Abstract

Modulational instability of continuous waves in transmission systems with semiconductor optical amplifiers and in-line filters was theoretically and experimentally analyzed. Stable and unstable domains were identified. Even in the normal-dispersion region, modulationally unstable domains can exist for an appropriate filter detuning.

© 2000 Optical Society of America

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References

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1998 (1)

G. Onishchukov, V. Lokhnygin, A. Shipulin, and P. Riedel, Electron. Lett. 34, 1597 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

1995 (1)

1993 (1)

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

1990 (1)

1984 (1)

1980 (1)

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, S. A. Darmanyan, and P. Khabibulaev, Optical Solitons (Springer-Verlag, Berlin, 1993).
[CrossRef]

Anderson, D.

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

Cross, M. C.

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

Cucala, L.

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

Darmanyan, S. A.

F. Kh. Abdullaev, S. A. Darmanyan, and P. Khabibulaev, Optical Solitons (Springer-Verlag, Berlin, 1993).
[CrossRef]

Desaix, M.

Ferreira, M.

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

Gabitov, I.

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

Gölles, M.

G. Onishchukov, V. Lokhnygin, A. Shipulin, and M. Gölles, in Digest of Optical Amplifiers and Their Applications (Optical Society of America, Washington, D.C., 1999), paper ThD4.

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]

Hasegawa, A.

Haunstein, H.

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

Hohenberg, P. C.

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

Khabibulaev, P.

F. Kh. Abdullaev, S. A. Darmanyan, and P. Khabibulaev, Optical Solitons (Springer-Verlag, Berlin, 1993).
[CrossRef]

Lisak, M.

Lokhnygin, V.

G. Onishchukov, V. Lokhnygin, A. Shipulin, and P. Riedel, Electron. Lett. 34, 1597 (1998).
[CrossRef]

G. Onishchukov, V. Lokhnygin, A. Shipulin, and M. Gölles, in Digest of Optical Amplifiers and Their Applications (Optical Society of America, Washington, D.C., 1999), paper ThD4.

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. W.

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

Mecozzi, A.

Onishchukov, G.

G. Onishchukov, V. Lokhnygin, A. Shipulin, and P. Riedel, Electron. Lett. 34, 1597 (1998).
[CrossRef]

G. Onishchukov, V. Lokhnygin, A. Shipulin, and M. Gölles, in Digest of Optical Amplifiers and Their Applications (Optical Society of America, Washington, D.C., 1999), paper ThD4.

Reid, J. J. E.

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

Riedel, P.

G. Onishchukov, V. Lokhnygin, A. Shipulin, and P. Riedel, Electron. Lett. 34, 1597 (1998).
[CrossRef]

Settembre, M.

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

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

Shipulin, A.

G. Onishchukov, V. Lokhnygin, A. Shipulin, and P. Riedel, Electron. Lett. 34, 1597 (1998).
[CrossRef]

G. Onishchukov, V. Lokhnygin, A. Shipulin, and M. Gölles, in Digest of Optical Amplifiers and Their Applications (Optical Society of America, Washington, D.C., 1999), paper ThD4.

Smets, R. C. J.

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

Turitsyn, S.

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

Electron. Lett. (1)

G. Onishchukov, V. Lokhnygin, A. Shipulin, and P. Riedel, Electron. Lett. 34, 1597 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[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]

Opt. Lett. (4)

Rev. Mod. Phys. (1)

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

Other (3)

J. J. E. Reid, L. Cucala, M. Ferreira, M. Settembre, H. Haunstein, and R. C. J. Smets, in Technical Digest of European Conference on Optical Communication ’98 (IEEE Lasers and Electro-Optics Society, Madrid, 1998), paper WdD01.

G. Onishchukov, V. Lokhnygin, A. Shipulin, and M. Gölles, in Digest of Optical Amplifiers and Their Applications (Optical Society of America, Washington, D.C., 1999), paper ThD4.

F. Kh. Abdullaev, S. A. Darmanyan, and P. Khabibulaev, Optical Solitons (Springer-Verlag, Berlin, 1993).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

MI gain [dB/(25 km)] as a function of filter detuning λF and modulational frequency ωM, with βF=0.091 ps2/km and ρ=0.026/kmpJ for fiber input powers of (a) 1 mW and (b) 10 mW. ωN/2π=40 GHz and λN=0.25 nm.

Fig. 2
Fig. 2

MI gain [dB/(25 km)] as a function of filter detuning λF and modulational frequency ωM with βF=0.091 ps2/km, χ=3.1/W km, and ρ=0.026/kmpJ for fiber input power 1 mW (left-hand column) and 10 mW (right-hand column). ωN/2π=40 GHz and λN=0.25 nm.

Fig. 3
Fig. 3

Comparison between (top) experimental and (bottom) numerical evolution of spectral power cm2 of a 3-mW signal at the blue BPF side in the normal-dispersion regime according to Eq. (4).

Fig. 4
Fig. 4

Propagation of an amplitude-modulated cw-signal at normal dispersion, ωS=0, ωM/2π=4.5 GHz, for input powers (a) a0Q02=1 mW and (b) a0Q02=10 mW; t0=3.73 ps and za=25 km.

Equations (5)

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

iQz=-2βFωSQt+βD2+iβF2Qt2-χQ2Q+iδeQ-ρα+iQ-tQ2 exp-t-ttrdt,
iz+2βFωSt-βD2+iβF2t2+χQ02+*=-ρα+iQ02-t+*exp-t-ttrdt.
λ+βFωM22+2ρQ02tr1-iωMtrλ+βFωM2+aa-2χQ02-2ραQ02tr1-iωMtr=0,
idcmdz=iδ-βD2mωM2-iβFmωM-ωS2cm-j,k,l:m=j-k+lχ+ρα+itr1-im-jωMtrcjck*cl.
NSR20dωM exp2zRλωMHRωM0dωMHRωM

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