Abstract

We report the existence and stability of nonlocal defect solitons (NDSs) in parity–time-symmetric photonic lattices with spatially modulated nonlocal nonlinearity. We reveal that solitons exist in the semi-infinite gap and a defect in the real part of nonlinear lattices plays a significant role in controlling the extent of the stability domains. We show that the existence and stability of the NDSs can be profoundly affected by the parameters of the nonlinear lattice structures.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  32. Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
    [CrossRef]
  33. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett. 31, 2595–2597 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  37. Y. V. Bludov and V. V. Konotop, “Localized modes in arrays of boson-fermion mixtures,” Phys. Rev. A 74, 043616 (2006).
    [CrossRef]
  38. W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
    [CrossRef]
  39. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002).
    [CrossRef]
  40. N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
    [CrossRef]
  41. W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
    [CrossRef]
  42. P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
    [CrossRef]
  43. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef]
  44. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef]
  45. R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express 19, 23706–23715 (2011).
    [CrossRef]
  46. J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277, 862–6876 (2008).
  47. M. J. Ablowitz and Z. H. Musslimani, “Spectral renormalization method for computing self-localized solutions to nonlinear systems,” Opt. Lett. 30, 2140–2142 (2005).
    [CrossRef]
  48. Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett. 35, 1716–1718 (2010).
    [CrossRef]

2013 (1)

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

2012 (6)

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Rom. Acad. A 13, 46–54 (2012).

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012).
[CrossRef]

C. Yin, Y. He, H. Li, and J. Xie, “Solitons in parity-time symmetric potentials with spatially modulated nonlocal nonlinearity,” Opt. Express 20, 19355–19362 (2012).
[CrossRef]

2011 (7)

2010 (4)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).
[CrossRef]

Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett. 35, 1716–1718 (2010).
[CrossRef]

K. Zhou, Z. Guo, J. Wang, and S. Liu, “Defect modes in defective parity-time symmetric periodic complex potentials,” Opt. Lett. 35, 2928–2930 (2010).
[CrossRef]

2009 (5)

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

J. Belmonte-Beitia, V. V. Konotop, V. M. Perez-Garcia, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chao, Solitons & Fractals 41, 1158–1166 (2009).

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

2008 (7)

F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Nonlinear switching of low-index modes in photonic lattices,” Phys. Rev. A 78, 013847 (2008).
[CrossRef]

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

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

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

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277, 862–6876 (2008).

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1749 (2008).
[CrossRef]

Y. Kominis and K. Hizanidis, “Power dependent soliton location and stability in complex photonic structures,” Opt. Express 16, 12124–12138 (2008).
[CrossRef]

2007 (4)

C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, “Faster than Hermitian quantum mechanics,” Phys. Rev. Lett. 98, 040403 (2007).
[CrossRef]

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, “Solitary waves under the competition of linear and nonlinear periodic potentials,” J. Phys. A 40, 14151–14163 (2007).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

2006 (5)

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Y. V. Bludov and V. V. Konotop, “Localized modes in arrays of boson-fermion mixtures,” Phys. Rev. A 74, 043616 (2006).
[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Perez-Garcia, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).
[CrossRef]

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

2005 (2)

M. J. Ablowitz and Z. H. Musslimani, “Spectral renormalization method for computing self-localized solutions to nonlinear systems,” Opt. Lett. 30, 2140–2142 (2005).
[CrossRef]

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

2003 (2)

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

C. M. Bender, D. C. Brody, and H. Jones, “Must a Hamiltonian be Hermitian?” Am. J. Phys. 71, 1095–1102 (2003).
[CrossRef]

2002 (2)

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[CrossRef]

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

2001 (1)

Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282, 343–348 (2001).
[CrossRef]

1998 (2)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett 80, 5243–5246 (1998).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Ablowitz, M. J.

Ahmed, Z.

Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282, 343–348 (2001).
[CrossRef]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Assanto, G.

Bang, O.

