Abstract

We theoretically study gap random-phase lattice solitons (gap-RPLSs) in nonlinear waveguide arrays with self-defocusing nonlinearity. We find that the intensity structure and statistical (coherence) properties of gap-RPLSs conform to the lattice periodicity, while their Floquet-Bloch power spectrum is multi-humped with peaks in the anomalous diffractions regions. It is shown that a gap-RPLS can be generated when a simple incoherent beam with bell-shaped power spectrum and single-hump intensity is launched at a proper angle into the waveguide array. The input incoherent beam evolves in the lattice while shedding off some radiation, and eventually attains the features of gap-RPLS.

© 2005 Optical Society of America

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    [Crossref]
  2. Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with higher group retardation,” Zh. Tekh. Fiz. 51, 902–907 (1981).
  3. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical-response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
    [Crossref] [PubMed]
  4. D.N. Christodoulides and R.I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
    [Crossref] [PubMed]
  5. Yu. Kivshar, “Self-localization in arrays of de-focusing waveguides,” Opt. Lett. 18, 1147–1149 (1993).
    [Crossref] [PubMed]
  6. J. Feng, “Alternative scheme for studying gap solitons in infinite periodic Kerr media”, Opt. Lett. 20, 1302–1304 (1993).
    [Crossref]
  7. 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]
  8. S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity”, JETP 86, 682–686 (1998).
    [Crossref]
  9. H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
    [Crossref] [PubMed]
  10. R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
    [Crossref] [PubMed]
  11. 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] [PubMed]
  12. 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 (London) 422, 147 (2003).
    [Crossref]
  13. O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
    [Crossref] [PubMed]
  14. A.A. Sukhorukov and Y.S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902 (2003).
    [Crossref] [PubMed]
  15. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings”, Opt. Lett. 28, 710–712 (2003)
    [Crossref] [PubMed]
  16. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
    [Crossref] [PubMed]
  17. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
    [Crossref] [PubMed]
  18. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (2004).
    [Crossref]
  19. 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] [PubMed]
  20. O. Cohen, G. Bartal, H. Buljan, J.W. Fleischer, T. Carmon, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500 (2005).
    [Crossref]
  21. H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
    [Crossref]
  22. G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
    [Crossref] [PubMed]
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  24. M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
    [Crossref] [PubMed]
  25. D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
    [Crossref]
  26. M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
    [Crossref]
  27. Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
    [Crossref] [PubMed]
  28. V.V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
    [Crossref]
  29. A.W. Snyder and D.J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
    [Crossref]
  30. M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
    [Crossref] [PubMed]
  31. D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
    [Crossref] [PubMed]
  32. S.A. Ponomarenko, “Twisted Gaussian Schell-model solitons,” Phys. Rev. E 64, 036618 (2001).
    [Crossref]
  33. Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
    [Crossref]
  34. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
    [Crossref]
  35. H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
    [Crossref] [PubMed]
  36. T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett.93, (2004).
    [Crossref] [PubMed]
  37. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
    [Crossref] [PubMed]
  38. M. Segev and D.N. Christodoulides, Incoherent Solitons in Spatial Solitons, S. Trillo and W. Torruellas eds. (Springer, Berlin, 2001) pp. 87–125.

2005 (3)

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

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

K. Motzek, A.A. Sukhorukov, F. Kaiser, and Y.S. Kivshar, “Incoherent multi-gap optical solitons in nonlinear photonic lattices,” Optics Express 132916 (2005).
[Crossref] [PubMed]

2004 (4)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[Crossref] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (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] [PubMed]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
[Crossref] [PubMed]

2003 (8)

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings”, Opt. Lett. 28, 710–712 (2003)
[Crossref] [PubMed]

H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[Crossref] [PubMed]

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] [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 (London) 422, 147 (2003).
[Crossref]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[Crossref] [PubMed]

A.A. Sukhorukov and Y.S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902 (2003).
[Crossref] [PubMed]

D.N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature (London) 424817–823 (2003).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

2002 (2)

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[Crossref]

