Abstract

We investigate the generation of discrete spatial solitons in arrays of coupled waveguides. Light was launched into the center of the array, and different beam sizes and array geometries were tested. At low power, the propagating field spreads as it couples to more waveguides. When the intensity is increased, localization is observed around the input waveguides, leading to the formation of a discrete soliton. For wide input beams, exciting a few waveguides, soliton splitting, which is due to instability induced by multiphoton absorption, is observed. All of these effects are described well by a coupled-mode formalism.

© 2002 Optical Society of America

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  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
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    [CrossRef]
  4. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
    [CrossRef] [PubMed]
  5. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
    [CrossRef] [PubMed]
  6. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
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    [CrossRef]
  18. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
    [CrossRef]
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    [CrossRef]
  20. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
    [CrossRef]
  21. Y. S. Kivshar and D. K. Campbell, “Peierls–Nabarro potential barrier for highly localized nonlinear modes,” Phys. Rev. E 48, 3077–3081 (1993).
    [CrossRef]
  22. R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, “Spatially solitary waves in arrays of nonlinear waveguides,” Opt. Lett. 19, 323–325 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  27. C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
    [CrossRef]
  28. P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
    [CrossRef]
  29. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2000

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

1999

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

1998

I. Relke, “Instability of solitons in an inhomogeneous array of optical fibers,” Phys. Rev. E 57, 6105–6111 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (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. Flach and C. R. Willis, “Discrete breathers,” Phys. Rep. 295, 182–264 (1998).
[CrossRef]

1997

1996

W. Królikowski and Y. S. Kivshar, “Soliton-based optical switching in waveguide arrays,” J. Opt. Soc. Am. B 13, 876–887 (1996).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

1995

P. Marquié, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

1994

Y. S. Kivshar, W. Królikowski, and O. A. Chubukalo, “Dark solitons in discrete lattices,” Phys. Rev. E 50, 5020–5032 (1994).
[CrossRef]

R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, “Spatially solitary waves in arrays of nonlinear waveguides,” Opt. Lett. 19, 323–325 (1994).
[CrossRef] [PubMed]

1993

Y. S. Kivshar and D. K. Campbell, “Peierls–Nabarro potential barrier for highly localized nonlinear modes,” Phys. Rev. E 48, 3077–3081 (1993).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

1992

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

1991

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
[CrossRef]

1990

1988

1985

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite’ optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[CrossRef]

1983

A. C. Scott and L. Macneil, “Binding energy versus nonlinearity for a ‘small’ stationary soliton,” Phys. Lett. A 98A, 87–89 (1983).
[CrossRef]

1980

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

1979

A. S. Davydov, “Solitons in molecular systems,” Phys. Scr. 20, 387–394 (1979).
[CrossRef]

1972

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JEPT 34, 62–69 (1972)].

1965

1959

T. Holstein, “Studies of polaron motion,” Ann. Phys. (N.Y.) 8, 325–289 (1959).
[CrossRef]

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Aitchison, J. S.

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

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[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]

P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
[CrossRef]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
[CrossRef] [PubMed]

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite’ optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[CrossRef]

Bilbault, J. M.

P. Marquié, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[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]

Campbell, D. K.

Y. S. Kivshar and D. K. Campbell, “Peierls–Nabarro potential barrier for highly localized nonlinear modes,” Phys. Rev. E 48, 3077–3081 (1993).
[CrossRef]

Christodoulides, D. N.

Chubukalo, O. A.

Y. S. Kivshar, W. Królikowski, and O. A. Chubukalo, “Dark solitons in discrete lattices,” Phys. Rev. E 50, 5020–5032 (1994).
[CrossRef]

Crosignani, B.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Davydov, A. S.

A. S. Davydov, “Solitons in molecular systems,” Phys. Scr. 20, 387–394 (1979).
[CrossRef]

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Denardo, B.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

Di Porto, P.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Eisenberg, H. S.

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

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[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]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Flach, S.

S. Flach and C. R. Willis, “Discrete breathers,” Phys. Rep. 295, 182–264 (1998).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite’ optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[CrossRef]

Galvin, B.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Greenfield, A.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Holstein, T.

