Abstract

We show that the gain saturation of semiconductor optical amplifiers can lead to enhanced sideband instability in soliton transmissions, provided that the amplifier spacing is comparable with the dispersion length. With sliding filters the pulse can be stabilized and the radiation created is partially absorbed.

© 1997 Optical Society of America

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References

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  1. J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.
  2. P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.
  3. A. Shipulin, G. Onishchukov, P. Riedel, D. Michaelis, U. Peschel, and F. Lederer, Electron. Lett. 33, 507 (1997).
    [CrossRef]
  4. A. Mecozzi, Opt. Lett. 20, 1616 (1995).
    [CrossRef] [PubMed]
  5. S. Wabnitz, Opt. Lett. 20, 1979 (1995).
    [CrossRef] [PubMed]
  6. S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
    [CrossRef]
  7. N. J. Smith, K. J. Blow, and I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
    [CrossRef]
  8. G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
    [CrossRef]
  9. L. Gagnon and P. A. Belànger, Phys. Rev. A 43, 6187 (1991).
    [CrossRef] [PubMed]
  10. G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
    [CrossRef]
  11. A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  12. L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 369 (1991).
  13. K. J. Blow and N. J. Doran, IEEE Photon. Technol. Lett. 3, 369 (1991).
    [CrossRef]
  14. S. K. Turitsyn, Phys. Rev. E 54, R3125 (1996).
    [CrossRef]

1997 (1)

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

1996 (1)

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

1995 (2)

1992 (3)

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

N. J. Smith, K. J. Blow, and I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

1991 (3)

L. Gagnon and P. A. Belànger, Phys. Rev. A 43, 6187 (1991).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 369 (1991).

K. J. Blow and N. J. Doran, IEEE Photon. Technol. Lett. 3, 369 (1991).
[CrossRef]

1990 (1)

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]

Andonovic, I.

N. J. Smith, K. J. Blow, and I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Belànger, P. A.

L. Gagnon and P. A. Belànger, Phys. Rev. A 43, 6187 (1991).
[CrossRef] [PubMed]

Blow, K. J.

N. J. Smith, K. J. Blow, and I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

K. J. Blow and N. J. Doran, IEEE Photon. Technol. Lett. 3, 369 (1991).
[CrossRef]

Boffetta, G.

G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

Boot, A.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

Boot, A. J.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

Cuipers, G.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

de Waardt, H.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

Doran, N. J.

K. J. Blow and N. J. Doran, IEEE Photon. Technol. Lett. 3, 369 (1991).
[CrossRef]

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 369 (1991).

Gabitov, I.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

Gagnon, L.

L. Gagnon and P. A. Belànger, Phys. Rev. A 43, 6187 (1991).
[CrossRef] [PubMed]

Hasegawa, A.

Haus, H. A.

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 369 (1991).

Jenne, J.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

Kelly, S. M. J.

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

Kodama, Y.

Kuindersma, P. I.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

Lederer, F.

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

Liendenbaum, C. T. H. F.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

Mattheus, A.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

Mecozzi, A.

Michaelis, D.

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

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 369 (1991).

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]

Osborne, A. R.

G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

Peschel, U.

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

Reid, J.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

Reid, J. J.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

Riedel, P.

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

Shipulin, A.

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

Smith, N. J.

N. J. Smith, K. J. Blow, and I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Tiemeijer, L. F.

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

Tiemejer, L.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

Turitsyn, S. K.

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

Wabnitz, S.

Electron. Lett. (2)

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

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

K. J. Blow and N. J. Doran, IEEE Photon. Technol. Lett. 3, 369 (1991).
[CrossRef]

J. Comput. Phys. (1)

G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

J. Lightwave Technol. (2)

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 369 (1991).

N. J. Smith, K. J. Blow, and I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

L. Gagnon and P. A. Belànger, Phys. Rev. A 43, 6187 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (1)

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

Other (2)

J. J. Reid, C. T. H. F. Liendenbaum, L. F. Tiemeijer, A. J. Boot, P. I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1994), pp. 61–64.

P. I. Kuindersma, G. Cuipers, J. Jenne, J. Reid, L. Tiemejer, H. de Waardt, and A. Boot, presented at the 22nd European Conference on Optical Communications ECOC’96, Oslo, 1996.

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Figures (3)

Fig. 1
Fig. 1

Evolution of (a) radiation energy (normalized with total energy) and (b) imaginary parts of eigenvalues of the Zakharov–Shabat eigenvalue problem for different kinds of lumped amplification for a single soliton (t0=4  ps and Esol=0.071  pJ): solid curves, linear amplification without gain saturation h0=3.3; dashed curves, with gain saturation (h0=3.34; sat=2.7 pJ; tc=200 ps) and no SPM α=0; dashed–dotted curves, with gain saturation and SPM (α=5; h0=3.34; sat=2.7 pJ; tc=200 ps); dotted curves, with gain saturation and SPM α=8; h0=3.34; sat=2.7 pJ; tc=200 ps); and dashed–double-dotted curves, with gain saturation, SPM, and sliding filters (bandwidth B=1 nm; sliding rate α0=0.0268 nm/ amplifier spacing; h0=3.41; sat=2.7 pJ; tc=200 ps; α=8).

Fig. 2
Fig. 2

Evolution of a single soliton and its spectrum (setup as in Fig.  1, dashed and dotted curves (a) without SPM a=0 and (b) with SPM α=8.

Fig. 3
Fig. 3

Evolution of amplitude and chirp of the pulse in the presence of gain saturation and SPM without sliding filters (dotted curves, setup as in Fig.  1, dotted curves) and with sliding filters (dashed–double-dotted curves, setup as in Fig.  1, similar curves). (b) Pulse shape of the propagating pulse with sliding filters at Z=10 (solid curve), 20 (dashed curve), 30 (dashed–dotted curve), 40 (dotted curve).

Equations (3)

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EL, t=exp1-iαh/2E0, t,
dhdt=h0-htc-E0, t2satexp h-1.
zc=6satαa02EsolG0LaG0-14πLdLa-11/2,

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