Abstract

We reveal the critical behavior of the fundamental defect mode, which can be supported by an optical lattice with a local defect in the nonlocal nonlinear medium. In such a system, there are several system parameters, and it is found that whether the fundamental defect mode can locate in the defect or not depends on the parameter value higher or lower than its critical value. Furthermore, the critical values of these parameters are predicted in this article.

© 2013 Optical Society of America

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    [CrossRef]
  29. H. Zhang, D. Xu, and L. Li, “An approximate solution for describing a fundamental soliton in nonlocal nonlinear media,” J. Opt. A 11, 125203 (2009).
    [CrossRef]
  30. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Relaxation methods,” in Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University, 2001), pp. 753–763.
  31. Z. Xu, Y. V. Kartashov, and L. Torner, “Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media,” Opt. Lett. 30, 3171–3173 (2005).
    [CrossRef]
  32. M. L. Chiofalo, S. Succi, and M. P. Tosi, “Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm,” Phys. Rev. E 62, 7438–7444 (2000).
    [CrossRef]
  33. W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–864 (2006).
    [CrossRef]
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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]

2011

Z. Lu and Z. Zhang, “Defect solitons in parity-time symmetric superlattices,” Opt. Express 19, 11457–11462 (2011).
[CrossRef]

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, “Scattering of linear and nonlinear waves in waveguide array with a PT-symmetric defect,” Phys. Rev. A 84, 013833 (2011).
[CrossRef]

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

Z. Lu and Z.-M. Zhang, “Surface line defect solitons in square optical lattice,” Opt. Express 19, 2410–2416 (2011).
[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).
[CrossRef]

H. Leblond, B. A. Malomed, and D. Mihalache, “Spatiotemporal vortex solitons in hexagonal arrays of waveguides,” Phys. Rev. A 83, 063825 (2011).
[CrossRef]

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

Y. V. Kartashov, S. López-Aguayo, V. A. Vysloukh, and L. Torner, “Stripe-like quasi-nondiffracting optical lattices,” Opt. Express 19, 9505–9511 (2011).
[CrossRef]

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

2010

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

X. Zhu, H. Wang, and L.-X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18, 20786–20792 (2010).
[CrossRef]

L. Dong and F. Ye, “Shaping solitons by lattice defects,” Phys. Rev. A 82, 053829 (2010).
[CrossRef]

2009

2006

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
[CrossRef]

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–864 (2006).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

2005

2004

D. 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, 123903 (2004).
[CrossRef]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

2003

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

2002

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E 66, 066615 (2002).
[CrossRef]

2001

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

2000

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

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Split-step Fourier method” in Nonlinear Fiber Optics, 4th ed (Academic, 2006), pp. 41–45.

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

Alexander, T. J.

D. 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, 123903 (2004).
[CrossRef]

Bang, O.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E 66, 066615 (2002).
[CrossRef]

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

Bao, W.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–864 (2006).
[CrossRef]

Belic, M. R.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

Brazhnyi, V. A.

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).
[CrossRef]

Buljan, H.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Chen, W. H.

Chen, Z.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. 30, 1506–1508 (2005).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

D. 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, 123903 (2004).
[CrossRef]

Chern, I.-L.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–864 (2006).
[CrossRef]

Chiofalo, M. L.

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

Christodoulides, D. N.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

Cohen, O.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Denz, C.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Dmitriev, S. V.

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, “Scattering of linear and nonlinear waves in waveguide array with a PT-symmetric defect,” Phys. Rev. A 84, 013833 (2011).
[CrossRef]

Dong, L.

L. Dong and F. Ye, “Shaping solitons by lattice defects,” Phys. Rev. A 82, 053829 (2010).
[CrossRef]

Dreisow, F.

Efremidis, N. K.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

Fedele, F.

Flannery, B. P.

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

Fleischer, J. W.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Frantzeskakis, D. J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

He, Y. J.

