Abstract

We show that oscillating dark solitons exist on a stable continuous plane-wave background in a cavity with a saturable defocusing nonlinearity. These oscillations can be attributed to a linear internal mode of the soliton with a complex eigenvalue emerging above a definite input field intensity. Using a simple analytical model, we find that the self-oscillations appear as a consequence of an interaction between the center of the soliton and the surrounding ring.

© 1998 Optical Society of America

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References

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  1. W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
    [CrossRef] [PubMed]
  2. N. N. Rosanov and G. V. Khodova, J. Opt. Soc. Am. B 7, 1057 (1990).
    [CrossRef]
  3. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
    [CrossRef]
  4. D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
    [CrossRef]
  5. O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
    [CrossRef]
  6. S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
    [CrossRef]
  7. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
    [CrossRef]

1997 (4)

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
[CrossRef]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

1996 (1)

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

1995 (1)

O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
[CrossRef]

1990 (1)

Aranson, I.

O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
[CrossRef]

Brambilla, M.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Firth, W. J.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

Khodova, G. V.

Kramer, L.

O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
[CrossRef]

Lederer, F.

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

Longhi, S.

Lugiato, L. A.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Michaelis, D.

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

Peschel, U.

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

Popp, S.

O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
[CrossRef]

Prati, F.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Rosanov, N. N.

Scroggie, A. J.

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Spinelli, L.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Steinmeyer, G.

Stiller, O.

O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
[CrossRef]

Wong, W. S.

J. Opt. Soc. Am. B (2)

Phys. Rev. A (1)

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
[CrossRef] [PubMed]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Physica D (1)

O. Stiller, S. Popp, I. Aranson, and L. Kramer, Physica D 87, 361 (1995).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Domain of existence, shape, and oscillations of a dark CS: (a) Shape of an oscillating dark CS Uin=4.35. (b) Oscillation of the CS dip. (c) Dip intensity of the stationary CS and extrema of the dip intensity of the oscillating dark CS compared with the CPW solution. Solid curves, stable solutions; dashed curves, unstable solutions; filled circles, stable oscillating CS’s. (d) Real and (e) imaginary parts of the eigenvalues of the mode with the largest instability gain at the lower CS branch.

Fig. 2
Fig. 2

Discrete model: (a) 1D cavity soliton and stable solution of discrete model with UB=U0; Uin=5.08, 2κ0.47. (b) Evolution of the dip and the nearest neighbors (discrete model with UBU0). The inset shows the schematic of the model κ0.47.

Fig. 3
Fig. 3

Decay of an unstable bright CS into a cluster of dark CS’s Uin=4.24.

Equations (4)

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iT+2X2+2Y2+Δ+i-sU2U2+1U=Uin,
λ0U0,Δ=-1±1U02+12×s2U04-Δ-KII2-s×U02+12+s21/2.
iT+Δ+i-sUD2UD2+1UD+2κUB-UD=Uin,
iT+Δ+i-sUB2UB2+1UB+κUD+U0-2UB=Uin.

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