P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Bekenstein, R.

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. V. Konotop, V. M. Perez-Garcia, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chao, Solitons & Fractals 41, 1158–1166 (2009).

Bender, C. M.

C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, “Faster than Hermitian quantum mechanics,” Phys. Rev. Lett. 98, 040403 (2007).
[CrossRef]

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).
[CrossRef]

C. M. Bender, D. C. Brody, and H. Jones, “Must a Hamiltonian be Hermitian?” Am. J. Phys. 71, 1095–1102 (2003).
[CrossRef]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[CrossRef]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett 80, 5243–5246 (1998).
[CrossRef]

Bendix, O.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Bludov, Y. V.

Y. V. Bludov and V. V. Konotop, “Localized modes in arrays of boson-fermion mixtures,” Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett 80, 5243–5246 (1998).
[CrossRef]

Brazhnyi, V. A.

V. A. Brazhnyi, V. V. Konotop, and V. M. Perez-Garcia, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).
[CrossRef]

Brody, D. C.

C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, “Faster than Hermitian quantum mechanics,” Phys. Rev. Lett. 98, 040403 (2007).
[CrossRef]

C. M. Bender, D. C. Brody, and H. Jones, “Must a Hamiltonian be Hermitian?” Am. J. Phys. 71, 1095–1102 (2003).
[CrossRef]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[CrossRef]

Brzdakiewicz, K. A.

Chen, D.

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Rom. Acad. A 13, 46–54 (2012).

Chen, L.

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Rom. Acad. A 13, 46–54 (2012).

Chen, Y.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Chen, Z.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Chen, Z. G.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

Christodoulides, D. N.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

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

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Conti, C.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Denz, C.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

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

Fleischmann, R.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Fratalocchi, A.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

Ghofraniha, N.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Guo, Q.

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Guo, Z.

He, Y.

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

C. Yin, Y. He, H. Li, and J. Xie, “Solitons in parity-time symmetric potentials with spatially modulated nonlocal nonlinearity,” Opt. Express 20, 19355–19362 (2012).
[CrossRef]

Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett. 35, 1716–1718 (2010).
[CrossRef]

He, Y. J.

Hizanidis, K.

Hu, B.

Hu, S.

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012).
[CrossRef]

Hu, W.

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Hua, L.

Z. Shi, X. Jiang, X. Zhu, and L. Hua, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[CrossRef]

Jiang, X.

Z. Shi, X. Jiang, X. Zhu, and L. Hua, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[CrossRef]

H. Li, Z. Shi, X. Jiang, and X. Zhu, “Gray solitons in PT symmetric potentials,” Opt. Lett. 36, 3290–3292 (2011).
[CrossRef]

Jones, C. K. R. T.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, “Solitary waves under the competition of linear and nonlinear periodic potentials,” J. Phys. A 40, 14151–14163 (2007).
[CrossRef]

Jones, H.

C. M. Bender, D. C. Brody, and H. Jones, “Must a Hamiltonian be Hermitian?” Am. J. Phys. 71, 1095–1102 (2003).
[CrossRef]

Jones, H. F.

C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, “Faster than Hermitian quantum mechanics,” Phys. Rev. Lett. 98, 040403 (2007).
[CrossRef]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[CrossRef]

Kartashov, Y. V.

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1749 (2008).
[CrossRef]

F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Nonlinear switching of low-index modes in photonic lattices,” Phys. Rev. A 78, 013847 (2008).
[CrossRef]

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

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

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Kevrekidis, P. G.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, “Solitary waves under the competition of linear and nonlinear periodic potentials,” J. Phys. A 40, 14151–14163 (2007).
[CrossRef]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Kominis, Y.

Konotop, V. V.

J. Belmonte-Beitia, V. V. Konotop, V. M. Perez-Garcia, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chao, Solitons & Fractals 41, 1158–1166 (2009).

