Abstract

Two families of gap and twisted surface lattice solitons in diffusive nonlinear periodic media with spatially modulated nonlinearity are reported. It is shown that the existence and stability of such solitons are extremely spatially modulated nonlinearity sensitive. For self-focusing nonlinearity, gap surface solitons belonging to the semi-infinite gap are stable in whole existence domain, twisted surface solitons are also linearly stable in low modulated strength region and a very narrow unstable region near the upper cutoff appears in high modulated strength region. In the self-defocusing case, surface gap solitons belonging to the first gap can propagate stably in whole existence domain except for an extremely narrow region close to the Bloch band, twisted solitons belonging to this gap are unstable in the entire existence domain.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
    [Crossref] [PubMed]
  9. 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(21), 213904 (2005).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  12. K. Zhan, C. Hou, and Y. Du, “Self-deflection of steady-state bright spatial soliton in biased centrosymmetric photorefractive crystals,” Opt. Commun. 283(1), 138–141 (2010).
    [Crossref]
  13. H. Zhang, F. Xu, D. Zhu, L. Zhang, D. Xu, and Y. Tian, “Soliton controlling and steering in asymmetric nonlocal media with optical lattices,” Opt. Express 22(1), 995–1007 (2014).
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    [Crossref] [PubMed]
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  20. H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
    [Crossref]
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  23. J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
    [Crossref]
  24. A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear Localized Waves in a Periodic Medium,” Phys. Rev. Lett. 87(8), 083901 (2001).
    [Crossref] [PubMed]
  25. M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
    [Crossref]

2015 (1)

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

2014 (2)

2012 (1)

H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
[Crossref]

2011 (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–305 (2011).
[Crossref]

2010 (2)

K. Zhan, C. Hou, and Y. Du, “Self-deflection of steady-state bright spatial soliton in biased centrosymmetric photorefractive crystals,” Opt. Commun. 283(1), 138–141 (2010).
[Crossref]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

2008 (3)

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).
[Crossref] [PubMed]

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface lattice solitons in diffusive nonlinear media,” Opt. Lett. 33(8), 773–775 (2008).
[Crossref] [PubMed]

2007 (2)

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[Crossref]

M. I. Carvalho, M. Facão, and D. N. Christodoulides, “Self-bending of dark and gray photorefractive solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016602 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (3)

F. Chen, M. Stepić, C. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (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(21), 213904 (2005).
[Crossref] [PubMed]

2004 (1)

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

2003 (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

2001 (1)

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear Localized Waves in a Periodic Medium,” Phys. Rev. Lett. 87(8), 083901 (2001).
[Crossref] [PubMed]

1998 (1)

1996 (1)

1995 (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120(5-6), 311–315 (1995).
[Crossref]

1973 (1)

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[Crossref]

Alexander, T. J.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

Bartal, G.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

Bishop, A. R.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

Buljan, H.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

Carmon, T.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (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(21), 213904 (2005).
[Crossref] [PubMed]

Carvalho, M. I.

M. I. Carvalho, M. Facão, and D. N. Christodoulides, “Self-bending of dark and gray photorefractive solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016602 (2007).
[Crossref] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120(5-6), 311–315 (1995).
[Crossref]

Chen, F.

Chen, Z.

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[Crossref] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

Christodoulides, D. N.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).
[Crossref] [PubMed]

M. I. Carvalho, M. Facão, and D. N. Christodoulides, “Self-bending of dark and gray photorefractive solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016602 (2007).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

D. N. Christodoulides and T. H. Coskun, “Diffraction-free planar beams in unbiased photorefractive media,” Opt. Lett. 21(18), 1460–1462 (1996).
[Crossref] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120(5-6), 311–315 (1995).
[Crossref]

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(21), 213904 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

Coskun, T. H.

Crosignani, B.

Degasperis, A.

DelRe, E.

Di Porto, P.

Du, Y.

K. Zhan, C. Hou, and Y. Du, “Self-deflection of steady-state bright spatial soliton in biased centrosymmetric photorefractive crystals,” Opt. Commun. 283(1), 138–141 (2010).
[Crossref]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

El-Ganainy, R.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).
[Crossref] [PubMed]

Facão, M.

