Abstract

We demonstrate numerically that partially incoherent light can be trapped in the spectral band gaps of a photonic lattice, creating partially incoherent multi-component spatial optical solitons in a self-defocusing nonlinear periodic medium. We find numerically such incoherent multi-gap optical solitons and discuss how to generate them in experiment by interfering incoherent light beams at the input of a nonlinear periodic medium.

© 2005 Optical Society of America

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  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) [English translation: Tech. Phys. 26, 541–544 (1981)].
  2. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical-response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
    [Crossref] [PubMed]
  3. C. M. de Sterke and J. E. Sipe , “Gap solitons,” in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.
  4. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
    [Crossref] [PubMed]
  5. 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, 053902–4 (2003).
    [Crossref] [PubMed]
  6. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
    [Crossref]
  7. J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
    [Crossref] [PubMed]
  8. 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, 023902–4 (2003).
    [Crossref] [PubMed]
  9. 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]
  10. O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (2003).
    [Crossref] [PubMed]
  11. A. A. Sukhorukov and Yu. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902–4 (2003).
    [Crossref] [PubMed]
  12. D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618-17 (2004).
    [Crossref]
  13. B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).
  14. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
    [Crossref] [PubMed]
  15. 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, 223901–4 (2004).
    [Crossref] [PubMed]
  16. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons”, Nature 433, 500–503 (2005).
    [Crossref] [PubMed]
  17. 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]
  18. 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]
  19. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Exp. 12, 2831, (2004).
    [Crossref]
  20. T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
    [Crossref]
  21. M. Segev and D. N. Christodoulides , “Incoherent solitons: self-trapping of weakly-correlated wave-packets,” in Spatial Optical Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W. E. Torruellas, eds., (Springer-Verlag, New York, 2001), pp. 87–125.

2005 (2)

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

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
[Crossref]

2004 (5)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Exp. 12, 2831, (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, 223901–4 (2004).
[Crossref] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
[Crossref]

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. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618-17 (2004).
[Crossref]

2003 (6)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (2003).
[Crossref] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902–4 (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 422, 147–150 (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, 023902–4 (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, 053902–4 (2003).
[Crossref] [PubMed]

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)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[Crossref] [PubMed]

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]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
[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, 053902–4 (2003).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[Crossref] [PubMed]

Bartal, G.

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

Buljan, H.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons”, Nature 433, 500–503 (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, 223901–4 (2004).
[Crossref] [PubMed]

Carmon, T.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons”, Nature 433, 500–503 (2005).
[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, 023902–4 (2003).
[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]

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, 223901–4 (2004).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (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, 023902–4 (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 422, 147–150 (2003).
[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. Segev and D. N. Christodoulides , “Incoherent solitons: self-trapping of weakly-correlated wave-packets,” in Spatial Optical Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W. E. Torruellas, eds., (Springer-Verlag, New York, 2001), pp. 87–125.

Christodoulides, D.N.

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

Cohen, O.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons”, Nature 433, 500–503 (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, 223901–4 (2004).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (2003).
[Crossref] [PubMed]

Coskun, T. H.

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]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[Crossref] [PubMed]

C. M. de Sterke and J. E. Sipe , “Gap solitons,” in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.

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, 223901–4 (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 422, 147–150 (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, 023902–4 (2003).
[Crossref] [PubMed]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[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, 053902–4 (2003).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[Crossref] [PubMed]

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, 223901–4 (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, 023902–4 (2003).
[Crossref] [PubMed]

Fleischer, J.W.

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

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (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 422, 147–150 (2003).
[Crossref] [PubMed]

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]

B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Exp. 12, 2831, (2004).
[Crossref]

Kivshar, Yu. S.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
[Crossref]

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618-17 (2004).
[Crossref]

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]

A. A. Sukhorukov and Yu. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902–4 (2003).
[Crossref] [PubMed]

B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).

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]

B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[Crossref] [PubMed]

Ku, T. S.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
[Crossref]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
[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, 053902–4 (2003).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[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, M.

