Abstract

The mutual capture of two colored solitons is enhanced by a modulator, to a level which enables its practical exploitation, e.g., for a read- write mechanism in a soliton buffer. The enhanced capture was analyzed using closed form particle-like soliton perturbation, and verified by numerical simulations. Optimal modulator frequency and modulation depth are obtained. This mutual capture can be utilized for all-optical soliton logic and memory.

© 2004 Optical Society of America

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References

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  1. R.A. Barry, V.W.S. Chan, K.L. Hall, E.S. Kintzer, J.D. Moors, K.A. Rauschenbach, E.A. Swanson, L.E. Adams, C.R. Doerr, S.G. Finn, H.A. Haus, E.P. Ippen, W.S. Wong, M. Haner, ???All-optical network consortium ??? ultrafast TDM netwarks,??? J. Sel. Areas In Com. 14, 999-1012 (1996).
    [CrossRef]
  2. E. Feigenbaum, M. Orenstein, ???Colored solitons interactions: particle-like and beyond,??? Opt. Express 12, 2193-2206 (2004),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2193">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2193</a>
    [CrossRef] [PubMed]
  3. M. Nakazawa, H. Kubota, E. Yamada, K. Suzuki, ???Infinite-distance soliton transmission with soliton controls in time and frequency domains,??? Elec. Lett. 28, p. 1099-1100 (1992).
    [CrossRef]
  4. J.D. Moors, W.S. Wong, H.A. Haus, ???Stability and timing maintenance in soliton transmission and storage rings,??? Opt. Comm. 113, p. 153-175 (1994).
    [CrossRef]
  5. H.A. Haus, ???Lecture 11??? in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V.E. Zakarov and S. Wabnitz Ed. (Springer, NY,1999).
  6. M. Karlsson, D Anderson, A Höök, M. Lisak, "A variational approach to optical soliton collisions," Phys. Scripta 50, 265-270 (1994).
    [CrossRef]
  7. N. C. Panoiu, I. V. Mel`nikov, D. Mihalache, C. Etrich, F. Lederer, ???Soliton generation in optical fibers for dual-frequency input,??? Phys. Rev. E 60, 4868-4876 (1999).
    [CrossRef]
  8. V. V. Afanasjev, V. A. Vysloukh, ???Interaction of initially overlapping solitons with different frequencies,??? J. Opt. Soc. Am. B 11, 2385-2393 (1994).
    [CrossRef]
  9. N.C. Panoiu, D. Mihalache, D. Mazilu, L.C. Crasovan, I.V. Mel???nikov, ???Soliton dynamics of symmetry-endowed two-soiton solutions of the nonlinear Schrodinger equation,??? Chaos 10, 625-640 (2000).
    [CrossRef]
  10. C. Etrich, N.C. Panoiu, D. Mihalache, F. Lederer, ???Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system,??? Phys. Rev. E 63, 016609 (2001).
    [CrossRef]
  11. N.C. Panoiu, I.V. Mel???nikov, D. Mihalache, C. Etrich, F. Lederer, ???Soliton generation from a multi-frequency optical signal,??? J. Opt. B: Quantum Semiclass. Opt. 4, R53-R68 (2002).
    [CrossRef]
  12. G.P. Agrawal, Nonlinear Fiber Optics, 2nd ed.(Academic,NY, 1995).
  13. 13. V.I. Karpman, V.V. Solov???ev, ???A perturbational approach to the two-soliton systems,??? Physica D 3, 487-502 (1981).
    [CrossRef]
  14. H.A. Haus, W.S. Wong, ???Solitons in optical communications,??? Rev. of Mod. Phys. 68, 423-444 (1996).
    [CrossRef]
  15. S.M.J. Kelly, ???Characteristic sideband instability of periodically amplified average soliton,??? Elec. Lett. 28, 806-807 (1992).
    [CrossRef]
  16. H.A. Haus, W.S. Wong, F.I. Kharti, ???Continuum generation by perturbation of soliton,??? J. Opt. Soc. Am. B. 14, 304 -313(1997)
    [CrossRef]

Chaos (1)

N.C. Panoiu, D. Mihalache, D. Mazilu, L.C. Crasovan, I.V. Mel???nikov, ???Soliton dynamics of symmetry-endowed two-soiton solutions of the nonlinear Schrodinger equation,??? Chaos 10, 625-640 (2000).
[CrossRef]

Elec. Lett. (2)

M. Nakazawa, H. Kubota, E. Yamada, K. Suzuki, ???Infinite-distance soliton transmission with soliton controls in time and frequency domains,??? Elec. Lett. 28, p. 1099-1100 (1992).
[CrossRef]

S.M.J. Kelly, ???Characteristic sideband instability of periodically amplified average soliton,??? Elec. Lett. 28, 806-807 (1992).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

N.C. Panoiu, I.V. Mel???nikov, D. Mihalache, C. Etrich, F. Lederer, ???Soliton generation from a multi-frequency optical signal,??? J. Opt. B: Quantum Semiclass. Opt. 4, R53-R68 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Am. B. (1)

