Abstract

Switching of bistable solitons in a recently proposed doubly and inhomogeneously doped fiber system [Phys. Rev. E 58, 5021 (1998)] is studied numerically. It is shown that both upswitching and downswitching of solitons between bistable states are realizable in the given model if the amplification of the input soliton for upswitching and the extraction of energy from it for downswitching are suitably adjusted.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agarwal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  2. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional coupler,” Opt. Lett. 13, 672–674 (1988).
    [CrossRef]
  3. A. B. Aceves and M. Santagiustina, “Bistable and tristable soliton switching in collinear arrays of linearly coupled waveguides,” Phys. Rev. E 56, 1113–1123 (1997).
    [CrossRef]
  4. P. L. Chu, B. A. Malomed, and G. D. Peng, “Analytical solution for soliton switching in a nonlinear twin-core fiber,” Opt. Lett. 18, 328–320 (1993).
    [CrossRef] [PubMed]
  5. A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
    [CrossRef] [PubMed]
  6. R. H. Enns, R. Fung, and S. S. Rangnekar, “Application of optical cross-talk to switching between bistable soliton states,” IEEE J. Quantum Electron. 27, 252–258 (1991).
    [CrossRef]
  7. L. J. Mulder and R. H. Enns, “Optical switching between damped bistable soliton states using periodic amplifiers,” IEEE J. Quantum Electron. 24, 1567–1570 (1988).
    [CrossRef]
  8. G. Dattoli, F. P. Orsitto, and A. Torre, “Evidence of multistability of light solitons in SF6 absorption measurements,” Opt. Lett. 14, 456–458 (1989).
    [CrossRef] [PubMed]
  9. R. Mcleod, K. Wagner, and S. Blair, “(3+1) dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
    [CrossRef] [PubMed]
  10. A. Kumar, “Bistability and hyteresis of solitons in doubly inhomogeneously doped fibers with saturating nonlinearity,” Phys. Rev. E 58, 5021–5024 (1998).
    [CrossRef]
  11. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  12. R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
    [CrossRef]

1998 (1)

A. Kumar, “Bistability and hyteresis of solitons in doubly inhomogeneously doped fibers with saturating nonlinearity,” Phys. Rev. E 58, 5021–5024 (1998).
[CrossRef]

1997 (1)

A. B. Aceves and M. Santagiustina, “Bistable and tristable soliton switching in collinear arrays of linearly coupled waveguides,” Phys. Rev. E 56, 1113–1123 (1997).
[CrossRef]

1995 (1)

R. Mcleod, K. Wagner, and S. Blair, “(3+1) dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

1993 (1)

1992 (1)

R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
[CrossRef]

1991 (1)

R. H. Enns, R. Fung, and S. S. Rangnekar, “Application of optical cross-talk to switching between bistable soliton states,” IEEE J. Quantum Electron. 27, 252–258 (1991).
[CrossRef]

1989 (1)

1988 (2)

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional coupler,” Opt. Lett. 13, 672–674 (1988).
[CrossRef]

L. J. Mulder and R. H. Enns, “Optical switching between damped bistable soliton states using periodic amplifiers,” IEEE J. Quantum Electron. 24, 1567–1570 (1988).
[CrossRef]

1985 (1)

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
[CrossRef] [PubMed]

Aceves, A. B.

A. B. Aceves and M. Santagiustina, “Bistable and tristable soliton switching in collinear arrays of linearly coupled waveguides,” Phys. Rev. E 56, 1113–1123 (1997).
[CrossRef]

Blair, S.

R. Mcleod, K. Wagner, and S. Blair, “(3+1) dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Chu, P. L.

Dattoli, G.

Edmundson, D. E.

R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
[CrossRef]

Enns, R. H.

R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
[CrossRef]

R. H. Enns, R. Fung, and S. S. Rangnekar, “Application of optical cross-talk to switching between bistable soliton states,” IEEE J. Quantum Electron. 27, 252–258 (1991).
[CrossRef]

L. J. Mulder and R. H. Enns, “Optical switching between damped bistable soliton states using periodic amplifiers,” IEEE J. Quantum Electron. 24, 1567–1570 (1988).
[CrossRef]

Fung, R.

R. H. Enns, R. Fung, and S. S. Rangnekar, “Application of optical cross-talk to switching between bistable soliton states,” IEEE J. Quantum Electron. 27, 252–258 (1991).
[CrossRef]

Kaplan, A. E.

R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
[CrossRef]

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
[CrossRef] [PubMed]

Kumar, A.