Heinrich, M.

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]

Hu, Y.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Jovic, D. M.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Kartashov, Y. V.

Kevrekidis, P. G.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Kivshar, Y. S.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, “Scattering of linear and nonlinear waves in waveguide array with a PT-symmetric defect,” Phys. Rev. A 84, 013833 (2011).
[CrossRef]

D. 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, 123903 (2004).
[CrossRef]

Krolikowski, W.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E 66, 066615 (2002).
[CrossRef]

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

Leblond, H.

H. Leblond, B. A. Malomed, and D. Mihalache, “Spatiotemporal vortex solitons in hexagonal arrays of waveguides,” Phys. Rev. A 83, 063825 (2011).
[CrossRef]

Lederer, F.

Li, L.

H. Zhang, D. Xu, and L. Li, “An approximate solution for describing a fundamental soliton in nonlocal nonlinear media,” J. Opt. A 11, 125203 (2009).
[CrossRef]

López-Aguayo, S.

Y. V. Kartashov, S. López-Aguayo, V. A. Vysloukh, and L. Torner, “Stripe-like quasi-nondiffracting optical lattices,” Opt. Express 19, 9505–9511 (2011).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

Lou, C.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

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.

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]

Makasyuk, I.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

D. 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, 123903 (2004).
[CrossRef]

Malomed, B. A.

H. Leblond, B. A. Malomed, and D. Mihalache, “Spatiotemporal vortex solitons in hexagonal arrays of waveguides,” Phys. Rev. A 83, 063825 (2011).
[CrossRef]

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

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Martin, H.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

D. 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, 123903 (2004).
[CrossRef]

Mihalache, D.

H. Leblond, B. A. Malomed, and D. Mihalache, “Spatiotemporal vortex solitons in hexagonal arrays of waveguides,” Phys. Rev. A 83, 063825 (2011).
[CrossRef]

Miller, A.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

Musslimani, Z. H.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

Neshev, D.

D. 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, 123903 (2004).
[CrossRef]

Nolte, S.

Ostrovskaya, E. A.

D. 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, 123903 (2004).
[CrossRef]

Pertsch, T.

Press, W. H.

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

Rasmussen, J. J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E 66, 066615 (2002).
[CrossRef]

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

Schwartz, T.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

Segev, M.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

Succi, S.

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

Suchkov, S. V.

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, “Scattering of linear and nonlinear waves in waveguide array with a PT-symmetric defect,” Phys. Rev. A 84, 013833 (2011).
[CrossRef]

Sukhorukov, A. A.

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, “Scattering of linear and nonlinear waves in waveguide array with a PT-symmetric defect,” Phys. Rev. A 84, 013833 (2011).
[CrossRef]

Szameit, A.

Teukolsky, S. A.

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

Torner, L.

Tosi, M. P.

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

Tunermann, A.

Vetterling, W. T.

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

Vysloukh, V. A.

Wang, H.

Wang, H. Z.

Wang, J.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

Wyller, J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E 66, 066615 (2002).
[CrossRef]

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

Xu, D.

H. Zhang, D. Xu, and L. Li, “An approximate solution for describing a fundamental soliton in nonlocal nonlinear media,” J. Opt. A 11, 125203 (2009).
[CrossRef]

Xu, Z.

Yang, J.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. 30, 1506–1508 (2005).
[CrossRef]

Ye, F.

L. Dong and F. Ye, “Shaping solitons by lattice defects,” Phys. Rev. A 82, 053829 (2010).
[CrossRef]

Ye, Z.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

Yin Lim, F.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–864 (2006).
[CrossRef]

Zhang, H.

H. Zhang, D. Xu, and L. Li, “An approximate solution for describing a fundamental soliton in nonlocal nonlinear media,” J. Opt. A 11, 125203 (2009).
[CrossRef]

Zhang, P.

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

Zhang, Z.

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]

Zhu, X.