M. I. Carvalho, M. Facão, and D. N. Christodoulides, “Self-bending of dark and gray photorefractive solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016602 (2007).
[Crossref] [PubMed]

Fleischer, J. W.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

Frantzeskakis, D. J.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

Gong, D.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

Hou, C.

K. Zhan and C. Hou, “Lattice surface solitons in diffusive nonlinear media driven by the quadratic electro-optic effect,” Opt. Express 22(10), 11646–11653 (2014).
[Crossref] [PubMed]

K. Zhan, C. Hou, and Y. Du, “Self-deflection of steady-state bright spatial soliton in biased centrosymmetric photorefractive crystals,” Opt. Commun. 283(1), 138–141 (2010).
[Crossref]

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Kartashov, Y. V.

Kevrekidis, P. G.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

Kip, D.

Kivshar, Y. S.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear Localized Waves in a Periodic Medium,” Phys. Rev. Lett. 87(8), 083901 (2001).
[Crossref] [PubMed]

Kolokolov, A. A.

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[Crossref]

Lakoba, T. I.

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[Crossref]

Makasyuk, I.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

Makris, K. G.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).
[Crossref] [PubMed]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–305 (2011).
[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(21), 213904 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

Martin, H.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Musslimani, Z. H.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).
[Crossref] [PubMed]

Neshev, D. N.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

Ostrovskaya, E. A.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

Palange, E.

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Porter, M. A.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

Rizza, C.

Rodrigues, A. S.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

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(21), 213904 (2005).
[Crossref] [PubMed]

Runde, D.

Rüter, C.

Schmelcher, P.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

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(21), 213904 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

Shandarov, V.

Shi, G.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120(5-6), 311–315 (1995).
[Crossref]

Stepic, M.

Sukhorukov, A. A.

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear Localized Waves in a Periodic Medium,” Phys. Rev. Lett. 87(8), 083901 (2001).
[Crossref] [PubMed]

Tan, P.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

Tian, H.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
[Crossref]

Tian, Y.

Torner, L.

Vakhitov, M. G.

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[Crossref]

Vysloukh, V. A.

Wang, H. F.

H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
[Crossref]

Xu, D.

Xu, F.

Xu, Z.

Yang, J.

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[Crossref]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[Crossref] [PubMed]

Yao, B.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
[Crossref]

Ye, F.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
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Zhan, K.

K. Zhan and C. Hou, “Lattice surface solitons in diffusive nonlinear media driven by the quadratic electro-optic effect,” Opt. Express 22(10), 11646–11653 (2014).
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K. Zhan, C. Hou, and Y. Du, “Self-deflection of steady-state bright spatial soliton in biased centrosymmetric photorefractive crystals,” Opt. Commun. 283(1), 138–141 (2010).
[Crossref]

Zhang, H.

Zhang, L.

Zhang, R.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

Zhou, Z.

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

Zhou, Z. X.

H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
[Crossref]

Zhu, D.

Appl. Phys. Express (1)

H. Tian, B. Yao, Z. X. Zhou, and H. F. Wang, “Voltage-controlled diffraction modulation in manganese-doped potassium sodium tantalate niobate single crystals,” Appl. Phys. Express 5(1), 012602 (2012).
[Crossref]

Appl. Phys. Lett. (1)

H. Tian, B. Yao, P. Tan, Z. Zhou, G. Shi, D. Gong, and R. Zhang, “Double-loop hysteresis in tetragonal KTa0.58Nb0.42O3 correlated to recoverable reorientations of the asymmetric polar domains,” Appl. Phys. Lett. 106(10), 102903 (2015).
[Crossref]

Nature (2)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
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O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433(7025), 500–503 (2005).
[Crossref] [PubMed]

Opt. Commun. (2)

K. Zhan, C. Hou, and Y. Du, “Self-deflection of steady-state bright spatial soliton in biased centrosymmetric photorefractive crystals,” Opt. Commun. 283(1), 138–141 (2010).
[Crossref]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120(5-6), 311–315 (1995).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. A (1)

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78(1), 013611 (2008).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

M. I. Carvalho, M. Facão, and D. N. Christodoulides, “Self-bending of dark and gray photorefractive solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016602 (2007).
[Crossref] [PubMed]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).
[Crossref] [PubMed]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[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(21), 213904 (2005).
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D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[Crossref] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear Localized Waves in a Periodic Medium,” Phys. Rev. Lett. 87(8), 083901 (2001).
[Crossref] [PubMed]

