Abstract

We study semianalytically soliton dynamics in a soliton-based communication line for which the amplifier spacing is larger than the soliton period (referred to as the quasi-adiabatic regime). This regime allows us to overcome the limit on the soliton duration (TFWHM ~ 15 ps) imposed by the average-soliton regime. Our calculations show that periodically stable propagation of short solitons (TFWHM = 1–5 ps) is possible for an amplifier spacing ranging from 5 to 20 km. We discuss the dynamical features associated with the propagation of short solitons in the quasi-adiabatic regime and present a simple model capable of predicting the width and the mean frequency of the steady-state soliton. We compare the model with appropriate numerical simulations. Our analysis may also be applied to fiber lasers that produce ultrashort solitons (TFWHM < 1 ps) in a relatively long-cavity configuration.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. A. Hasegawa and Y. Kodama, "Guiding-center soliton in optical fibers," Opt. Lett. 15, 1443–1445 (1990); "Guiding-center soliton," Phys. Rev. Lett. 66, 161–164 (1991).
    [CrossRef] [PubMed]
  4. L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, "Long-distance soliton propagation using lumped amplifiers and dispersion-shifted fiber," J. Lightwave Technol. 9, 194–197 (1991).
    [CrossRef]
  5. M. Nakazawa, K. Suzuki, H. Kubota, E. Yamada, and Y. Kimura, "Dynamic optical soliton communication," IEEE J. Quantum Electron. 26, 2095–2102 (1990).
    [CrossRef]
  6. X. Tang and P. Ye, "Comparison of dynamic soliton communication and path-averaged soliton communication," Fiber Integ. Opt. 13, 261–270 (1993).
    [CrossRef]
  7. B. A. Malomed, "Propagation of a soliton in a nonlinear waveguide with dissipation and pumping," Opt. Commun. 61, 192–194 (1987).
    [CrossRef]
  8. S. M. J. Kelly, "Characteristic sideband instability of periodically amplified average soliton," Electron. Lett. 28, 806–807 (1992).
    [CrossRef]
  9. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 28.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. R. Vallée and R.-J. Essiambre, "Long-distance soliton transmission with a nonlinear twin-core fiber," Opt. Lett. 19, 2095–2097 (1994).
    [CrossRef] [PubMed]
  14. M. Matsumoto, H. Ikeda, and A. Hasegawa, "Suppression of noise accumulation in bandwidth-limited soliton transmission by means of nonlinear loop mirrors," Opt. Lett. 19, 183–185 (1994).
    [CrossRef] [PubMed]
  15. J. P. Gordon and H. A. Haus, "Random walk of coherently amplified solitons in optical fiber transmission," Opt. Lett. 11, 665–667 (1986).
    [CrossRef] [PubMed]
  16. B. A. Malomed, "Strong periodic amplification of solitons in a lossy optical fiber: analytical results," J. Opt. Soc. Am. B 11, 1261–1266 (1994).
    [CrossRef]
  17. L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, "The sliding-frequency guiding filter: an improved form of soliton jitter control," Opt. Lett. 17, 1575–1577 (1992).
    [CrossRef] [PubMed]
  18. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995), Chap. 5.
  19. K. J. Blow, N. J. Doran, and D. Wood, "Suppression of the soliton self-frequency shift by bandwidth-limited amplification," J. Opt. Soc. Am. B 5, 1301–1304 (1988).
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1994 (3)

1993 (2)

X. Tang and P. Ye, "Comparison of dynamic soliton communication and path-averaged soliton communication," Fiber Integ. Opt. 13, 261–270 (1993).
[CrossRef]

M. W. Chbat, P. R. Prucnal, M. N. Islam, C. E. Soccolich, and J. P. Gordon, "Long-range interference effects of soliton reshaping in optical fibers," J. Opt. Soc. Am. B 10, 1386–1395 (1993).
[CrossRef]

1992 (2)

1991 (2)

1990 (2)

M. Nakazawa, K. Suzuki, H. Kubota, E. Yamada, and Y. Kimura, "Dynamic optical soliton communication," IEEE J. Quantum Electron. 26, 2095–2102 (1990).
[CrossRef]

A. Hasegawa and Y. Kodama, "Guiding-center soliton in optical fibers," Opt. Lett. 15, 1443–1445 (1990); "Guiding-center soliton," Phys. Rev. Lett. 66, 161–164 (1991).
[CrossRef] [PubMed]

1988 (3)

1987 (1)

B. A. Malomed, "Propagation of a soliton in a nonlinear waveguide with dissipation and pumping," Opt. Commun. 61, 192–194 (1987).
[CrossRef]

1986 (2)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995), Chap. 5.

Bekki, N.

Blow, K. J.

Chbat, M. W.

Doran, N. J.

Essiambre, R.-J.

Evangelides, S. G.

L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, "The sliding-frequency guiding filter: an improved form of soliton jitter control," Opt. Lett. 17, 1575–1577 (1992).
[CrossRef] [PubMed]

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

Gordon, J. P.

Hasegawa, A.

Haus, H. A.