2001 (2)

S.A. Ponomarenko, “Twisted Gaussian Schell-model solitons,” Phys. Rev. E 64, 036618 (2001).
[Crossref]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

2000 (3)

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
[Crossref] [PubMed]

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

1998 (5)

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

V.V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[Crossref]

A.W. Snyder and D.J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[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]

S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity”, JETP 86, 682–686 (1998).
[Crossref]

1997 (2)

D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

1996 (1)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
[Crossref] [PubMed]

1993 (2)

J. Feng, “Alternative scheme for studying gap solitons in infinite periodic Kerr media”, Opt. Lett. 20, 1302–1304 (1993).
[Crossref]

Yu. Kivshar, “Self-localization in arrays of de-focusing waveguides,” Opt. Lett. 18, 1147–1149 (1993).
[Crossref] [PubMed]

1988 (1)

1987 (1)

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical-response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[Crossref] [PubMed]

1981 (1)

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with higher group retardation,” Zh. Tekh. Fiz. 51, 902–907 (1981).

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

Aitchison, J.S.

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
[Crossref] [PubMed]

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]

Anderson, D.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[Crossref]

V.V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[Crossref]

Bartal, G.

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

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[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]

Buljan, H.

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

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

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] [PubMed]

H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett.93, (2004).
[Crossref] [PubMed]

Carmon, T.

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

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett.93, (2004).
[Crossref] [PubMed]

Chen, W.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical-response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
[Crossref] [PubMed]

Chen, Z.G.

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

Christodoulides, D. N.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Christodoulides, D.N.

O. Cohen, G. Bartal, H. Buljan, J.W. Fleischer, T. Carmon, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500 (2005).
[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] [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 (London) 422, 147 (2003).
[Crossref]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[Crossref] [PubMed]

D.N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature (London) 424817–823 (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] [PubMed]

H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[Crossref] [PubMed]

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[Crossref]

D.N. Christodoulides and R.I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

M. Segev and D.N. Christodoulides, Incoherent Solitons in Spatial Solitons, S. Trillo and W. Torruellas eds. (Springer, Berlin, 2001) pp. 87–125.

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

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

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

Coskun, T. H.

M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

Coskun, T.H.

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[Crossref]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity”, JETP 86, 682–686 (1998).
[Crossref]

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] [PubMed]

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] [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 (London) 422, 147 (2003).
[Crossref]

H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[Crossref] [PubMed]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

Eisenberg, H.S.

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
[Crossref] [PubMed]

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]

Eugenieva, E.

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Fedele, R.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
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Feng, J.

J. Feng, “Alternative scheme for studying gap solitons in infinite periodic Kerr media”, Opt. Lett. 20, 1302–1304 (1993).
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Fleischer, J.W.

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

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

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] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[Crossref] [PubMed]

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] [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 (London) 422, 147 (2003).
[Crossref]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

Haelterman, M.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
[Crossref] [PubMed]

Hall, B.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[Crossref]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (2004).
[Crossref]

Joseph, R.I.

Kaiser, F.

K. Motzek, A.A. Sukhorukov, F. Kaiser, and Y.S. Kivshar, “Incoherent multi-gap optical solitons in nonlinear photonic lattices,” Optics Express 132916 (2005).
[Crossref] [PubMed]

Kip, D.

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Kivshar, Y.

Kivshar, Y.S.

K. Motzek, A.A. Sukhorukov, F. Kaiser, and Y.S. Kivshar, “Incoherent multi-gap optical solitons in nonlinear photonic lattices,” Optics Express 132916 (2005).
[Crossref] [PubMed]

A.A. Sukhorukov and Y.S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902 (2003).
[Crossref] [PubMed]

Kivshar, Yu.

Kivshar, Yu. S.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (2004).
[Crossref]

Kobyakov, A.

S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity”, JETP 86, 682–686 (1998).
[Crossref]

Krolikowski, W.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (2004).
[Crossref]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings”, Opt. Lett. 28, 710–712 (2003)
[Crossref] [PubMed]

Lederer, F.