H.A. Haus, W.S. Wong, F.I. Kharti, ???Continuum generation by perturbation of soliton,??? J. Opt. Soc. Am. B. 14, 304 -313(1997)
[CrossRef]

J. Sel. Areas In Com. (1)

R.A. Barry, V.W.S. Chan, K.L. Hall, E.S. Kintzer, J.D. Moors, K.A. Rauschenbach, E.A. Swanson, L.E. Adams, C.R. Doerr, S.G. Finn, H.A. Haus, E.P. Ippen, W.S. Wong, M. Haner, ???All-optical network consortium ??? ultrafast TDM netwarks,??? J. Sel. Areas In Com. 14, 999-1012 (1996).
[CrossRef]

Opt. Comm. (1)

J.D. Moors, W.S. Wong, H.A. Haus, ???Stability and timing maintenance in soliton transmission and storage rings,??? Opt. Comm. 113, p. 153-175 (1994).
[CrossRef]

Opt. Express (1)

E. Feigenbaum, M. Orenstein, ???Colored solitons interactions: particle-like and beyond,??? Opt. Express 12, 2193-2206 (2004),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2193">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2193</a>
[CrossRef] [PubMed]

Phys. Rev. E (2)

C. Etrich, N.C. Panoiu, D. Mihalache, F. Lederer, ???Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system,??? Phys. Rev. E 63, 016609 (2001).
[CrossRef]

N. C. Panoiu, I. V. Mel`nikov, D. Mihalache, C. Etrich, F. Lederer, ???Soliton generation in optical fibers for dual-frequency input,??? Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

Phys. Scripta (1)

M. Karlsson, D Anderson, A Höök, M. Lisak, "A variational approach to optical soliton collisions," Phys. Scripta 50, 265-270 (1994).
[CrossRef]

Physica D (1)

13. V.I. Karpman, V.V. Solov???ev, ???A perturbational approach to the two-soliton systems,??? Physica D 3, 487-502 (1981).
[CrossRef]

Rev. of Mod. Phys. (1)

H.A. Haus, W.S. Wong, ???Solitons in optical communications,??? Rev. of Mod. Phys. 68, 423-444 (1996).
[CrossRef]

Other (2)

G.P. Agrawal, Nonlinear Fiber Optics, 2nd ed.(Academic,NY, 1995).

H.A. Haus, ???Lecture 11??? in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V.E. Zakarov and S. Wabnitz Ed. (Springer, NY,1999).

Supplementary Material (2)

» Media 1: AVI (442 KB)     
» Media 2: AVI (589 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Schematics of Read-Write of storage ring using colored solitons capture. The first and last data bits (red) are captured to control bits (blue) and read out (green).

Fig. 2.
Fig. 2.

Modulation index (M/zm) required for capture vs. modulator frequency (ωm). Each curve is normalized by its minimum modulation index. β”=-2, δ=1.3 (a) different p0 , W=1. (b) different W, p0=0.16×2π.

Fig. 3.
Fig. 3.

Modulator assisted selective DATA bit capture using CONTROL bit. (a) (0.37Mb) No modulator, Data soliton=“1”, Control soliton=“1”. Modulator applied, Data soliton=“1”: (b) (0.36Mb) Control soliton=“1” (c) Control soliton=“0”. p1,2=±0.2×2π, τ1,2=0, θ12=0, ωm=εW, M/zm=0.13/z0, gain=0.05/z0, β”=-2, δ=1.3,W=1.

Fig. 4.
Fig. 4.

Modulator assisted capture threshold vs. modulation depth, w/wo second soliton. τ1,2=0, θ12=0, W=1. ωm=εW. β”=-2, δ=1.3.

Fig. 5.
Fig. 5.

Decay coefficient of captured soliton oscillations vs. the modulator frequency. p1,2=±0.1×2π, gain=τ1,212=0, M/zm=0.1/z0, β”=-2, δ=1.3, W=1.

Fig. 6.
Fig. 6.

Oscillation decay coefficient vs. M-phase. p1,2=±0.05×2π, W=1, M=0.5, zm=1.2z0. β”=-2, δ=1.3, distributed gain=0.017/z0.

Equations (9)

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z ( β p ) = 2 δ 2 W 4 + d ξ { tanh ( ε W ξ ) sech 2 ( ε W ξ ) sech 2 ( ε W ( ξ + 2 τ ) ) }
z τ = ( β p )
z τ = β p + S τ
z 2 τ z ( β p ) V z τ = z S τ ; V = z S τ
T = 1 + 1 2 M ( cos ( ω m ( t t m ) ) 1 )
s = j z u = j ( 1 T z m ) u = j ( M 2 z m ) ( 1 cos ( ω m ( t t m ) ) ) u
2 p 10 ( δ β W z m )
S τ M = ( M z m ) 1 2 ε W + dt { ( t τ ) sech 2 ( ε W ( t τ ) ) cos ( ω m ( t t m ) ) }
V = M z m cos ( ω m Δ τ m ) f V ( ω m ) ; f V + d ξ { ( 1 2 ξ tanh ( ξ ) ) sech 2 ( ξ ) cos ( ω m ε W ξ ) }

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