T. Holstein, “Studies of polaron motion,” Ann. Phys. (N.Y.) 8, 325–289 (1959).
[CrossRef]

Jackel, J. L.

Jones, A. L.

Joseph, R. I.

Kang, J. U.

Kennedy, G. T.

Kivshar, Y. S.

W. Królikowski and Y. S. Kivshar, “Soliton-based optical switching in waveguide arrays,” J. Opt. Soc. Am. B 13, 876–887 (1996).
[CrossRef]

Y. S. Kivshar, W. Królikowski, and O. A. Chubukalo, “Dark solitons in discrete lattices,” Phys. Rev. E 50, 5020–5032 (1994).
[CrossRef]

Y. S. Kivshar and D. K. Campbell, “Peierls–Nabarro potential barrier for highly localized nonlinear modes,” Phys. Rev. E 48, 3077–3081 (1993).
[CrossRef]

Kobyakov, A.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Królikowski, W.

W. Królikowski and Y. S. Kivshar, “Soliton-based optical switching in waveguide arrays,” J. Opt. Soc. Am. B 13, 876–887 (1996).
[CrossRef]

Y. S. Kivshar, W. Królikowski, and O. A. Chubukalo, “Dark solitons in discrete lattices,” Phys. Rev. E 50, 5020–5032 (1994).
[CrossRef]

Larranza, A.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

Leaird, D. E.

Lederer, F.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, “Spatially solitary waves in arrays of nonlinear waveguides,” Opt. Lett. 19, 323–325 (1994).
[CrossRef] [PubMed]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
[CrossRef]

Macneil, L.

A. C. Scott and L. Macneil, “Binding energy versus nonlinearity for a ‘small’ stationary soliton,” Phys. Lett. A 98A, 87–89 (1983).
[CrossRef]

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite’ optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[CrossRef]

Marquié, P.

P. Marquié, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Millar, P.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Morandotti, R.

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

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[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]

Muschall, R.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, “Spatially solitary waves in arrays of nonlinear waveguides,” Opt. Lett. 19, 323–325 (1994).
[CrossRef] [PubMed]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
[CrossRef]

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Oliver, M. K.

Peschel, T.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

Putterman, S.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

Relke, I.

I. Relke, “Instability of solitons in an inhomogeneous array of optical fibers,” Phys. Rev. E 57, 6105–6111 (1998).
[CrossRef]

Remoissenet, M.

P. Marquié, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Schmidt-Hattenberger, C.

R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, “Spatially solitary waves in arrays of nonlinear waveguides,” Opt. Lett. 19, 323–325 (1994).
[CrossRef] [PubMed]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
[CrossRef]

Scott, A. C.

A. C. Scott and L. Macneil, “Binding energy versus nonlinearity for a ‘small’ stationary soliton,” Phys. Lett. A 98A, 87–89 (1983).
[CrossRef]

Segev, M.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JEPT 34, 62–69 (1972)].

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Sibbett, W.

Silberberg, Y.

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

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[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. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
[CrossRef] [PubMed]

Y. Silberberg, “Solitons and 2-photon absorption,” Opt. Lett. 15, 1005–1007 (1990).
[CrossRef] [PubMed]

Smith, P. W. E.

Stegeman, G. I.

P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Trutschel, U.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
[CrossRef]

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Villeneuve, A.

Vogel, E. M.

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Weiner, A. M.

Willis, C. R.

S. Flach and C. R. Willis, “Discrete breathers,” Phys. Rep. 295, 182–264 (1998).
[CrossRef]

Wright, W.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JEPT 34, 62–69 (1972)].

Ann. Phys. (N.Y.)

T. Holstein, “Studies of polaron motion,” Ann. Phys. (N.Y.) 8, 325–289 (1959).
[CrossRef]

Appl. Phys. Lett.

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Commun.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fiber array with circularly distributed multiple cores,” Opt. Commun. 82, 461–465 (1991).
[CrossRef]

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite’ optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[CrossRef]

Opt. Lett.

Phys. Lett. A

A. C. Scott and L. Macneil, “Binding energy versus nonlinearity for a ‘small’ stationary soliton,” Phys. Lett. A 98A, 87–89 (1983).
[CrossRef]

Phys. Rep.