D.N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature (London) 424817–823 (2003).
[Crossref]

S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity”, JETP 86, 682–686 (1998).
[Crossref]

Lisak, M.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[Crossref]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

Manela, O.

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

Martin, H.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

Millot, G.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
[Crossref] [PubMed]

Mills, D. L.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical-response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[Crossref] [PubMed]

Mitchell, D.J.

A.W. Snyder and D.J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[Crossref]

Mitchell, M.

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
[Crossref] [PubMed]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
[Crossref] [PubMed]

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]

Motzek, K.

K. Motzek, A.A. Sukhorukov, F. Kaiser, and Y.S. Kivshar, “Incoherent multi-gap optical solitons in nonlinear photonic lattices,” Optics Express 132916 (2005).
[Crossref] [PubMed]

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] [PubMed]

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (2004).
[Crossref]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings”, Opt. Lett. 28, 710–712 (2003)
[Crossref] [PubMed]

Ostrovskaya, E.

Picozzi, A.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
[Crossref] [PubMed]

Pitois, S.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
[Crossref] [PubMed]

Ponomarenko, S.A.

S.A. Ponomarenko, “Twisted Gaussian Schell-model solitons,” Phys. Rev. E 64, 036618 (2001).
[Crossref]

Ryzhov, Yu. N.

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with higher group retardation,” Zh. Tekh. Fiz. 51, 902–907 (1981).

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] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett.93, (2004).
[Crossref] [PubMed]

Sears, S. M.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

Segev, M.

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

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

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] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[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 (London) 422, 147 (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] [PubMed]

H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[Crossref] [PubMed]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[Crossref]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett.93, (2004).
[Crossref] [PubMed]

M. Segev and D.N. Christodoulides, Incoherent Solitons in Spatial Solitons, S. Trillo and W. Torruellas eds. (Springer, Berlin, 2001) pp. 87–125.

Semenov, V. E.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[Crossref]

Shih, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
[Crossref] [PubMed]

Shkunov, V.V.

V.V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[Crossref]

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

D.N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature (London) 424817–823 (2003).
[Crossref]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
[Crossref] [PubMed]

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]

Snyder, A.W.

A.W. Snyder and D.J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[Crossref]

Soljacic, M.

H. Buljan, M. Segev, M. Soljačić, N.K. Efremidis, and D.N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[Crossref] [PubMed]

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Sorel, M.

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

Sotin, V. E.

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with higher group retardation,” Zh. Tekh. Fiz. 51, 902–907 (1981).

Sukhorukov, A. A.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (2004).
[Crossref]

Sukhorukov, A.A.

K. Motzek, A.A. Sukhorukov, F. Kaiser, and Y.S. Kivshar, “Incoherent multi-gap optical solitons in nonlinear photonic lattices,” Optics Express 132916 (2005).
[Crossref] [PubMed]

A.A. Sukhorukov and Y.S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902 (2003).
[Crossref] [PubMed]

Vishwanath, A.

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

Voloshchenko, Yu. I.

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with higher group retardation,” Zh. Tekh. Fiz. 51, 902–907 (1981).

JETP (1)

S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity”, JETP 86, 682–686 (1998).
[Crossref]

Nature (London) (3)

D.N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature (London) 424817–823 (2003).
[Crossref]

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 (London) 422, 147 (2003).
[Crossref]

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

Opt. Lett. (5)

Optics Express (1)

K. Motzek, A.A. Sukhorukov, F. Kaiser, and Y.S. Kivshar, “Incoherent multi-gap optical solitons in nonlinear photonic lattices,” Optics Express 132916 (2005).
[Crossref] [PubMed]

P. Natl. Acad. Sci. USA (1)

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” P. Natl. Acad. Sci. USA 99, 5223–5227 (2002).
[Crossref]

Phys. Rev. E (2)

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[Crossref]

S.A. Ponomarenko, “Twisted Gaussian Schell-model solitons,” Phys. Rev. E 64, 036618 (2001).
[Crossref]

Phys. Rev. Lett. (19)