A. Kumar, “Bistability and hyteresis of solitons in doubly inhomogeneously doped fibers with saturating nonlinearity,” Phys. Rev. E 58, 5021–5024 (1998).
[CrossRef]

Malomed, B. A.

Mcleod, R.

R. Mcleod, K. Wagner, and S. Blair, “(3+1) dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Mulder, L. J.

L. J. Mulder and R. H. Enns, “Optical switching between damped bistable soliton states using periodic amplifiers,” IEEE J. Quantum Electron. 24, 1567–1570 (1988).
[CrossRef]

Orsitto, F. P.

Peng, G. D.

Rangnekar, S. S.

R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
[CrossRef]

R. H. Enns, R. Fung, and S. S. Rangnekar, “Application of optical cross-talk to switching between bistable soliton states,” IEEE J. Quantum Electron. 27, 252–258 (1991).
[CrossRef]

Santagiustina, M.

A. B. Aceves and M. Santagiustina, “Bistable and tristable soliton switching in collinear arrays of linearly coupled waveguides,” Phys. Rev. E 56, 1113–1123 (1997).
[CrossRef]

Stegeman, G. I.

Torre, A.

Trillo, S.

Wabnitz, S.

Wagner, K.

R. Mcleod, K. Wagner, and S. Blair, “(3+1) dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Wright, E. M.

IEEE J. Quantum Electron. (2)

R. H. Enns, R. Fung, and S. S. Rangnekar, “Application of optical cross-talk to switching between bistable soliton states,” IEEE J. Quantum Electron. 27, 252–258 (1991).
[CrossRef]

L. J. Mulder and R. H. Enns, “Optical switching between damped bistable soliton states using periodic amplifiers,” IEEE J. Quantum Electron. 24, 1567–1570 (1988).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

R. H. Enns, D. E. Edmundson, S. S. Rangnekar, and A. E. Kaplan, “Optical switching between bistable soliton states: a theoretical review,” Opt. Quantum Electron. 24, 1295–1314 (1992).
[CrossRef]

Phys. Rev. A (1)

R. Mcleod, K. Wagner, and S. Blair, “(3+1) dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

A. Kumar, “Bistability and hyteresis of solitons in doubly inhomogeneously doped fibers with saturating nonlinearity,” Phys. Rev. E 58, 5021–5024 (1998).
[CrossRef]

A. B. Aceves and M. Santagiustina, “Bistable and tristable soliton switching in collinear arrays of linearly coupled waveguides,” Phys. Rev. E 56, 1113–1123 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
[CrossRef] [PubMed]

Other (2)

G. P. Agarwal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Soliton energy versus nonlinear propagation constant shift β for α=0.08, δ=5.0, and σ=1.175.

Fig. 2
Fig. 2

(a) Upswitching of the LPSB soliton with peak intensity u0=1.35 and β=5.6484×10-3 for κ=0.1, A=3.0, and L=0.085Lc. (b) Localized radiation that leaks into the second core during the switching depicted in (a). (c) Upswitching of the LPSB soliton with peak intensity u0=1.35 and β=5.6484×10-3, for κ=0.5, A=3.0, and L=0.38Lc.

Fig. 3
Fig. 3

(a) Downswitching of the input soliton with peak intensity u0=10.0 (β=9.4677×10-3) to a soliton of peak intensity u0=1.15 (β=5.2133×10-3) for κ=0.5. (b) Evolution of the radiation acquired by the second core during the downswitching depicted in (a).

Fig. 4
Fig. 4

(a) Intermediate downswitching to a soliton of peak intensity u0=8.62 (β=8.1817×10-3) and further propagation of the switched pulse for the input soliton with peak intensity u0=12.0 (β=1.149×10-2) with A=0.85 and κ=0.1. (b) Evolution of the radiation acquired by the second core during the intermediate switching process depicted in (a). (c) Final downswitching of the intermediate soliton to a soliton of peak intensity u0=1.35 (β=5.648×10-3) and further propagation of the switched pulse with A=0.45 and κ=0.1.

Equations (6)

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

iuξ+122uτ2+f(|u|2)u=-κv,
ivξ+122vτ2+f(|v|2)v=-κu,
κ=cκlωn2IS,
f(|u|2)=1-ln(1+|u|2)|u|2-αδ[σ|u|2-|u|2 ln(1+|u|2)+ln(1+e-σ|u|2)],
q(ξ, τ)=ψ(τ) exp(iβξ),
limτ± ψ(τ)=limτ±dψ(τ)dτ=0

Metrics