J. Comput. Phys.

W. Bao, I.-L. Chern, and F. Yin Lim, “Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates,” J. Comput. Phys. 219, 836–864 (2006).
[CrossRef]

J. Opt. A

H. Zhang, D. Xu, and L. Li, “An approximate solution for describing a fundamental soliton in nonlocal nonlinear media,” J. Opt. A 11, 125203 (2009).
[CrossRef]

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

H. Leblond, B. A. Malomed, and D. Mihalache, “Spatiotemporal vortex solitons in hexagonal arrays of waveguides,” Phys. Rev. A 83, 063825 (2011).
[CrossRef]

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

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]

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, “Scattering of linear and nonlinear waves in waveguide array with a PT-symmetric defect,” Phys. Rev. A 84, 013833 (2011).
[CrossRef]

J. Wang, Z. Ye, A. Miller, Y. Hu, C. Lou, P. Zhang, Z. Chen, and J. Yang, “Nonlinear beam deflection in photonic lattices with negative defects,” Phys. Rev. A 83, 033836(2011).
[CrossRef]

L. Dong and F. Ye, “Shaping solitons by lattice defects,” Phys. Rev. A 82, 053829 (2010).
[CrossRef]

Phys. Rev. E

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

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E 66, 066615 (2002).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

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

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).
[CrossRef]

Phys. Rev. Lett.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386(1998).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

D. 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, 123903 (2004).
[CrossRef]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef]

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

Rev. Mod. Phys.

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

Other

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

G. P. Agrawal, “Split-step Fourier method” in Nonlinear Fiber Optics, 4th ed (Academic, 2006), pp. 41–45.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Profile of the fundamental defect mode (red curve) for the attractive-defected lattices (blue curve). (b) Propagation and evolution of the fundamental attractive defect mode in the system described by Eqs. (1) and (3)–(5). The corresponding parameters are b=2, d=0.2, h=0.5, and p=0.8.

Fig. 2.
Fig. 2.

Dependence of peak amplitude (blue curve) and width (red curve) of the fundamental defect mode on (a) defect strength h at p=0.8, U=2, and d=1, (b) nonlocal degree d at p=0.8, U=2, and h=0.5, (c) lattice depth p at h=0.5, U=2, and d=1, and (d) propagation constant b at h=0.5, p=0.8, and d=0.2.

Fig. 3.
Fig. 3.

Profiles (column 1) and propagation against white noise whose maximal value is 0.1 (column 2) of three defect solitons for the repulsive defect at (a) h=0.3, (b) h=0.4, and (c) h=1. Other parameters are U=2, d=1, and p=0.4.

Fig. 4.
Fig. 4.

Critical defect strength hcr versus (a) lattice depth p at d=1 and (b) nonlocal degree d at p=0.5; critical lattice depth pcr versus (c) defect strength h at d=1 and (d) nonlocal degree d at h=0.5; critical nonlocal degree dcr versus (e) lattice depth p at h=0.5 and (f) defect strength h at p=0.5. The other parameter is U=2.

Fig. 5.
Fig. 5.

Profiles (column 1) and propagation against white noise whose maximal value is 0.1 (column 2) of three defect solitons for the repulsive defect at (a) p=0.2, (b) p=0.3, and (c) p=1. Other parameters are U=2, d=1, and h=0.5.

Fig. 6.
Fig. 6.

Profiles (column 1) and propagation against white noise whose maximal value is 0.1 (column 2) of three defect solitons for the repulsive defect at (a) d=0.3, (b) d=0.4, and (c) d=1. Other parameters are U=2, p=0.5, and h=0.5.

Equations (5)

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

iqz+122qx2+nq+pR(x)q=0.
n(x,z)=+G(xx)I(x,z)dx,
R(x)=cos2(x)[1+hfD(x)],
fD(x)=exp(x8128).
n=|q(x,z)|2+d2nx2.

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