Abstract

We derive evolution equations describing light propagation in an array of coupled-waveguide resonators and predict the existence of discrete cavity solitons. We identify stable, unstable, and oscillating solitons by varying the coupling strength between the anticontinuous and the continuous limit.

© 2004 Optical Society of America

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References

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  1. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  3. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  4. W. J. Firth, Phys. Rev. Lett. 61, 329 (1988).
    [CrossRef] [PubMed]
  5. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef] [PubMed]
  6. S. Aubry, Physica D 86, 284 (1995).
    [CrossRef]
  7. W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).
  8. M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
    [CrossRef]

2001 (1)

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

1999 (1)

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

1998 (2)

W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

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

1995 (1)

S. Aubry, Physica D 86, 284 (1995).
[CrossRef]

1988 (2)

1987 (1)

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

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

Aubry, S.

S. Aubry, Physica D 86, 284 (1995).
[CrossRef]

Bayer, M.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Boyd, A. R.

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

Christodoulides, D. N.

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

Firth, W. J.

W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

W. J. Firth, Phys. Rev. Lett. 61, 329 (1988).
[CrossRef] [PubMed]

Forchel, A.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Gutbrod, T.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Harkness, G. K.

W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

Joseph, R. I.

Knipp, P. A.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Lefever, R.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Lugiato, L. A.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

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

Reinecke, T. L.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Reithmaier, J. P.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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

Sorel, M.

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

Werner, R.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Asian J. Phys. (1)

W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

Opt. Lett. (1)

Phys. Rev. Lett. (5)

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

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

W. J. Firth, Phys. Rev. Lett. 61, 329 (1988).
[CrossRef] [PubMed]

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Physica D (1)

S. Aubry, Physica D 86, 284 (1995).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Coupled cavities formed by a waveguide array with mirrors on each end facet.

Fig. 2
Fig. 2

Hysteresis loops of DCSs for the defocusing case: thick gray curve, homogeneous solution (solid, stable; dashed, unstable; dotted, modulationally unstable); black curve, peak power of DCSs (solid, stable; dashed, unstable). Insets, stable DCSs of different order; parameters: α=1,Δeff=3,C=0.25,φin=0.

Fig. 3
Fig. 3

DCSs without a continuous limit (defocusing case); parameters: α=-1, Ain2=3.3, Δeff=3 (solid curve, stable; dashed curve, unstable).

Fig. 4
Fig. 4

Coexistence of different types of stable DCS; parameters: α=-1, Δeff=3, C=0.25, Ain2=3.3.

Fig. 5
Fig. 5

DCSs with a continuous limit (focusing case, α=1, Ain2=3.3, Δeff=-3). (a) Transition from the anticontinuous toward the continuous limit (solid curve, stable; dashed curve, oscillatory unstable). Inset, respective eigenvalue λ of the linearized problem assuming a growth of small perturbations expλt. (b) Oscillating DCS C=5.

Equations (6)

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±iz+ivgt+β0un±+cun+1±+un-1±+pn±=0,
u+κ,ω,z=1τaτκ,ω×expiβ0+ωvg+2c cos κz-d-izddzp+κ,ω,z×expiβ0+ωvg+2c cos κz-z,u-κ,ω,z=ρτaτκ,ω×exp-iβ0+ωvg+2c cos κz-d+izddzp-κ,ω,z×exp-iβ0+ωvg+2c cos κz-z.
expiβ0+ω/vg+2c cos κd-ρ2 expiβ0+ω/vg+2c cos κdaτ=τ2ain+iτ0ddzp+ exp-iβ0+ω/vg+2c cos κz+ ρp- expiβ0+ω/vg+2c cos κz.
2dvgt+1-ρ2-iDanτ-2icdan+1τ+an-1τ=τ2ain+iτ0ddzp+ exp-iβ0z+ρp- expiβ0z.
2dvgt+1-ρ2-iDanτ-2icdan+1τ+an-1τ=1-ρ2ain+i6d1-ρ2n2Aeffωcanτ2anτ.
iddT+Δ+i+αAn2An+CAn+1+An-1=A˜nin,

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