Abstract

Properly designed adiabatic expansion of soliton reduces permanent frequency shifts of wavelength-division multiplexed solitons caused by initial overlap. The scheme combined with a dispersion-managed transmission line provides solutions to soliton wavelength-division multiplexing problems.

© 1996 Optical Society of America

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References

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  1. Y. Kodama, A. Hasegawa, Opt. Lett. 16, 208 (1991).
    [CrossRef] [PubMed]
  2. L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Electron. Lett. 32, 471 (1996).
    [CrossRef]
  3. R. Ohhira, A. Hasegawa, Y. Kodama, Opt. Lett. 20, 701 (1995).
    [CrossRef] [PubMed]
  4. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990); Phys. Rev. Lett. 66, 161 (1991).
    [CrossRef] [PubMed]
  5. A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 181.
  6. W. Forysiak, F. M. Knox, N. J. Doran, Opt. Lett. 19, 174 (1994).
    [CrossRef] [PubMed]
  7. A. Hasegawa, S. Kumar, Y. Kodama, Opt. Lett. 21, 39 (1996).
    [CrossRef] [PubMed]

1996 (2)

L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Electron. Lett. 32, 471 (1996).
[CrossRef]

A. Hasegawa, S. Kumar, Y. Kodama, Opt. Lett. 21, 39 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

1991 (1)

1990 (1)

Doran, N. J.

Forysiak, W.

Hasegawa, A.

Knox, F. M.

Kodama, Y.

Kumar, S.

Mamyshev, P. V.

L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Electron. Lett. 32, 471 (1996).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Electron. Lett. 32, 471 (1996).
[CrossRef]

Neubelt, M. J.

L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Electron. Lett. 32, 471 (1996).
[CrossRef]

Ohhira, R.

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Figures (4)

Fig. 1
Fig. 1

Frequency shift |ΔK(Zi)| versus β. The solid curve shows the theoretical results, and squares show the results of direct numerical simulation of Eq. (1). Parameters are ΔB = 10, T0 = 2.0, Zi = 6.8, Γ = 2.1, and Za = 0.1.

Fig. 2
Fig. 2

Frequency shift |ΔK(Zi)| versus initial separation T0. The solid curve shows the results with dispersion-increasing fiber (β = 0.57), and the dashed curve shows the results with constant dispersion [d(Z) = 1]. Parameters are ΔB = 10, Zi = 6.8, Γ = 2.1, and Za = 0.1.

Fig. 3
Fig. 3

Same as Fig. 1, with T0 = 1.2, Zi = 10, ΔB = 10, Γ = 2.1, and Za = 0.1.

Fig. 4
Fig. 4

Frequency shift |ΔK(Zi)| versus initial separation T0. The solid curve shows the results in a system with reduced gain (δ = 0.03), and the dashed curve shows the results with δ = 0 obtained from Eq. (13). Parameters are d(Z) = 1, ΔB = 10, Zi = 6.8, Γ = 2.1, and Za = 0.1.

Equations (14)

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i u Z + d ( Z ) 2 2 u T 2 + a 2 ( Z ) u 2 u = 0 .
a ( Z ) = a ( 0 ) exp [ - Γ ( Z - n Z a ) ] , n Z a < Z < ( n + 1 ) Z a ,
a ( 0 ) = [ 2 Γ Z a 1 - exp ( - 2 Γ Z a ) ] 1 / 2 .
u j = η j ( Z ) sech { η j ( Z ) [ T - T j ( Z ) ] d ( Z ) } × exp [ - i κ j ( Z ) T + i σ j ( Z ) ] ,             j = 1 , 2 ,
η ( Z ) = K d ( Z )
d Δ K d Z = - 4 η 4 ( Z ) a 2 ( Z ) d d α { f [ α ( Z ) ] } ,
α ( Z ) = Δ B 0 Z d ( Z ) d ( Z ) - T 0 d ( Z ) , f ( α ) = α cosh α - sinh α sinh 3 α .
Δ K ( Z ) = - 4 { η 4 ( Z ) a 2 ( Z ) f [ α ( Z ) ] α ( Z ) - η 4 ( 0 ) a 2 ( 0 ) f [ α ( 0 ) ] α ( 0 ) } + 4 0 Z [ η 4 ( Z ) a 2 ( Z ) α ( Z ) ] f [ α ( Z ) ] d Z .
Δ K ( ) = 4 η 4 ( 0 ) f [ T 0 / d ( 0 ) ] Δ B ,
Δ K ( Z i ) 4 η 4 ( 0 ) a 2 ( 0 ) f ( 1.763 T 0 / T in ) α ( 0 ) + 4 0 Z i [ a 2 ( Z ) d 2 ( Z ) α ( Z ) ] f [ α ( Z ) ] d Z .
expansion ratio = pulse width at  Z i T in = 1 d ( 0 ) .
d ( Z ) = β + ( 1 - β ) Z / Z i ,
Δ K ( Z i ) = 0 Z i a 1 2 ( Z ) exp [ 6 δ ( Z i - Z ) ] d d α [ f ( α ( Z ) ] d Z ,
α ( Z ) = exp [ 2 δ ( Z i - Z ) ] ( Δ B Z - T 0 ) .

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