Abstract

The dynamic behavior of ultrahigh-bit-rate solitons is studied. We predict the radiated energy from a soliton by employing perturbation theory. The process of loss cancellation is analyzed, and it is shown that distributed erbium-doped fibers, tens of soliton periods long, provide an improved transmission compared with that for lumped amplification.

© 1995 Optical Society of America

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References

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  1. L. F. Mollenauer, S. G. Evangiledes, and H. A. Haus, "Longdistance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
    [CrossRef]
  2. K. J. Blow and N. J. Doran, "Average soliton dynamics and the operation of soliton systems with lumped amplifiers," IEEE Photon. Technol. Lett. 3, 369–371 (1991).
    [CrossRef]
  3. A. Hasegawa and Y. Kodama, "Guiding-center soliton in optical fibers," Opt. Lett. 15, 1443–1445 (1990).
    [CrossRef] [PubMed]
  4. L. F. Mollenauer, J. P. Gordon, and M. N. Islam, "Soliton propagation in long fibers with periodically compensated loss," IEEE J. Quantum Electron. QE-22, 157–173 (1986).
    [CrossRef]
  5. J. P. Gordon, "Dispersive perturbations of solitons of the nonlinear Schrödinger equation," J. Opt. Soc. Am. B 9, 91–97 (1992).
    [CrossRef]
  6. J. N. Elgin, "Perturbations of optical solitons," Phys. Rev. A 47, 4331–4341 (1993).
    [CrossRef] [PubMed]
  7. D. U. Noske, N. Pandit, and J. R. Taylor, "Source of spectral and temporal instability in soliton fiber lasers," Opt. Lett. 17, 1515–1517 (1992).
    [CrossRef] [PubMed]
  8. K. Rottwitt, J. H. Povlsen, S. Gundersen, and A. Bjarklev, "Stability in distributed and lumped gain transmission systems," Opt. Lett. 18, 867–869 (1993).
    [CrossRef] [PubMed]
  9. J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662–664 (1986).
    [CrossRef] [PubMed]
  10. D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).
  11. K. Kurokawa, H. Kubota, and M. Nakazawa, "Femtosecond soliton interaction in a distributed erbium-doped fiber amplifier," IEEE J. Quantum Electron. 30, 2220–2226 (1994).
    [CrossRef]
  12. K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
    [CrossRef]
  13. K. Rottwitt, J. H. Povlsen, and A. Bjarklev, "Long distance transmission through distributed erbium doped fibers," J. Lightwave Technol. 11, 2105–2116 (1993).
    [CrossRef]
  14. D. J. Kaup, "Perturbation theory for solitons in optical fibers," Phys. Rev. A 42, 5689–5694 (1990).
    [CrossRef] [PubMed]

1994 (1)

K. Kurokawa, H. Kubota, and M. Nakazawa, "Femtosecond soliton interaction in a distributed erbium-doped fiber amplifier," IEEE J. Quantum Electron. 30, 2220–2226 (1994).
[CrossRef]

1993 (3)

K. Rottwitt, J. H. Povlsen, and A. Bjarklev, "Long distance transmission through distributed erbium doped fibers," J. Lightwave Technol. 11, 2105–2116 (1993).
[CrossRef]

J. N. Elgin, "Perturbations of optical solitons," Phys. Rev. A 47, 4331–4341 (1993).
[CrossRef] [PubMed]

K. Rottwitt, J. H. Povlsen, S. Gundersen, and A. Bjarklev, "Stability in distributed and lumped gain transmission systems," Opt. Lett. 18, 867–869 (1993).
[CrossRef] [PubMed]

1992 (3)

D. U. Noske, N. Pandit, and J. R. Taylor, "Source of spectral and temporal instability in soliton fiber lasers," Opt. Lett. 17, 1515–1517 (1992).
[CrossRef] [PubMed]

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

J. P. Gordon, "Dispersive perturbations of solitons of the nonlinear Schrödinger equation," J. Opt. Soc. Am. B 9, 91–97 (1992).
[CrossRef]

1991 (2)

L. F. Mollenauer, S. G. Evangiledes, and H. A. Haus, "Longdistance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
[CrossRef]

K. J. Blow and N. J. Doran, "Average soliton dynamics and the operation of soliton systems with lumped amplifiers," IEEE Photon. Technol. Lett. 3, 369–371 (1991).
[CrossRef]

1990 (2)

A. Hasegawa and Y. Kodama, "Guiding-center soliton in optical fibers," Opt. Lett. 15, 1443–1445 (1990).
[CrossRef] [PubMed]

D. J. Kaup, "Perturbation theory for solitons in optical fibers," Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

1986 (2)

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, "Soliton propagation in long fibers with periodically compensated loss," IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[CrossRef]

J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662–664 (1986).
[CrossRef] [PubMed]

Ainslie, B. J.