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, “Solitary waves under the competition of linear and nonlinear periodic potentials,” J. Phys. A 40, 14151–14163 (2007).
[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Perez-Garcia, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).
[CrossRef]

Y. V. Bludov and V. V. Konotop, “Localized modes in arrays of boson-fermion mixtures,” Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Kottos, T.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Krolikowski, W.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Krolikowski, W. Z.

P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Lan, S.

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Larsen, P. V.

P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Li, H.

Li, H. G.

Li, L.

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Rom. Acad. A 13, 46–54 (2012).

Li, R.

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Rom. Acad. A 13, 46–54 (2012).

Li, X.

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Li, Y.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Liu, J.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Liu, S.

Lu, D.

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012).
[CrossRef]

Lu, Z. E.

Luther-Davies, B.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Ma, X.

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012).
[CrossRef]

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

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

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Malomed, B. A.

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

Meister, B. K.

C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, “Faster than Hermitian quantum mechanics,” Phys. Rev. Lett. 98, 040403 (2007).
[CrossRef]

Mihalache, D.

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett. 35, 1716–1718 (2010).
[CrossRef]

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

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

M. J. Ablowitz and Z. H. Musslimani, “Spectral renormalization method for computing self-localized solutions to nonlinear systems,” Opt. Lett. 30, 2140–2142 (2005).
[CrossRef]

Neshev, D.

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Nikolov, N. I.

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Pang, W.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Peccianti, M.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

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

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. V. Konotop, V. M. Perez-Garcia, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chao, Solitons & Fractals 41, 1158–1166 (2009).

V. A. Brazhnyi, V. V. Konotop, and V. M. Perez-Garcia, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).
[CrossRef]

Rapti, Z.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, “Solitary waves under the competition of linear and nonlinear periodic potentials,” J. Phys. A 40, 14151–14163 (2007).
[CrossRef]

Ruocco, G.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Saffman, M.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Segev, M.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

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

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Shapiro, B.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Shi, Z.

Z. Shi, X. Jiang, X. Zhu, and L. Hua, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[CrossRef]

H. Li, Z. Shi, X. Jiang, and X. Zhu, “Gray solitons in PT symmetric potentials,” Opt. Lett. 36, 3290–3292 (2011).
[CrossRef]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Sorensen, M. P.

P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Torner, L.

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

F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Nonlinear switching of low-index modes in photonic lattices,” Phys. Rev. A 78, 013847 (2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1749 (2008).
[CrossRef]

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

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

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Trillo, S.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

P. V. Larsen, M. P. Sorensen, O. Bang, W. Z. Krolikowski, and S. Trillo, “Nonlocal description of X waves in quadratic nonlinear materials,” Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Vekslerchik, V. E.

J. Belmonte-Beitia, V. V. Konotop, V. M. Perez-Garcia, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chao, Solitons & Fractals 41, 1158–1166 (2009).

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Vysloukh, V. A.

Wang, H.

Wang, J.

Xie, J.

Xu, Z.

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Yang, J.

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277, 862–6876 (2008).

Yang, N.

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Rom. Acad. A 13, 46–54 (2012).

Ye, F.

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

F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Nonlinear switching of low-index modes in photonic lattices,” Phys. Rev. A 78, 013847 (2008).
[CrossRef]

Yin, C.

Yu, Z.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Zhang, H.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Zhang, T.

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Zhang, Z. M.

Zheng, L. X.

Zheng, Y.

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012).
[CrossRef]

Zhou, J.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Zhou, K.

Zhu, X.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Z. Shi, X. Jiang, X. Zhu, and L. Hua, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[CrossRef]

X. Zhu, H. Wang, L. X. Zheng, H. G. Li, and Y. J. He, “Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices,” Opt. Lett. 36, 2680–2682 (2011).
[CrossRef]

H. Li, Z. Shi, X. Jiang, and X. Zhu, “Gray solitons in PT symmetric potentials,” Opt. Lett. 36, 3290–3292 (2011).
[CrossRef]

Am. J. Phys. (1)

C. M. Bender, D. C. Brody, and H. Jones, “Must a Hamiltonian be Hermitian?” Am. J. Phys. 71, 1095–1102 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, “Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals,” Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Chao, Solitons & Fractals (1)

J. Belmonte-Beitia, V. V. Konotop, V. M. Perez-Garcia, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chao, Solitons & Fractals 41, 1158–1166 (2009).

