Abstract

A new approach to multiport switching in arrays of nonlinear waveguides is proposed. Whereas other schemes have relied on suppressing the inherent transverse discreteness of these arrays, this approach takes advantage of that feature. One of the effects of discreteness is to keep intense beams trapped in a single waveguide for the length of the array. Switching may be achieved by use of a controlled perturbation to displace such a trapped beam in the transverse direction. This displacement is quantized to an integer number of waveguides, thus permitting unambiguous selection of the output channel.

© 1996 Optical Society of America

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References

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  1. G. I. Stegeman, in Nonlinear Waves in Solid State Physics, A. D. Boardman, ed. (Plenum, New York, 1990), p. 463.
    [CrossRef]
  2. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  3. C. Schmidt-Hattenberger, U. Trutschel, F. Lederer, Opt. Lett. 16, 294 (1991).
    [CrossRef] [PubMed]
  4. W. Królikowski, U. Trutschel, M. Cronin-Golomb, C. Schmidt-Hattenberger, Opt. Lett. 19, 320 (1994).
    [CrossRef] [PubMed]
  5. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  6. N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
    [CrossRef]
  7. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, S. Wabnitz, Phys. Rev. E. 53, 1172 (1996).
    [CrossRef]
  8. O. Bang, M. Peyrard, Physica D 81, 9 (1995).
    [CrossRef]
  9. O. Bang, M. Peyrard, Phys. Rev. E 53, 4143 (1996).
    [CrossRef]
  10. M. Matsumoto, S. Katayama, A. Hasegawa, Opt. Lett. 20, 1758 (1995).
    [CrossRef] [PubMed]

1996 (2)

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

O. Bang, M. Peyrard, Phys. Rev. E 53, 4143 (1996).
[CrossRef]

1995 (2)

1994 (1)

1991 (1)

1990 (1)

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

1988 (1)

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Aceves, A. B.

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

Bang, O.

O. Bang, M. Peyrard, Phys. Rev. E 53, 4143 (1996).
[CrossRef]

O. Bang, M. Peyrard, Physica D 81, 9 (1995).
[CrossRef]

Christodoulides, D. N.

Cronin-Golomb, M.

De Angelis, C.

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

Finlayson, N.

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

Hasegawa, A.

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Joseph, R. I.

Katayama, S.

Królikowski, W.

Lederer, F.

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

C. Schmidt-Hattenberger, U. Trutschel, F. Lederer, Opt. Lett. 16, 294 (1991).
[CrossRef] [PubMed]

Matsumoto, M.

Muschall, R.

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

Peyrard, M.

O. Bang, M. Peyrard, Phys. Rev. E 53, 4143 (1996).
[CrossRef]

O. Bang, M. Peyrard, Physica D 81, 9 (1995).
[CrossRef]

Schmidt-Hattenberger, C.

Stegeman, G. I.

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

G. I. Stegeman, in Nonlinear Waves in Solid State Physics, A. D. Boardman, ed. (Plenum, New York, 1990), p. 463.
[CrossRef]

Trillo, S.

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

Trutschel, U.

Wabnitz, S.

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

Appl. Phys. Lett. (1)

N. Finlayson, G. I. Stegeman, Appl. Phys. Lett. 56, 2276 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

O. Bang, M. Peyrard, Phys. Rev. E 53, 4143 (1996).
[CrossRef]

Phys. Rev. E. (1)

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

Physica D (1)

O. Bang, M. Peyrard, Physica D 81, 9 (1995).
[CrossRef]

Other (1)

G. I. Stegeman, in Nonlinear Waves in Solid State Physics, A. D. Boardman, ed. (Plenum, New York, 1990), p. 463.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Examples of methods (A) and (B) of displacing a trapped beam. Each plot shows the contour of the intensity |En(z)|2 found by numerical integration of Eq. (1) with the initial condition as explained in the text. Common parameters: L = 80, N = 101, I m hi = 2 . 0. Individual parameters: (A) k = −0.52, (B) I m lo = 0 . 2, k = 0.52, θ = 0, Δn = 40. The displacement is (A) eight waveguides and (B) two waveguides.

Fig. 2
Fig. 2

Displacement of a trapped beam of maximum intensity I m hi after it has been given a linear phase gradient exp(ikn) at the input, as a function of I m hi for different values of k. The curves are the results of numerical simulation of Eq. (1) with the initial condition as explained in the text. Fixed parameters: L = 40, N = 101.

Fig. 3
Fig. 3

Number of waveguides by which a trapped beam of maximum intensity I m hi is displaced after collision with an angled beam of maximum intensity I m lo of (a) 0.05, (b) 0.1, (c) 0.15, and (d) 0.2 as a function of (top) phase constant θ and (bottom) I m hi. The curves are the results of numerical simulation of Eq. (1) with the initial condition as explained in the text. Fixed parameters: L = 80, N = 101, Δn = 40, k = 0.52, and (top) I m hi = 3 and (bottom) θ = 0.

Equations (5)

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i E n z + ( E n + 1 2 E n + E n 1 ) + | E n | 2 E n = 0 , n = 1 , 2 , ... , N ,
E n ( z ) I m sech { I m / 2 D [ n tan ( α ) z ] } × exp { i [ k n ( β 1 2 I m ) z + 0 ] } .
β = 2 I m [ 1 + I m 2 + O ( I m 4 ) ] , U n = { 1 1 2 I m 2 + O ( I m 4 ) n = 0 I m −| n | [ 1 + 1 2 I m 2 + O ( I m 4 ) ] n 0 .
I m 0 . 2 , | k | < π / 2 ,
I m 1 . 7

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