Abstract

A two-parameter family of single- and multiple-hump solitary waves in a fiber transmission line with periodically aligned semiconductor optical amplifiers and fixed in-line filters can be identified, provided that the dispersion length considerably exceeds the spacing period and that the average-soliton concept can be adopted. These solitary waves are robust against fluctuations of the input amplitude. We show that the finite gain recovery time of the amplifier leads to the formation of topological solitons. Multiple-hump solutions decay into pulses with equal amplitudes if the dispersion length is comparable with the amplifier spacing.

© 1999 Optical Society of America

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1999 (1)

N. N. Akhmediev, M. J. Lederer, and B. Luther-Davies, Phys. Rev. E 57, 3664 (1999).
[CrossRef]

1997 (4)

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, Opt. Lett. 22, 1406 (1997).
[CrossRef]

1996 (2)

1995 (3)

1991 (2)

1989 (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, M. J. Lederer, and B. Luther-Davies, Phys. Rev. E 57, 3664 (1999).
[CrossRef]

Gabitov, I.

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

Gölles, M.

I. M. Uzunov, M. Gölles, and F. Lederer, Opt. Lett. 22, 1406 (1997).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Grigoryan, V. S.

Hägele, V.

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

Hasegawa, A.

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

Kodama, Y.

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

Lederer, F.

I. M. Uzunov, M. Gölles, and F. Lederer, Opt. Lett. 22, 1406 (1997).
[CrossRef]

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Lederer, M. J.

N. N. Akhmediev, M. J. Lederer, and B. Luther-Davies, Phys. Rev. E 57, 3664 (1999).
[CrossRef]

Luther-Davies, B.

N. N. Akhmediev, M. J. Lederer, and B. Luther-Davies, Phys. Rev. E 57, 3664 (1999).
[CrossRef]

Matera, F.

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

Mattheus, A.

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

Mattheus, A. W.

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

Mecozzi, A.

Michaelis, D.

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

Muradyan, T. S.

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Onishchukov, G.

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

Peschel, U.

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

Riedel, P.

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

Settembre, M.

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

Shipulin, A.

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

Turitsyn, S.

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

Turitsyn, S. K.

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

S. K. Turitsyn, Phys. Rev. E 54, R3125 (1996).
[CrossRef]

Uzunov, I. M.

I. M. Uzunov, M. Gölles, and F. Lederer, Opt. Lett. 22, 1406 (1997).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Wabnitz, S.

Zengerle, R.

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

Electron. Lett. (1)

A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

J. Lightwave Technol. (1)

M. Settembre, F. Matera, V. Hägele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, J. Lightwave Technol. 15, 962 (1997).
[CrossRef]

J. Opt. Commun. (1)

V. Hägele, A. Mattheus, R. Zengerle, I. Gabitov, and S. K. Turitsyn, J. Opt. Commun. 18, 213 (1997).

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

Opt. Lett. (4)

Phys. Rev. E (3)

S. K. Turitsyn, Phys. Rev. E 54, R3125 (1996).
[CrossRef]

N. N. Akhmediev, M. J. Lederer, and B. Luther-Davies, Phys. Rev. E 57, 3664 (1999).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Time-dependent gain h(t) and pulse shape at the SOA output with h0=2.788 and tc=200 ps: exact solution (filled circles), first approximation (dashed curve), and second approximation (thicker solid curves) for (a), (c) Esat=2.2 pJ and (b), (d) Esat=0.5 pJ, where |Ain(t)|2=2 mW sech(t/4 ps). The thinner solid curves apply to Esat.

Fig. 2
Fig. 2

SW solutions for infinite gain recovery time and without TOD.

Fig. 3
Fig. 3

Evolution of a double-hump SW (κ=-0.4952, Γ=0.33812) for infinite gain recovery time without TOD. Shown are the profile at Z=3 (solid curve) together with a noisy input signal (x0=0.14) (filled circles) and the solitary-wave solution (open squares); inset, evolution of the chirp parameters of the leading (solid line) and the trailing (dashed line) pulses.

Fig. 4
Fig. 4

Robustness of the two-parameter family SW solutions against input noise (x0=0.28) at Z=3: (a) infinity gain recovery time tc, (b) tc=200 ps.

Fig. 5
Fig. 5

Decay of the SW solution if the average concept fails: (a) Za=0.2, (b) Za=2.

Fig. 6
Fig. 6

Excitation of SW’s near the stationary regime but with a flat phase Q(0, T)=Σj=1NAj sech[(T-Tj)/wj]exp(iϕj) for N=2, 4 with A2k-1=0.518, w2k-1=2, A2k=0.217, w2k=5, Tk+1-Tk=23.5, and ϕk+1-ϕk=π(-1)k.

Fig. 7
Fig. 7

SW solutions (Γ=0.33812, κ=-0.4952) with finite gain recovery time Tc=50 and without TOD: (a) topological soliton, (b) evolution of the topological soliton.

Fig. 8
Fig. 8

Properties of the SW solution (Γ=0.33812, κ=-0.4952) as a function of the recovery time: (a) background D2()P0, (b) separation and ratio P1/P2 of peak power of the first two humps.

Fig. 9
Fig. 9

SW solutions and their evolution with TOD β3=0.066: (a), (c) infinite gain recovery; (b), (d) topological soliton with finite gain recovery time Tc=50.

Equations (19)

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

iAz+ik0At-k022At2+σ|A|2A=-iγA+ik063At3,
Aout(t)Ain(t)=exp[(1-iα)h/2],
dhdt=h0-htc-|A(0, t)|2Esat[exp(h)-1].
h(t)=h0-1Esat-t|A(t)|2{exp[h(t)]-1}×exp-t-ttcdt,
h(1)(t)h0-exp(h0)-1Esat-t|A(t)|2×exp-t-ttcdt
T(ω)=11-2i(ω-ω0)/ΔωF.
iQZ+iκQT+122QT2+|Q|2Q=R[A],
R[A]=iβ2QT2+iβ33QT3+iδQ-ρ(α+i)Q×-T|Q(T)|2 exp-T-TTcdT.
R[Qj]=-ρ(α+i)Qj-T|Q3-j|2 exp-T-TTcdT,
j=1, 2
Q(Z, T)=D(T)expiΓZ+i-TΩ(τ)dτ.
u(T)=-TD(τ)2 exp-T-τTcdτ
βe2u+γcuu+γcu-12(u+γcu)2(u+γcu)2-2Ω2
=Γ+κΩ-2βδ+βκu+γcuu+γcu-u-ρα-2β+γcρu,
2βe2Ω+Ωu+γcuu+γcu
=-κ2u+γcuu+γcu+2β(Γ+κΩ)+δ-2β(u+γcu)-ρ(1+2αβ)u,
βe2(λ12-4Ω12)=2(Γ+κΩ1-2βδ+βκλ1),
Ω1=4βΓ+2δ-κλ1-4βκ+4βe2λ1.
N(Z)=-||Q(Z, T)|2-D(T)2|dT-||Q(0, T)|2-D(T)2|dT,

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