth, “Scattering of reorientational optical solitary waves at dielectric perturbations,” Phys. Rev. A85, 013804 (2012).
[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. i. equivalent-particle theory for a single interface,” Phys. Rev. A39, 1809–1827 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. ii. multiple-particle and multiple-interface extensions,” Phys. Rev. A39, 1828–1840 (1989).
[CrossRef] [PubMed]

Phys. Rev. E

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E53, 1172–1189 (1996).
[CrossRef]

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping bragg solitons by a pair of defects,” Phys. Rev. E71, 066601 (2005).
[CrossRef]

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system,” Phys. Rev. E53, 6476–6485 (1996).
[CrossRef]

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, “Motion of discrete solitons assisted by nonlinearity management,” Phys. Rev. E71, 066614 (2005).
[CrossRef]

K. Forinash, M. Peyrard, and B. Malomed, “Interaction of discrete breathers with impurity modes,” Phys. Rev. E49, 3400–3411 (1994).
[CrossRef]

Phys. Rev. Lett.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett.101, 153902 (2008).
[CrossRef] [PubMed]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett.100, 153901 (2008).
[CrossRef] [PubMed]

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, “Nonlinear scattering and trapping by local photonic potentials,” Phys. Rev. Lett.99, 133901 (2007).
[CrossRef] [PubMed]

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett.107, 183902 (2011).
[CrossRef] [PubMed]

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

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Non-specular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett.98, 113902 (2007).
[CrossRef] [PubMed]

Physics Reports

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports518, 1–79 (2012).
[CrossRef]

Rev. Mod. Phys.

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys.85, 299–366 (2013).
[CrossRef]

Science

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science286, 1518–1523 (1999).
[CrossRef] [PubMed]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

Other

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).

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Figures (13)

Fig. 1
Fig. 1

Sketch of the soliton interaction (blue arrow) with a finite linear photonic potential (box) of width wp across x and of length Lpd along z (units in the laboratory frame). A soliton is launched along the axis z in (x = 〈x0〉, z = 0). After the interaction the soliton emerges with a finite angle θ depending on both beam power and input location. In the sketched example the defect has a positive index increase (darker area) and is able to transversely trap the beam.

Fig. 2
Fig. 2

Force experienced by the input beam for the case of a repulsive potential and various l values. The magnitude of the force increases with l. The maximum force becomes increasingly localized near 〈X〉 = 1 due to the flattening of the index well with l.

Fig. 3
Fig. 3

(a) Refractive index well for l = 1, 2, 8. The index well flattens with l (top to bottom). (b) Corresponding refractive index gradient (top to bottom in the left half). (c) Comparison of force as given by Eq. (6) (symbols) and by Eq. (7) (solid lines) for l = 2, u0 = 1, 2 and 10 (bottom to top).

Fig. 4
Fig. 4

Beam intensity evolution for l = 1 (top), l = 4 (middle) and l = 8 (bottom) for various u0. Here d = 0.5, Z0 = 2.25, Δ = −1 and the beam is launched at 〈X0 = 0.

Fig. 5
Fig. 5

Beam intensity evolution for l = 1 (top), l = 4 (middle) and l = 8 (bottom) for various u0. Here d = 0.5, Z0 = 2.25, Δ = −1 and the beam is launched at 〈X0 = 1.

Fig. 6
Fig. 6

Soliton deflection versus soliton amplitude u0 for 〈X0 = 1 (blue), 1.5 (black) and 2 (red) for l = 1 (dashed line (○)) and 4 (dashed-dotted line (⋄)). Here Δ = −3 and d = 0.5. Symbols correspond to numerical result and solid line corresponds to analytical which overlaps for large u0.

Fig. 7
Fig. 7

Intensity evolution for various u0, d and Δ = −1. The white rectangles represent the potential.

Fig. 8
Fig. 8

Soliton deflection versus power for l = 2, 〈X0 = 1, Δ = −1 and d = 0.5 (⋄), 1 (□) and 10 (*) computed via Eq. (7). Symbols are numerical results and the lines corresponds to analytical predictions.

Fig. 9
Fig. 9

Beam intensity evolution for a defect with d = 15, l = 2, Δ = 1 when the beam is launched at 〈X0 = 0, 0.5, 1 for u0 varying from 4 to 12, as marked.

Fig. 10
Fig. 10

(a) Soliton trajectory and (b) corresponding beam radius for d = 0.5 and Δ = 1. (c) Variation in output angle with u0 for d = 10 and Δ = 1 (○), 2 (+) and 3 (X) with the corresponding trajectories plotted in (d–f). In panels (a,d,e,f) solitons are launched in 〈X0 = 1 with l = 2 and u0 = 8 (*),12 (□) and 20 (⋄). Symbols correspond to numerical and lines correspond to theoretical predictions.

Fig. 11
Fig. 11

(a) Breather soliton properties: oscillation period (*), amplitude (□) and mean radius (○) versus inverse amplitude 1/u0. (b–c) Theoretical (solid line) and numerical (symbols) trajectories for breather solitons of widths 0.05 (blue diamond) and 0.1 (black circles) launched in (b) 〈X0 = 0.5 and (c) 〈X0 = 1.0. (d) Evolution profile of breather soliton in propagation for 〈X0 = 0.5 for initial radius 0.3 showing energy escape. The theoretical results here are derived by solving jointly Eq. (7) and Eq. (8). Here Δ = 1.

Fig. 12
Fig. 12

Trajectories of breathers with power u0 = 20 (blue), 14.29 (green), 12.5 (black) and 10.0 (red) launched in 〈X0 = 0.5 for defects of length (a) d = 10 and (b) d = 11. (c) Corresponding velocities (symbols) and comparison with theoretical results (lines). (d) Propagation of a breather of width 0.05 in an infinitely long potential.

Fig. 13
Fig. 13

Comparison of velocity variation of fundamental (dashed lines) and breather (solid lines) solitons versus amplitude for various defect lengths (along columns) when launched in 〈X0 = 0.5 (top) and 〈X0 = 1 (bottom).

Equations (8)

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( 2 + k 0 2 n 2 ) E ( x , y , z ) = 0 ,
2 i k 0 n 0 A z + 2 A x 2 + 2 k 0 2 n 0 n L A + 2 k 0 2 n 0 n 2 | A | 2 A = 0 ,
i u z + 1 2 2 u X 2 + | u | 2 u p V eff ( X , Z ) u = 0 ,
d 2 X d Z 2 = p ψ V eff X d X ,
d 2 X d Z 2 = p ψ ( V eff X + 2 V eff X 2 ( X X ) + 1 2 3 V eff X 3 ( X X ) 2 + ) | X = X d X ,
d 2 X d Z 2 = p m = 0 W m ( X ) ξ m ψ
d 2 X d Z 2 = p ( W 0 + W 2 ξ 2 ) .
u ( X , Z ) = 4 u 0 e i u 0 2 Z 2 cosh ( 3 u 0 X ) + 3 cosh ( u 0 X ) e 4 i u 0 2 Z cosh ( 4 u 0 X ) + 4 cosh ( 2 u 0 X ) + 3 cos ( 4 u 0 2 Z ) .

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