D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).

Bjarklev, A.

K. Rottwitt, J. H. Povlsen, S. Gundersen, and A. Bjarklev, "Stability in distributed and lumped gain transmission systems," Opt. Lett. 18, 867–869 (1993).
[CrossRef] [PubMed]

K. Rottwitt, J. H. Povlsen, and A. Bjarklev, "Long distance transmission through distributed erbium doped fibers," J. Lightwave Technol. 11, 2105–2116 (1993).
[CrossRef]

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

Blank, L. C.

D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).

Blow, K. J.

K. J. Blow and N. J. Doran, "Average soliton dynamics and the operation of soliton systems with lumped amplifiers," IEEE Photon. Technol. Lett. 3, 369–371 (1991).
[CrossRef]

Doran, N. J.

K. J. Blow and N. J. Doran, "Average soliton dynamics and the operation of soliton systems with lumped amplifiers," IEEE Photon. Technol. Lett. 3, 369–371 (1991).
[CrossRef]

Elgin, J. N.

J. N. Elgin, "Perturbations of optical solitons," Phys. Rev. A 47, 4331–4341 (1993).
[CrossRef] [PubMed]

Evangiledes, S. G.

L. F. Mollenauer, S. G. Evangiledes, and H. A. Haus, "Longdistance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
[CrossRef]

Gordon, J. P.

Gundersen, S.

Hasegawa, A.

Haus, H. A.

L. F. Mollenauer, S. G. Evangiledes, and H. A. Haus, "Longdistance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
[CrossRef]

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, "Soliton propagation in long fibers with periodically compensated loss," IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[CrossRef]

Kaup, D. J.

D. J. Kaup, "Perturbation theory for solitons in optical fibers," Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

Kodama, Y.

Kubota, H.

K. Kurokawa, H. Kubota, and M. Nakazawa, "Femtosecond soliton interaction in a distributed erbium-doped fiber amplifier," IEEE J. Quantum Electron. 30, 2220–2226 (1994).
[CrossRef]

Kurokawa, K.

K. Kurokawa, H. Kubota, and M. Nakazawa, "Femtosecond soliton interaction in a distributed erbium-doped fiber amplifier," IEEE J. Quantum Electron. 30, 2220–2226 (1994).
[CrossRef]

Lumholt, O.

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangiledes, and H. A. Haus, "Longdistance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, "Soliton propagation in long fibers with periodically compensated loss," IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[CrossRef]

Nakazawa, M.

K. Kurokawa, H. Kubota, and M. Nakazawa, "Femtosecond soliton interaction in a distributed erbium-doped fiber amplifier," IEEE J. Quantum Electron. 30, 2220–2226 (1994).
[CrossRef]

Noske, D. U.

Pandit, N.

Povlsen, J. H.

K. Rottwitt, J. H. Povlsen, S. Gundersen, and A. Bjarklev, "Stability in distributed and lumped gain transmission systems," Opt. Lett. 18, 867–869 (1993).
[CrossRef] [PubMed]

K. Rottwitt, J. H. Povlsen, and A. Bjarklev, "Long distance transmission through distributed erbium doped fibers," J. Lightwave Technol. 11, 2105–2116 (1993).
[CrossRef]

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

Rasmussen, T.

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

Rottwitt, K.

K. Rottwitt, J. H. Povlsen, and A. Bjarklev, "Long distance transmission through distributed erbium doped fibers," J. Lightwave Technol. 11, 2105–2116 (1993).
[CrossRef]

K. Rottwitt, J. H. Povlsen, S. Gundersen, and A. Bjarklev, "Stability in distributed and lumped gain transmission systems," Opt. Lett. 18, 867–869 (1993).
[CrossRef] [PubMed]

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

Spirit, D. M.

D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).

Taylor, J. R.

Whitley, T. J.

D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).

Williams, D. L.

D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).

