Abstract

The performance of switching junctions in two-dimensional discrete-soliton networks is analyzed theoretically by coupled-mode theory. Our analysis can be used for the design of routing junctions with specified operational characteristics. Appropriately engineering the intersection site can further improve the switching efficiency of these junctions. Our analytical results are verified by numerical simulations.

© 2001 Optical Society of America

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References

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  1. A. Scott, Phys. Rep. 217, 1 (1992).
    [CrossRef]
  2. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  4. Y. S. Kivshar, Opt. Lett. 18, 1147 (1993).
    [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. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchinson, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  9. 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).
  10. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
    [CrossRef]
  11. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  12. A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
    [CrossRef]
  13. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

2001

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

1998

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

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

1996

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

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]

1993

1992

A. Scott, Phys. Rep. 217, 1 (1992).
[CrossRef]

1988

1983

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]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

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

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

Boyd, A. R.

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

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

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]

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, 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).

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.

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]

Macneil, L.

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

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

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, 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.

A. Scott, Phys. Rep. 217, 1 (1992).
[CrossRef]

Scott, A. C.

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

Segev, M.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[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, A. R. Boyd, and J. S. Aitchinson, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Sorel, M.

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

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]

Appl. Phys. Lett.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Lett. A

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

Phys. Rep.

A. Scott, Phys. Rep. 217, 1 (1992).
[CrossRef]

Phys. Rev. E

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.

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]

Other

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).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

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Figures (4)

Fig. 1
Fig. 1

(a) Moderately confined signal DS; (b) strongly confined DS blocker; (c) routing a signal DS at a T junction when a blocker is positioned at site A; (d) routing a signal DS at an X junction when a blocker is positioned at A and another at B.

Fig. 2
Fig. 2

120° Y junction with a blocker placed at the entry of the lower arm m=1. The signal DS travels along the n line.

Fig. 3
Fig. 3

(a) Transmission coefficient T of a 120° junction as a function of blocking parameter Δβ1/c when αD=0.2 (solid curve) and αD=0.6 (dashed curve). (b) Reflection losses R (solid curve) and leakage losses L (dashed curve) as a function of Δβ1/c for αD=0.6. For both figures, Δβ0=0.

Fig. 4
Fig. 4

(a) A T discrete soliton switching junction with a blocker positioned at site A; (b) the transmission coefficient of this T junction as a function of Δβ1/c when αD=0.2 (solid curve), αD=0.6 (dashed curve), and Δβ0=0; (c) the transmission coefficient of the T junction as a function of Δβ0/c for αD=0.6 and Δβ1/c=9.

Equations (7)

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

iUz+12k0n22Ux2+2Uy2+k0n1Δfx,yU+k0γI0U2+V2U=0,
iVz+12k0n22Vx2+2Vy2+k0n1Δfx,yV+k0γI0V2+U2V=0,
Δβ1=k0γI0Ebx,y2E0x,y2dxdyE0x,y2dxdy,
ida-1dz+ca-2+a0+κa1+κam=1=0,
ida0dz+ca-1+a1+am=1+Δβ0a0=0,
ida1dz+ca0+a2+κa-1+κam=1=0,
idam=1dz+ca0+am=2+Δβ1am=1+κa-1+κa1=0,

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