Abstract

Bistable soliton (for which the nonlinear propagation constant shift is a double-valued function of energy) solutions to the pulse evolution equation for a doubly but inhomogeneously doped (with one of the dopants) fiber are obtained numerically. Their physical characteristics are obtained and studied. It is shown that the theoretical prediction can be experimentally verified by a pair of dopants from an already available lot of dopants.

© 1999 Optical Society of America

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References

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  4. R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
    [CrossRef]
  5. P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. A. Kumar, Phys. Rep. 187, 63 (1990).
    [CrossRef]
  9. A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
    [CrossRef]
  10. A. W. Snyder, D. J. Mitchell, and A. Buryak, J. Opt. Soc. Am. 13, 1146 (1996).
    [CrossRef]
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    [CrossRef]

1997

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
[CrossRef]

1996

A. W. Snyder, D. J. Mitchell, and A. Buryak, J. Opt. Soc. Am. 13, 1146 (1996).
[CrossRef]

1993

1992

R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
[CrossRef]

1991

R. H. Enns, R. Fung, and S. S. Rangnekar, IEEE J. Quantum Electron. 27, 253 (1991).
[CrossRef]

1990

A. Kumar, Phys. Rep. 187, 63 (1990).
[CrossRef]

1989

1988

1985

A. E. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

A. E. Kaplan, IEEE J. Quantum Electron. QE-21, 1538 (1985).
[CrossRef]

Buryak, A.

A. W. Snyder, D. J. Mitchell, and A. Buryak, J. Opt. Soc. Am. 13, 1146 (1996).
[CrossRef]

Buryak, A. V.

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
[CrossRef]

Chu, P. L.

Enns, R. H.

R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
[CrossRef]

R. H. Enns, R. Fung, and S. S. Rangnekar, IEEE J. Quantum Electron. 27, 253 (1991).
[CrossRef]

Fung, R.

R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
[CrossRef]

R. H. Enns, R. Fung, and S. S. Rangnekar, IEEE J. Quantum Electron. 27, 253 (1991).
[CrossRef]

Hasegawa, A.

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
[CrossRef]

Kaplan, A. E.

R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
[CrossRef]

A. E. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

A. E. Kaplan, IEEE J. Quantum Electron. QE-21, 1538 (1985).
[CrossRef]

Kivshar, Yu. S.

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
[CrossRef]

Kumar, A.

A. Kumar, Phys. Rep. 187, 63 (1990).
[CrossRef]

Malomed, B. A.

Mitchell, D. J.

A. W. Snyder, D. J. Mitchell, and A. Buryak, J. Opt. Soc. Am. 13, 1146 (1996).
[CrossRef]

Peng, G. D.

Rangnekar, S. S.

R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
[CrossRef]

R. H. Enns, R. Fung, and S. S. Rangnekar, IEEE J. Quantum Electron. 27, 253 (1991).
[CrossRef]

Snyder, A. W.

A. W. Snyder, D. J. Mitchell, and A. Buryak, J. Opt. Soc. Am. 13, 1146 (1996).
[CrossRef]

Stegeman, G. I.

Stolen, R. H.

Trillo, S.

Wabnitz, S.

Wright, E. M.

IEEE J. Quantum Electron.

A. E. Kaplan, IEEE J. Quantum Electron. QE-21, 1538 (1985).
[CrossRef]

R. H. Enns, R. Fung, and S. S. Rangnekar, IEEE J. Quantum Electron. 27, 253 (1991).
[CrossRef]

J. Opt. Soc. Am.

A. W. Snyder, D. J. Mitchell, and A. Buryak, J. Opt. Soc. Am. 13, 1146 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Quantum Electron.

R. H. Enns, R. Fung, S. S. Rangnekar, and A. E. Kaplan, Opt. Quantum Electron. 24, 295 (1992).
[CrossRef]

Phys. Rep.

A. Kumar, Phys. Rep. 187, 63 (1990).
[CrossRef]

Phys. Rev. Lett.

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
[CrossRef]

A. E. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

Other

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Soliton shape Ψτ for α=0.08, δ=5.0, and σ=1.175, corresponding to curve I of Fig.  1. Soliton a P=0.93 belongs to the lower positive slope branch of the Pβ curve and is stable, soliton b P=1.82 belongs to the negative slope branch of the Pβ curve and is unstable, and soliton c P=2.12 belongs to the upper positive slope branch of Pβ and is stable.

Equations (14)

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

2E-1c22DLt2=1c22DNLt2,
DL=0εtEt-tdt,
DNL=ε21+αε22frE2E1+E2/Is,
fr=expχr2r<a0ra,
Ex,y,z,t=eRrAz,texp-iωt-β0z,
iqξ+12qττ+fq2q=0,
fq2=1-ln1+q2q2-αδq2ln1+exp-σ×q2-q2ln1+q2.
q=A/Is,ξ=ωn21Is/cz,τ=ωn21Is/c-2β0/ω21/2t-zvg,
δ=n22/n21,
σ=a2/r02.
qξ,τ=Ψτexpiβξ,
limτΨτ=limτdΨτ/dτ=0.
Ψ4Ψ-Ψ28 Ψ2+1-β-ln1+ΨΨ+αδΨln1+Ψ-δαΨln1+exp-σΨ=0.
P=-q2dτ.

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