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004).
[Crossref] [PubMed]

V.V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[Crossref]

A.W. Snyder and D.J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[Crossref]

M. Soljačić, M. Segev, T.H. Coskun, D.N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).
[Crossref] [PubMed]

D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D.N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical-response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[Crossref] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

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]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction menagement,” Phys. Rev. Lett. 85, 1863–1866 (2000)
[Crossref] [PubMed]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 863296 (2001).
[Crossref] [PubMed]

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] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[Crossref] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[Crossref] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 4 (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] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Multiband vector lattice solitons” Phys. Rev. Lett. 91, 113901 (2003).
[Crossref] [PubMed]

A.A. Sukhorukov and Y.S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902 (2003).
[Crossref] [PubMed]

Science (2)

Z.G. Chen, M. Mitchell, M. Segev, T.H. Coskun, and D.N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[Crossref] [PubMed]

D. Kip, M. Soljačić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Zh. Tekh. Fiz. (1)

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with higher group retardation,” Zh. Tekh. Fiz. 51, 902–907 (1981).

Other (3)

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett.93, (2004).
[Crossref] [PubMed]

H. Buljan, G. Bartal, O. Cohen, T. Schwartz, O. Manela, T. Carmon, M. Segev, J.W. Fleischer, and D.N. Christodoulides, “Partially coherent waves in nonlinear periodic lattices,” Stud. Appl. Math., in print (2005).
[Crossref]

M. Segev and D.N. Christodoulides, Incoherent Solitons in Spatial Solitons, S. Trillo and W. Torruellas eds. (Springer, Berlin, 2001) pp. 87–125.

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Figures (6)

Fig. 1.
Fig. 1.

The band-gap structure of the lattice, and the power spectra of the first gap-RPLS example. (a) Band-gap structure of the lattice (solid lines), and propagation constants of the RPLS modes (closed circles). (b) Fourier power spectrum of a gap-RPLS in the self-defocusing nonlinear waveguide array (solid line); the humps in the spectrum are located mainly in the anomalous diffraction regions. The Fourier power spectrum of an input incoherent beam launched at an angle is indicated by the dot-dashed line, and spectrum of the output beam is given by the dashed line (the dot-dashed line and the dashed line almost fully coincide). (c) Same as in (b) but with the Floquet-Bloch power spectrum of the beams. See text for details.

Fig. 2.
Fig. 2.

The intensity structure and coherence properties of the first example of a gap-RPLS. (a) The complex coherence factor µ(x,x )∊[-1,1] of the gap-RPLS; black (white) corresponds to a value of -1 (1). (b) The intensity profile I(x)/IS (solid line) of a gap-RPLS. The intensity structure of an incoherent beam launched at angle θ=0.7π/Dk, and propagated for 50 mm (dashed line). Dotted line illustrates the diffraction-broadened beam after z=30 mm propagation in a linear lattice, for an input beam with a wavefunction identical to that of a gap-RPLS. The vertical lines represent the lattice sites.

Fig. 3.
Fig. 3.

The stable evolution of the (a) intensity structure, (b) Fourier power spectrum, and (c) Floquet-Bloch power spectrum of the first gap-RPLS example. The evolution of an incoherent beam launched at an angle θ=0.7π/Dk into the nonlinear waveguide array; (d) intensity structure, (e) Fourier power spectrum, and (f) Floquet-Bloch power spectrum.

Fig. 4.
Fig. 4.

Same as in Figure 1 for the second example of a gap-RPLS. See text for details.

Fig. 5.
Fig. 5.

Same as Figure 2 for the second example of a gap-RPLS. See text.

Fig. 6.
Fig. 6.

Same as Figure 3 for the second example of a gap-RPLS. See text for details.

Equations (2)

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i ψ m z + 1 2 k 2 ψ m x 2 + V ( x , z ) k n 0 ψ m ( x , z ) = 0 .
1 2 k d 2 u n , l d x 2 + V ( x ) k n 0 u n , 1 ( x , z ) = κ n , l u n , l ,

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