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

J. P. Gordon and H. A. Haus, "Random walk of coherently amplified solitons in optical fiber transmission," Opt. Lett. 11, 665–667 (1986).
[CrossRef] [PubMed]

Ikeda, H.

Islam, M. N.

Kelly, S. M. J.

S. M. J. Kelly, "Characteristic sideband instability of periodically amplified average soliton," Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Kimura, Y.

M. Nakazawa, K. Suzuki, H. Kubota, E. Yamada, and Y. Kimura, "Dynamic optical soliton communication," IEEE J. Quantum Electron. 26, 2095–2102 (1990).
[CrossRef]

Kodama, Y.

Kubota, H.

Kurokawa, K.

Malomed, B. A.

B. A. Malomed, "Strong periodic amplification of solitons in a lossy optical fiber: analytical results," J. Opt. Soc. Am. B 11, 1261–1266 (1994).
[CrossRef]

B. A. Malomed, "Propagation of a soliton in a nonlinear waveguide with dissipation and pumping," Opt. Commun. 61, 192–194 (1987).
[CrossRef]

Matsumoto, M.

Mollenauer, L. F.

Nakazawa, M.

Prucnal, P. R.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 28.

Smith, K.

Soccolich, C. E.

Suzuki, K.

M. Nakazawa, K. Suzuki, H. Kubota, E. Yamada, and Y. Kimura, "Dynamic optical soliton communication," IEEE J. Quantum Electron. 26, 2095–2102 (1990).
[CrossRef]

Tai, K.

Tang, X.

X. Tang and P. Ye, "Comparison of dynamic soliton communication and path-averaged soliton communication," Fiber Integ. Opt. 13, 261–270 (1993).
[CrossRef]

Vallée, R.

Wood, D.

Yamada, E.

Ye, P.

X. Tang and P. Ye, "Comparison of dynamic soliton communication and path-averaged soliton communication," Fiber Integ. Opt. 13, 261–270 (1993).
[CrossRef]

Electron. Lett. (1)

S. M. J. Kelly, "Characteristic sideband instability of periodically amplified average soliton," Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Fiber Integ. Opt. (1)

X. Tang and P. Ye, "Comparison of dynamic soliton communication and path-averaged soliton communication," Fiber Integ. Opt. 13, 261–270 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Nakazawa, K. Suzuki, H. Kubota, E. Yamada, and Y. Kimura, "Dynamic optical soliton communication," IEEE J. Quantum Electron. 26, 2095–2102 (1990).
[CrossRef]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

B. A. Malomed, "Propagation of a soliton in a nonlinear waveguide with dissipation and pumping," Opt. Commun. 61, 192–194 (1987).
[CrossRef]

Opt. Lett. (8)

Other (2)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 28.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995), Chap. 5.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the proposed transmission line. The amplifier spacing za can be larger than the soliton period zs. G’s, amplifier gain.

Fig. 2
Fig. 2

Comparison of soliton evolution (a) without and (b) with a FSA. The amplifier spacing is 20 km and the soliton width (FWHM) is 4.5 ps.

Fig. 3
Fig. 3

Steady-state (a) soliton width and (b) mean frequency shift for different effective gain models. (i) Solid curve, a Lorentzian amplifier spectrum with 50% insertion losses; (ii) short-dashed curve, a Lorentzian amplifier spectrum without insertion losses; (iii) long-and-short-dashed curve, a large-bandwidth amplifier spectrum with a narrow-bandwidth bandpass filter.

Fig. 4
Fig. 4

Steady-state soliton width plotted as a function of the gain bandwidth for three different amplifier spacings: (a) a Lorentzian amplifier spectrum with 50% insertion losses and (b) a large-bandwidth amplifier spectrum with a narrow-bandwidth bandpass filter.

Fig. 5
Fig. 5

Comparison of steady-state soliton widths for numerical simulations and the semianalytic model for some amplifier spacings.

Equations (11)

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G ( ν 0 , u 0 ) L = 1 ,
Δ ν amp ( ν 0 , u 0 ) + Δ ν SSFS ( u 0 ) = 0 ,
G ( ν 0 , u 0 ) = - G L ( ν ) v ( ν ) 2 d ν - v ( ν ) 2 d ν ,
G L ( ν ) = L I exp { g 0 / [ 1 + ( ν / Δ ν G ) 2 ] } ,
L = exp ( - α z a ) ( 1 - L FSA ) ,
Δ ν amp ( ν 0 , u 0 ) = - ν G L ( ν ) v ( ν ) 2 d ν - G L ( ν ) v ( ν ) 2 d ν .
ν 0 ( z ) z = - 4 15 π T R T 0 1 τ p 4 ( z ) ,
τ p ( z ) = τ p ( 0 ) exp ( α z ) .
Δ ν SSFS ( u 0 ) = T R [ 1 - exp ( 4 α z a ) 15 π α T 0 u 0 4 ,
G 0 ( z a ) = E G exp ( α z a ) 1 - L FSA ,
u z + i 2 β 2 2 u t 2 - i u 2 u = - α 2 u - T R u u 2 t + β 3 6 3 u t 3 ,

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