Radiophys. Quantum Electron. (1)

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[Crossref]

Rev. Mod. Phys. (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–305 (2011).
[Crossref]

Stud. Appl. Math. (1)

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) Bandgap lattice spectrum for different lattice depth p. Gray regions are Bloch bands. (b) Existence and stability regions for gap solitons in the plane of (σ, μ) of the self-focusing nonlinear system. (c) Energy flow versus μ for σ = −0.5 and 5 . (d) Energy flow versus σ for μ = 4 and 4.6.
Fig. 2
Fig. 2 Profiles and perturbation eigenvalue spectrums (inset) of gap solitons at μ = 4, σ = −0.1 (a) and μ = 4.6, σ = 5 (b) marked in Fig. 1(d). (c) and (d) are stable evolutions of gap solitons under 10% random noise perturbations corresponding to (a) and (b), respectively.
Fig. 3
Fig. 3 (a) Existence and stability regions for twisted solitons in self-focusing nonlinear media. (b) Energy flow versus μ for σ = −0.5 and 5. (c) Energy flow versus σ for μ = 3.8 and 4.4.Circles correspond to profiles shown in Fig. 4. In (b) and (c), stable and unstable branches are plotted by solid and dashed curves, respectively. (d) Perturbation growth rate versus σ at μ = 4.4.
Fig. 4
Fig. 4 Profiles and perturbation eigenvalue spectrums (inset) of twisted solitons at μ = 4, σ = 0.9 (a) and σ = 3 (b) corresponding to points marks as circles in Fig. 3(c). Unstable (c) and stable (d) propagations of twisted soliton shown in (a) and (b), respectively.
Fig. 5
Fig. 5 (a), (b) Areas of existence and stability of gap solitons for self-defocusing diffusive nonlinearity on the (σ, μ) plane. (c) Energy flow curves versus μ for σ = 5. The inset shows the case in low power domain. (d) Energy flow versus σ at μ = 3.535, solid and dash lines indicate their linear stability and instability, respectively. Imaginary part of perturbation growth rate versus σ at μ = 3.535 are shown in the inset of this figure.
Fig. 6
Fig. 6 Profiles of two gap solitons at μ = 4, σ = 0.9 (a) and σ = 3(b) marked in Fig. 5(d), the corresponding perturbation eigenvalue spectrums are shown in the insets. Evolution of unstable (c) and stable (d) gap solitons corresponding to (a) and (b), respectively.
Fig. 7
Fig. 7 (a) Existence and instability regions for twisted solitons in the plane of (σ, μ) of the self-defocusing nonlinear system. (b) Energy flow versus μ for σ = −0.3 and 3. (c) Energy flow versus σ for μ = 2 and 3.4. δ i versus σ are shown in the inset of this figure. (d) Dependence of μ cr on σ. Dash lines indicate existence region.
Fig. 8
Fig. 8 Profiles and perturbation eigenvalue spectrums (inset) of twisted solitons at μ = 2, σ = 0.2 (a) and μ = 3.4, σ = 2 (b) marked in Fig. 7(c). (c) and (d) are unstable evolutions of twisted solitons corresponding to (a) and (b), respectively.

Equations (4)

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i q z + 1 2 2 q x 2 + p R ( x ) q β χ ( x ) q ( 1 + S | q | 2 ) 2 ( | q | 2 x ) 2 = 0 ,
q ( x , z ) = { w ( x ) + [ v 1 ( x ) v 2 ( x ) ] e i δ z + [ v 1 * ( x ) + v 2 * ( x ) ] e i δ * z } e i μ z ,
δ v 1 = 1 2 d 2 v 2 d x 2 + [ 4 β χ w 2 ( 1 + S w 2 ) 2 ( d w d x ) 2 + μ p R ] v 2 ,
δ v 2 = 1 2 d 2 v 1 d x 2 + [ 4 β χ w 2 ( 3 S w 2 ) ( 1 + S w 2 ) 3 ( d w d x ) 2 + μ p R ] v 1 + 8 β χ w 3 ( 1 + S w 2 ) 2 d w d x d v 1 d x ,

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