J. Comput. Phys. (1)

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277, 862–6876 (2008).

J. Phys. A (1)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, “Solitary waves under the competition of linear and nonlinear periodic potentials,” J. Phys. A 40, 14151–14163 (2007).
[CrossRef]

Nat. Phys. (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Opt. Commun. (1)

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric linear lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012).
[CrossRef]

Opt. Express (5)

Opt. Lett. (8)

Phys. Lett. A (1)

Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282, 343–348 (2001).
[CrossRef]

Phys. Rev. A (9)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).
[CrossRef]

Z. Shi, X. Jiang, X. Zhu, and L. Hua, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) PT-symmetric complex-valued linear PLs for V1(x)=4cos2(x) (solid), W1(x)=0.8sin(2x) (dashed), and (b) the band structure corresponding to the lattice profile shown in (a).

Fig. 2.
Fig. 2.

(a)–(c) Depict the PT-symmetric complex-valued nonlinear PLs for v2=4, w2=0.5, k=1 (the solid line is the real part, and the dashed line is the imaginary part). With a defect in the real part: (a) negative defect ε=0.5, (b) zero defect ε=0, (c) positive defect ε=0.5. (d) Power P versus propagation constant μ for various defects ε with d=1. The solid line represents the stable regions and the dashed line represents the unstable regions. (e)–(g) are the growth rate Re(δ) versus μ with ε=0.5,ε=0, and ε=0.5.

Fig. 3.
Fig. 3.

Soliton profiles (solid line is the real part, dotted line is the imaginary part, and dashed-dotted line is the refractive index profile) and soliton evolutions for (a), (b) μ=2.8, and (c), (d) μ=3.3 with ε=0.5, for (e), (f) μ=3.1, and (g), (h) μ=4.5 with ε=0, for (i), (j) μ=3.3 and (k), (l) μ=5.0 with ε=0.5; for the other parameters are k=1, d=1, v2=4, and w2=0.5. (b), (f), and (j) are stable propagation, and (d), (h), and (l) are unstable propagation.

Fig. 4.
Fig. 4.

Stable region (gray shade) for the dependence of the propagation constant μ on the defect parameter ε when k=1, d=1, v2=4 and w2=0.5.

Fig. 5.
Fig. 5.

Power P versus the parameters of the nonlinear PT symmetric for various defects ε. (a) The relationship between P and v2 for w2=0.5 and k=1, (b) the relationship between P and w2 for v2=4 and k=1, (c) the relationship between P and k for v2=4 and w2=0.5. The solid line represents the stable regions and the dashed line represents the unstable regions. Other parameters are μ=3.5 and d=1.

Fig. 6.
Fig. 6.

(a) Power P versus the degree of the nonlocality degree of the nonlinear response d for various defects ε. (b)–(d) Stability domain (μ, d) with ε=0.5,ε=0, and ε=0.5, respectively. The gray regions are stable domains. Other parameters are d=1, k=1, v2=4, w2=0.5, and μ=3.5.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

iqz+122qx2+[V1(x)+iW1(x)]q+[1+V2(x)+iW2(x)]q+g(xλ)|q(λ)|2dλ=0,
122ux2+[V1(x)+iW1(x)]u+[1+V2(x)+iW2(x)]u+g(xλ)|u(λ)|2dλ=μu.
g(x)=1/(2d)exp(|x|/d),
122ux2+[V1(x)+iW1(x)]u=μu.
12(2x2+2iKxK2)FK+[V1(x)+iW1(x)]FK=μFK.

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