Abstract

We suggest a novel concept of diffraction management in waveguide arrays and predict the existence of discrete gap solitons that possess the properties of both conventional discrete and Bragg grating solitons. We demonstrate that one can control both the soliton velocity and the propagation direction by varying the input light intensity.

© 2002 Optical Society of America

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  1. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  2. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  3. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef]
  4. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  5. Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
    [CrossRef]
  6. F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds., Vol. 82 of Springer Series in Optical Sciences (Springer-Verlag, New York, 2001), pp. 269–292.
    [CrossRef]
  7. C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
    [CrossRef]
  8. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
    [CrossRef]
  9. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
    [CrossRef]
  10. D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
    [CrossRef]
  11. M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
    [CrossRef]
  12. U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
    [CrossRef]
  13. P. St. J. Russell, Phys. Rev. Lett. 56, 596 (1986).
    [CrossRef] [PubMed]
  14. N. G. R. Broderick, C. M. de Sterke, and B. J. Eggleton, Phys. Rev. E 52, R5788 (1995).
    [CrossRef]
  15. Yu. S. Kivshar and N. Flytzanis, Phys. Rev. A 46, 7972 (1992).
    [CrossRef] [PubMed]
  16. U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
    [CrossRef]
  17. R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.
  18. I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
    [CrossRef]

2002 (2)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

2001 (3)

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

2000 (1)

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

1999 (2)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

1998 (1)

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

1996 (1)

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

1995 (1)

N. G. R. Broderick, C. M. de Sterke, and B. J. Eggleton, Phys. Rev. E 52, R5788 (1995).
[CrossRef]

1993 (2)

Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
[CrossRef]

C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

1992 (1)

Yu. S. Kivshar and N. Flytzanis, Phys. Rev. A 46, 7972 (1992).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

P. St. J. Russell, Phys. Rev. Lett. 56, 596 (1986).
[CrossRef] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Barashenkov, I. V.

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Broderick, N. G. R.

N. G. R. Broderick, C. M. de Sterke, and B. J. Eggleton, Phys. Rev. E 52, R5788 (1995).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Claude, C.

C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Darmanyan, S.

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds., Vol. 82 of Springer Series in Optical Sciences (Springer-Verlag, New York, 2001), pp. 269–292.
[CrossRef]

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

de Sterke, C. M.

N. G. R. Broderick, C. M. de Sterke, and B. J. Eggleton, Phys. Rev. E 52, R5788 (1995).
[CrossRef]

Eggleton, B. J.

N. G. R. Broderick, C. M. de Sterke, and B. J. Eggleton, Phys. Rev. E 52, R5788 (1995).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

Flytzanis, N.

Yu. S. Kivshar and N. Flytzanis, Phys. Rev. A 46, 7972 (1992).
[CrossRef] [PubMed]

Joseph, R. I.

Kivshar, Yu. S.

Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
[CrossRef]

C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Yu. S. Kivshar and N. Flytzanis, Phys. Rev. A 46, 7972 (1992).
[CrossRef] [PubMed]

Kluth, O.

C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Kobyakov, A.

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds., Vol. 82 of Springer Series in Optical Sciences (Springer-Verlag, New York, 2001), pp. 269–292.
[CrossRef]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds., Vol. 82 of Springer Series in Optical Sciences (Springer-Verlag, New York, 2001), pp. 269–292.
[CrossRef]

Mandelik, D.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Modotto, D.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Muschall, R.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

Pelinovsky, D. E.

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Peschel, T.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, Phys. Rev. Lett. 56, 596 (1986).
[CrossRef] [PubMed]

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

Spatschek, K. H.

C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Zemlyanaya, E. V.

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. A (1)

Yu. S. Kivshar and N. Flytzanis, Phys. Rev. A 46, 7972 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (1)

C. Claude, Yu. S. Kivshar, O. Kluth, and K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
[CrossRef]

Phys. Rev. E (2)

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

N. G. R. Broderick, C. M. de Sterke, and B. J. Eggleton, Phys. Rev. E 52, R5788 (1995).
[CrossRef]

Phys. Rev. Lett. (8)

P. St. J. Russell, Phys. Rev. Lett. 56, 596 (1986).
[CrossRef] [PubMed]

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef]

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Other (2)

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds., Vol. 82 of Springer Series in Optical Sciences (Springer-Verlag, New York, 2001), pp. 269–292.
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, and J. S. Aitchison, in Quantum Electronics and Laser Science Conference, Vol. 74 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 239.

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Figures (3)

Fig. 1
Fig. 1

Schematic of a binary array of waveguides with alternating widths d1 and d2 and separation ds.

Fig. 2
Fig. 2

Characteristic dependences of the Bloch wave number Kb, group velocity vg, and the effective diffraction coefficient D on propagation constant β. Gray shading marks the transmission bands. Normalized detuning between the thick and thin waveguides is ρ=1.5.

Fig. 3
Fig. 3

Excitation of discrete gap solitons in a self-focusing medium γ=+1 by input beams with κ=0.6π, n0=1, ν=4, and normalized peak intensities C2 of (a) 0.3, (b) 0.75, (c) 0.9, and (d) 5. The parameters correspond to Fig. 2.

Equations (6)

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

idEndz+λnEn+En-1+En+1+γnEn2En=0,
an=A expiβz+iKbn, bn=B expiβz+iKbn,
Kb=cos-1-η/2, Aβ=B exp-iKb/22-η,
Enz=0=C exp-n-n02/ν2+iκn-n0,
E2n0=A1+A2exp-2n-n02/ν2+iKbn, E2n+10=B1+B2exp-2n+1-n02/ν2+iKbn,
p=P2P11-δ1+δ2,

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