IEEE J. Quantum Electron. (2)

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, "Soliton propagation in long fibers with periodically compensated loss," IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[CrossRef]

K. Kurokawa, H. Kubota, and M. Nakazawa, "Femtosecond soliton interaction in a distributed erbium-doped fiber amplifier," IEEE J. Quantum Electron. 30, 2220–2226 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. J. Blow and N. J. Doran, "Average soliton dynamics and the operation of soliton systems with lumped amplifiers," IEEE Photon. Technol. Lett. 3, 369–371 (1991).
[CrossRef]

J. Lightwave Technol. (3)

K. Rottwitt, A. Bjarklev, J. H. Povlsen, O. Lumholt, and T. Rasmussen, "Fundamental design of a distributed erbium-doped fiber amplifier for long-distance transmission," J. Lightwave Technol. 10, 1544–1552 (1992).
[CrossRef]

K. Rottwitt, J. H. Povlsen, and A. Bjarklev, "Long distance transmission through distributed erbium doped fibers," J. Lightwave Technol. 11, 2105–2116 (1993).
[CrossRef]

L. F. Mollenauer, S. G. Evangiledes, and H. A. Haus, "Longdistance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. A (2)

J. N. Elgin, "Perturbations of optical solitons," Phys. Rev. A 47, 4331–4341 (1993).
[CrossRef] [PubMed]

D. J. Kaup, "Perturbation theory for solitons in optical fibers," Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

Other (1)

D. M. Spirit, L. C. Blank, T. J. Whitley, D. L. Williams, and B. J. Ainslie, "Optical time domain reflectometry as a diagnostic for distributed optical fibre amplifiers," presented at the meeting on optical fiber measurement, York, UK, September 1991).

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Figures (3)

Fig. 1
Fig. 1

(a) Radiated energy from a soliton as a function of the fraction between the amplification period and the soliton period (ZA/Z0). The radiated energy is shown after one, two, and three amplifiers. Dashed curves, qe = a sech(bt); dotted curves, qe = 2η sech(2ηt)exp(−42x); solid curves, theory. The energy of the dotted curve always exceeds that of the dashed curve. (b) Traces of 10- and 2.5-ps pulses propagated through 10 and 5 amplifier sections, respectively. In (b) D = 1 ps/(nm km) and λ = 1.55 μm.

Fig. 2
Fig. 2

Radiated energy from a soliton as a function of the fraction between the amplification period and the soliton period (ZA/Z0). The radiated energy is shown after five amplifiers in a cascade coupled system. As in Fig. 1: dashed curve, qe = a sech(bt); dotted curve, qe = 2η sech(2ηt)exp(−42x); solid curve, perturbation theory.

Fig. 3
Fig. 3

(a) Radiated energy from a soliton as a function of the fraction ZA/Z0. The radiated energy is shown after one, two, and three d-EDF’s. As in Figs. 1 and 2: dashed curves, qe = a sech(bt); dotted curves, qe = 2η sech(2ηt)exp(−42x); solid curves, theory. (b) Traces of 10- and 2.5-ps pulses propagated through 10 and 5 fiber sections, respectively. In (b) D = 1 ps/(nm km) and λ = 1.55 μm.

Equations (10)

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

i q x - 2 q t 2 - 2 q q 2 = i F ,
q s ( x , t ) = 2 η 0 exp [ - 2 i ξ 0 t + 4 i ( ξ 0 2 - η 0 2 ) x ] × sech [ 2 η 0 ( t - 4 ξ 0 x ) ] ,
- q 2 d t = 4 η 0 - 1 π - log e ( 1 - b 2 ) d ξ .
b x = - 4 i ζ 2 b + Γ π exp ( 4 i η 0 2 x ) sech ( π ξ 2 η 0 ) .
B x = Γ π exp [ 4 i x ( η 0 2 + ξ 2 ) ] sech ( π ξ 2 η 0 ) .
W = - 1 π - log e ( 1 - B 2 ) d ξ .
Γ ( x ) = - Γ 0 + Γ 0 x a n = 1 N δ ( x - n x a ) ,
Γ ( x ) = Γ 0 cos ( 2 π x a x ) ,
W = - q - q e 2 d t ,
W ~ x a 2 π - [ π Γ 0 2 sech ( π ξ 2 η 0 ) ] 2 4 [ sin ( κ x a - π ) κ x a - π ] 2 × ( κ x a κ x a + π ) 2 d ξ ,

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