Abstract

An array of coupled nonlinear waveguides supports discrete soliton modes in which light is self-trapped in a few guides. We obtain an analytical description of these solitons and reveal that well-confined modes may be stably packed into the array. Power-controlled soliton steering may be achieved with linearly chirped solitons.

© 1994 Optical Society of America

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References

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  1. H. A. Haus, L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
    [CrossRef]
  2. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  3. D. N. Christodoulides, R. J. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  4. C. Schmidt-Hattenberger, U. Trutschel, F. Lederer, Opt. Lett. 16, 294 (1991).
    [CrossRef] [PubMed]
  5. T. Holstein, Ann. Phys. (Leipzig) 8, 325 (1959).
    [CrossRef]
  6. A. S. Davydov, N. I. Kislukha, Phys. Status Solidi B 59, 465 (1973).
    [CrossRef]
  7. A. C. Scott, L. MacNeil, Phys. Lett. 98 A, 87 (1983).
  8. M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
    [CrossRef]
  9. Ch. Claude, Yu. S. Kivshar, D. Kluth, K. H. Spatschek, Phys. Rev. B 47, 14228 (1993).
    [CrossRef]
  10. C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
    [CrossRef]
  11. C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
    [CrossRef]
  12. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  13. C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
    [CrossRef]
  14. V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

1993 (2)

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

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

1992 (2)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
[CrossRef]

1991 (2)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
[CrossRef]

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

1988 (1)

1983 (3)

A. C. Scott, L. MacNeil, Phys. Lett. 98 A, 87 (1983).

H. A. Haus, L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

1982 (1)

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

1981 (1)

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

1973 (1)

A. S. Davydov, N. I. Kislukha, Phys. Status Solidi B 59, 465 (1973).
[CrossRef]

1959 (1)

T. Holstein, Ann. Phys. (Leipzig) 8, 325 (1959).
[CrossRef]

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Christodoulides, D. N.

Claude, Ch.

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

Davydov, A. S.

A. S. Davydov, N. I. Kislukha, Phys. Status Solidi B 59, 465 (1973).
[CrossRef]

Haus, H. A.

H. A. Haus, L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

Holstein, T.

T. Holstein, Ann. Phys. (Leipzig) 8, 325 (1959).
[CrossRef]

Jensen, S. M.

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

Joseph, R. J.

Karpman, V. I.

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

Kislukha, N. I.

A. S. Davydov, N. I. Kislukha, Phys. Status Solidi B 59, 465 (1973).
[CrossRef]

Kivshar, Yu. S.

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

Kluth, D.

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

Lederer, F.

C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
[CrossRef]

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

MacNeil, L.

A. C. Scott, L. MacNeil, Phys. Lett. 98 A, 87 (1983).

Molina, M. I.

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

Molter-Orr, L.

H. A. Haus, L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

Muschall, R.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
[CrossRef]

Schmidt-Hattenberger, C.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
[CrossRef]

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

Scott, A. C.

A. C. Scott, L. MacNeil, Phys. Lett. 98 A, 87 (1983).

Solov’ev, V. V.

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

Spatschek, K. H.

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

Trutschel, U.

C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
[CrossRef]

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

Tsironis, G. P.

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

Ann. Phys. (1)

T. Holstein, Ann. Phys. (Leipzig) 8, 325 (1959).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. A. Haus, L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

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

Opt. Commun. (2)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 82, 461 (1991).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

C. Schmidt-Hattenberger, R. Muschall, U. Trutschel, F. Lederer, Opt. Quantum Electron. 24, 691 (1992).
[CrossRef]

Phys. Lett. (1)

A. C. Scott, L. MacNeil, Phys. Lett. 98 A, 87 (1983).

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Status Solidi B (1)

A. S. Davydov, N. I. Kislukha, Phys. Status Solidi B 59, 465 (1973).
[CrossRef]

Physica (1)

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

Physica D (1)

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Plot of normalized energy E0 versus α = E0/A2. Circles, exact DST solitons (see Ref. 7); dotted curve, the TCA; dashed curve, the CCA; solid curve, the three-waveguide approximation.

Fig. 2
Fig. 2

Interaction of DST solitons: (a) the well-confined case, C = 0.94; (b) the intermediate case, C = 0.73; (c) the distributed case, C = 0.32.

Fig. 3
Fig. 3

Soliton separation Δ versus distance ξ calculated from perturbation theory.

Fig. 4
Fig. 4

Evolution of chirped DST solitons with K = π/2 and C = 0.84 (left) or C = 0.94 (right).

Equations (6)

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i d E n d Z + β n E n + κ ( E n + 1 + E n - 1 ) + χ E n 2 E n = 0 ;             n = 2 , , N - 1.
i d Q n d ξ + Q n + 1 + Q n - 1 + 2 Q n 2 Q n = 0.
i q ξ + 2 q 2 q + 1 π - + d K - + d Y cos ( K ) q ( Y , ξ ) × exp [ i K ( X - Y ) ] = 0.
A 2 = 2 α 2 exp [ - 1 / ( 4 α 2 ) ]
i d Q 0 d ξ + 2 Q 1 + 2 Q 0 2 Q 0 = 0 , i d Q 1 d ξ + Q 0 + 2 Q 1 2 Q 1 = 0 ,
d ν d ξ = 8 A 3 exp ( - Δ A ) ,             d Δ d ξ = - 4 sin ( ν ) ,

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