Abstract

We show that reflection losses suffered by discrete solitons along sharp bends in two-dimensional waveguide-array networks can be almost eliminated. Analysis indicates that this can be accomplished by appropriately engineering the corner site of the bend. Our analytical results are verified by numerical simulations.

© 2001 Optical Society of America

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Corrections

Demetrios N. Christodoulides and Eugenia D. Eugenieva, "Minimizing bending losses in two-dimensional discrete soliton networks: errata," Opt. Lett. 27, 369-369 (2002)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-27-5-369

References

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  1. A. C. Scott, Philos. Trans. R. Soc. London Ser. A 315, 423 (1985).
    [CrossRef]
  2. A. S. Davydov, Biology and Quantum Mechanics (Pergamon, Oxford, 1982).
  3. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  4. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  5. W. Krolikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
    [CrossRef]
  6. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
    [CrossRef]
  7. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
    [CrossRef]
  8. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  9. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchinson, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  10. D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. (to be published).
  11. A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).
  12. A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
    [CrossRef]
  13. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
    [CrossRef] [PubMed]
  14. A. Talneau, L. Gouezigou, and N. Bouadma, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CTuAA6.

2001 (1)

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

2000 (1)

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

1998 (2)

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1996 (3)

W. Krolikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[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]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

1988 (1)

1985 (1)

A. C. Scott, Philos. Trans. R. Soc. London Ser. A 315, 423 (1985).
[CrossRef]

1983 (1)

A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
[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]

Aitchinson, J. S.

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

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Bouadma, N.

A. Talneau, L. Gouezigou, and N. Bouadma, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CTuAA6.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Christodoulides, D. N.

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

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. (to be published).

Darmanyan, S.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Davydov, A. S.

A. S. Davydov, Biology and Quantum Mechanics (Pergamon, Oxford, 1982).

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]

Eisenberg, H. S.

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

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. (to be published).

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Gouezigou, L.

A. Talneau, L. Gouezigou, and N. Bouadma, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CTuAA6.

Joannopoulos, J. D.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Joseph, R. I.

Kivshar, Y. S.

Kobyakov, A.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Krolikowski, W.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lederer, F.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[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]

Love, J. D.

A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Macneil, L.

A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Morandotti, R.

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

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

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]

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]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Scott, A. C.

A. C. Scott, Philos. Trans. R. Soc. London Ser. A 315, 423 (1985).
[CrossRef]

A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
[CrossRef]

Silberberg, Y.

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

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Sorel, M.

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

Synder, A. W.

A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Talneau, A.

A. Talneau, L. Gouezigou, and N. Bouadma, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CTuAA6.

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]

Villeneuve, P.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

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]

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

Opt. Lett. (1)

Philos. Trans. R. Soc. London Ser. A (1)

A. C. Scott, Philos. Trans. R. Soc. London Ser. A 315, 423 (1985).
[CrossRef]

Phys. Lett. A (1)

A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
[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]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Phys. Rev. Lett. (4)

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

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Other (4)

A. Talneau, L. Gouezigou, and N. Bouadma, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CTuAA6.

A. S. Davydov, Biology and Quantum Mechanics (Pergamon, Oxford, 1982).

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. (to be published).

A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

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Figures (4)

Fig. 1
Fig. 1

(a) Waveguide-array bend consisting of identical elements. (b) Intensity profile of the input discrete soliton. (c) Intensity of the transmitted DS wave after the bend at 7.4  cm. (d) Reflected intensity at 7.4  cm. The intensity scale is the same for (b), (c), and (d).

Fig. 2
Fig. 2

Unfolded equivalent photonic circuit of the waveguide-array bend.

Fig. 3
Fig. 3

(a) Reflection coefficient R of a 70° array bend as a function of the defect detuning parameter Δβ/c and for phase tilt αD=0.2 (solid curve), αD=0.6 (dashed curve), and αD=1.0 (dotted curve). (b) R as a function of αD for Δβ/c=-2.5 (solid curve), Δβ/c=-1.91 (dashed curve), and Δβ/c=0 (dotted curve).

Fig. 4
Fig. 4

(a) Intensity profile of a discrete soliton after a 70° bend when the corner site has been appropriately engineered. (b) More-involved waveguide-array path involving four consecutive bends.

Equations (7)

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

iUz+12k0n22Ux2+2Uy2+k0n1Δfx,yU+k0γI0U2U=0,
ida1dz+κa1+ca0+a-2=0,
ida0dz+Δβa0+ca1+a-1=0,
ida-1dz+κa-1+ca0+a2=0.
r=2κc1+κccosαD+Δβc1-κc21+κcexpiαD-2isinαD-Δβc1-κcexpiαD-κc1+exp2iαD,
t=r+1+κcexp-iαD1+κcexpiαD.
Δβc=-2κc1+κccosαD1-κc2.

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