S. Flach and C. R. Willis, “Discrete breathers,” Phys. Rep. 295, 182–264 (1998).
[CrossRef]

Phys. Rev. E

I. Relke, “Instability of solitons in an inhomogeneous array of optical fibers,” Phys. Rev. E 57, 6105–6111 (1998).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

P. Marquié, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

Y. S. Kivshar, W. Królikowski, and O. A. Chubukalo, “Dark solitons in discrete lattices,” Phys. Rev. E 50, 5020–5032 (1994).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Y. S. Kivshar and D. K. Campbell, “Peierls–Nabarro potential barrier for highly localized nonlinear modes,” Phys. Rev. E 48, 3077–3081 (1993).
[CrossRef]

Phys. Rev. Lett.

B. Denardo, B. Galvin, A. Greenfield, A. Larranza, S. Putterman, and W. Wright, “Observations of localized structures in nonlinear lattices: domain walls and kinks,” Phys. Rev. Lett. 68, 1730–1733 (1992).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999).
[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]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

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

Phys. Scr.

A. S. Davydov, “Solitons in molecular systems,” Phys. Scr. 20, 387–394 (1979).
[CrossRef]

Sov. Phys. JEPT

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JEPT 34, 62–69 (1972)].

Other

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Discrete solitons. II.Dynamical properties,” J. Opt. Soc. Am. B (to be published).

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Figures (9)

Fig. 1
Fig. 1

Solution for a linearly coupled array of 41 waveguides, when light is injected into the central waveguide, with E0=1. The intensity is shown in gray scale. The scale is chosen such that the peak intensity for every propagation distance along the waveguide is represented by black. The energy is spread mainly into two lobes. The number of central peaks is an indication to how many coupling lengths the light has propagated.

Fig. 2
Fig. 2

Experimental setup. Inset: Schematic drawing of the sample. The sample consists of a Al0.18Ga0.82As core layer and Al0.24Ga0.76As cladding layers grown on top of a GaAs substrate. A few samples with different separations d between the waveguides were tested.

Fig. 3
Fig. 3

Images of the output facet of a sample with d=4 µm for different powers. (a) Peak power, 70 W. Linear features are demonstrated: two main lobes and a few secondary peaks in between. (b) Peak power, 320 W. Intermediate power, the distribution is narrowing. (c) Peak power, 500 W. A discrete soliton is formed.

Fig. 4
Fig. 4

Single waveguide excitation: experimental and numerical results for samples with d=7 µm [(a) and (b) total propagation distance of 1.9 coupling lengths] and 5 µm [(c) and (d) total propagation distance of 3.0 coupling lengths]. Experimental results are represented by a solid curve, and numerical results are shown as vertical lines. The integrated power is normalized to unity.

Fig. 5
Fig. 5

Single waveguide excitation: output light distributions as a function of the input peak power. Vertical cross sections are the different power profiles corresponding to each input power. (a), (b), and (c) Samples of 1.9, 3.0, and 4.2 coupling lengths, respectively.

Fig. 6
Fig. 6

Wide excitation by power splitting: output profiles of (a) and (b) three-waveguide-wide (c) and (d) and five-waveguide-wide excitations. All the samples are of 3.0 coupling lengths.

Fig. 7
Fig. 7

Wide excitation by a wide smooth beam: output light distributions as a function of the input peak power as in Fig. 5. (a) A two-waveguide-wide excitation. (b) A three-waveguide-wide excitation. (c) A three-waveguide-wide excitation of a continuous slab waveguide.

Fig. 8
Fig. 8

Nonlinear contraction of power into a single waveguide.

Fig. 9
Fig. 9

(a) Temporal autocorrelations of a discrete soliton: the input pulse (solid curve), the output pulse center (thick dashed curve), and the output pulse wing (thin dashed curve). (b) The output pulse sketch. (c) A comparison between the spectra of the input (solid curve) and the output (dashed curve) pulses.

Equations (2)

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i dEndz+βEn+C(En-1+En+1)+γ|En|2En=0,
En(z)=A0(i)n exp(iβz)In(2Cz),

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