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]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
[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, 053902–4 (2003).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[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, 223901–4 (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]

B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618-17 (2004).
[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) [English translation: Tech. Phys. 26, 541–544 (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, 223901–4 (2004).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (2003).
[Crossref] [PubMed]

Segev, M.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons”, Nature 433, 500–503 (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, 223901–4 (2004).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (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, 023902–4 (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 422, 147–150 (2003).
[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. Segev and D. N. Christodoulides , “Incoherent solitons: self-trapping of weakly-correlated wave-packets,” in Spatial Optical Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W. E. Torruellas, eds., (Springer-Verlag, New York, 2001), pp. 87–125.

Shih, M. F.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
[Crossref]

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
[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, 053902–4 (2003).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[Crossref] [PubMed]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[Crossref] [PubMed]

C. M. de Sterke and J. E. Sipe , “Gap solitons,” in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[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) [English translation: Tech. Phys. 26, 541–544 (1981)].

Sukhorukov, A. A.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
[Crossref]

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. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618-17 (2004).
[Crossref]

A. A. Sukhorukov and Yu. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902–4 (2003).
[Crossref] [PubMed]

B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Exp. 12, 2831, (2004).
[Crossref]

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) [English translation: Tech. Phys. 26, 541–544 (1981)].

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Exp. 12, 2831, (2004).
[Crossref]

Nature (2)

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

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

Opt. Exp. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Exp. 12, 2831, (2004).
[Crossref]

Phys. Rev. E (1)

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618-17 (2004).
[Crossref]

Phys. Rev. Lett. (13)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902–4 (2003).
[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, 223901–4 (2004).
[Crossref] [PubMed]

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Yu. S. Kivshar, “Coherence controlled soliton interactions,” Phys. Rev. Lett. 94, 063904-4 (2005).
[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, 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]

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, 023902–4 (2003).
[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]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91, 113901–4 (2003).
[Crossref] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. 91, 113902–4 (2003).
[Crossref] [PubMed]

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

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[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, 053902–4 (2003).
[Crossref] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904-4 (2004).
[Crossref]

Other (4)

C. M. de Sterke and J. E. Sipe , “Gap solitons,” in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.

M. Segev and D. N. Christodoulides , “Incoherent solitons: self-trapping of weakly-correlated wave-packets,” in Spatial Optical Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W. E. Torruellas, eds., (Springer-Verlag, New York, 2001), pp. 87–125.

B. Hanna, D. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Experimental observation of multi-gap vector solitons,” In Nonlinear Guided Waves and Their Applications, Postconference ed. OSA pp. PD-5 (Optical Society of America, Washington DC, 2004).

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) [English translation: Tech. Phys. 26, 541–544 (1981)].

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Figures (5)

Fig. 1.
Fig. 1.

(a) Refractive index and (b) structure of the bandgap spectrum of the photonic lattice. The first and second gap are shaded. Right panel shows the propagation constants of the different components of the multi-gap soliton shown in Fig. 2. Six of them lie in the first gap, and three in the second band-gap. The power spectrum of the soliton, found as a sum of Fourier power spectra of individual components, is shown in (c).

Fig. 2.
Fig. 2.

The numerically obtained incoherent gap soliton. Shown are (a) the total soliton intensity, and its separate components in (b–g) the first gap and (h–j) second spectral gap.

Fig. 3.
Fig. 3.

(a,b) Propagation of an incoherent gap soliton for 20mm in the nonlinear and linear regimes, respectively. The corresponding output beam profiles are shown in (c,d).

Fig. 4.
Fig. 4.

Schematic for the generation of multi-gap solitons. First, an input partially incoherent beam splits into two beams by a beam splitter and then two beams are recombined at the input of the nonlinear periodic medium. Solid, dashed, and dotted lines stand for the mutually incoherent plane waves that partially incoherent light can be decomposed into. The plane waves interfere at the input face of the nonlinear medium.

Fig. 5.
Fig. 5.

Example of the generation of an incoherent multi-gap soliton. (a) Output (dashed) and input (solid) intensity profiles corresponding to case (b); (b–d) intensity patterns along the propagation direction for input excitation by inclined overlapping beams with the same profiles but different coherence properties: (b) partially incoherent, correlated counter-propagating Fourier components; (c) fully coherent; (d) partially incoherent, uncorrelated Fourier components.

Equations (2)

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i A z + D 2 A x 2 + k 0 2 [ ν 2 ( x ) + δ n 2 ( I ) ] A = 0 ,
A ( x , t ) = j G ( α j ) e i k 0 ( z + α j x ) cos [ k 0 θ ( x x i ) ] e i γ j ( t ) .

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