Abstract

We propose a setup to observe soliton ratchet effects using discrete cavity solitons in a 1D array of coupled waveguide optical resonators. The net motion of solitons can be generated by an adiabatic shaking of the holding beam with zero average inclination angle. The resulting soliton velocity can be controlled by different parameters of the holding beam.

© 2006 Optical Society of America

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References

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  1. W. J. Firth and G. K. Harkness, in Spatial Solitons, S.Trillo and W.Torruelas, eds. (Springer, 2001), p. 343.
  2. U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
    [CrossRef]
  3. N. Akhmediev, A. Ankiewicz, eds., Dissipative Solitons, Vol. 66 of Lecture Notes in Physics (Springer, 2005).
    [CrossRef]
  4. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
    [CrossRef] [PubMed]
  5. B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
    [CrossRef] [PubMed]
  6. Y. F. Chen and Y. P. Lan, Phys. Rev. Lett. 93, 013901 (2004).
    [CrossRef]
  7. U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
    [CrossRef]
  8. S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
    [CrossRef] [PubMed]
  9. M. Salerno and Y. Zolotaryuk, Phys. Rev. E 65, 056603 (2003).
    [CrossRef]
  10. A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
    [CrossRef] [PubMed]
  11. U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
    [CrossRef] [PubMed]
  12. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef] [PubMed]
  13. S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
    [CrossRef]
  14. O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
    [CrossRef]

2005

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

2004

U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
[CrossRef] [PubMed]

Y. F. Chen and Y. P. Lan, Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

2003

M. Salerno and Y. Zolotaryuk, Phys. Rev. E 65, 056603 (2003).
[CrossRef]

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

2002

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
[CrossRef] [PubMed]

2001

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

2000

B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

1987

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

Ackermann, T.

B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Akhmediev, N.

N. Akhmediev, A. Ankiewicz, eds., Dissipative Solitons, Vol. 66 of Lecture Notes in Physics (Springer, 2005).
[CrossRef]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, eds., Dissipative Solitons, Vol. 66 of Lecture Notes in Physics (Springer, 2005).
[CrossRef]

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Barland, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Bortolozzo, U.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Chen, Y. F.

Y. F. Chen and Y. P. Lan, Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

Coqui, C.

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

Egorov, O.

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
[CrossRef] [PubMed]

Etrich, C.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Fedorov, S.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Feldmann, M.

B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and G. K. Harkness, in Spatial Solitons, S.Trillo and W.Torruelas, eds. (Springer, 2001), p. 343.

Fistul, M. F.

S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
[CrossRef] [PubMed]

Flach, S.

S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
[CrossRef] [PubMed]

Giudici, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Harkness, G. K.

W. J. Firth and G. K. Harkness, in Spatial Solitons, S.Trillo and W.Torruelas, eds. (Springer, 2001), p. 343.

Jager, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Kemp, A.

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

Knodl, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Kozyreff, G.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Lan, Y. P.

Y. F. Chen and Y. P. Lan, Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

Lange, W.

B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Lederer, F.

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
[CrossRef] [PubMed]

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Lefever, R.

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

Lugiato, L. A.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

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

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Michaelis, D.

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Miller, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
[CrossRef] [PubMed]

Pastur, L.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Peschel, U.

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
[CrossRef] [PubMed]

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Ramazza, P. L.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Rosanov, N.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Salerno, M.

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

M. Salerno and Y. Zolotaryuk, Phys. Rev. E 65, 056603 (2003).
[CrossRef]

Schäpers, B.

B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Skryabin, D. V.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Tidi, M.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Tissoni, G.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Tredicce, J. R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Ustinov, A. V.

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

Weiss, C. O.

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

Zolotaryuk, Y.

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

M. Salerno and Y. Zolotaryuk, Phys. Rev. E 65, 056603 (2003).
[CrossRef]

S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

Nature

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. E

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

M. Salerno and Y. Zolotaryuk, Phys. Rev. E 65, 056603 (2003).
[CrossRef]

Phys. Rev. Lett.

A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
[CrossRef] [PubMed]

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

B. Schäpers, M. Feldmann, T. Ackermann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
[CrossRef] [PubMed]

Y. F. Chen and Y. P. Lan, Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tidi, and G. Kozyreff, Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. F. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
[CrossRef] [PubMed]

Other

N. Akhmediev, A. Ankiewicz, eds., Dissipative Solitons, Vol. 66 of Lecture Notes in Physics (Springer, 2005).
[CrossRef]

W. J. Firth and G. K. Harkness, in Spatial Solitons, S.Trillo and W.Torruelas, eds. (Springer, 2001), p. 343.

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Figures (4)

Fig. 1
Fig. 1

Schematic setup of coupled waveguides with mirrors at the end facets.

Fig. 2
Fig. 2

(a) Dark and (b) bright DCS profiles. Black lines and circles: stationary DCSs for the input power a 2 = 3.3 at normal incidence ϕ in = 0 . Model parameters are (a) α = 1 , Δ = 3 , C = 0.55 ; (b) α = 1 , Δ = 3 , C = 15 . Gray lines and crosses: snapshots of moving DCSs for the ratchet case with the same parameters as in Fig. 3.

Fig. 3
Fig. 3

Density plots of A n 2 for soliton motion in the ratchet case with initial conditions corresponding to stationary DCSs. Model parameters are the same as in Fig. 2a (a) Dark DCS driven by the single shaking beam [Eqs. (2, 7)], a 2 = 3.3 , ϕ a = ϕ b = 0.025 , ω = 0.01 , θ = 1.72 π . (b) Bright DCS driven by two shaking beams [Eq. (8)], a 2 = b 2 = 1.2 , ϕ a = ϕ b = 0.001 , ω = 0.002 , θ = 0.57 π .

Fig. 4
Fig. 4

Soliton displacement per period T as a function of the relative phase θ for dark (green line) and bright (black line) solitons. All the parameters are the same as in Figs. 3a, 3b, respectively.

Equations (10)

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

( i τ + Δ + i + α A n 2 ) A n + C ( A n + 1 + A n 1 2 A n ) = A n in ,
A n in = a exp ( i ϕ in n ) ,
[ Δ 4 C sin 2 ( ϕ in ) + i + α a GS 2 ] a GS = a .
X ( τ ) = n n A n ( τ ) 2 I GS ( τ ) n A n ( τ ) 2 I GS ( τ ) , V ( τ ) = X ̇ ( τ ) .
ϕ in ( τ + T 2 ) = ϕ in ( τ ) .
S ̂ a : τ τ + T 2 , n n .
ϕ in ( τ ) = ϕ a sin ( ω τ ) + ϕ b sin ( 2 ω τ + θ ) .
A n in = a exp [ i ϕ in ( 1 ) ( τ ) n ] + b exp [ i ϕ in ( 2 ) ( τ ) n ] ,
ϕ in ( 1 ) = ϕ a sin ( ω τ ) n , ϕ in ( 2 ) = ϕ b sin ( 2 ω τ + θ ) n .
V = 1 T 0 T V [ ϕ in ( τ ) ] d τ .

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