Abstract

A new technique for achieving subpicosecond–femtosecond optical soliton communication over long distances is proposed. The technique uses adiabatic soliton trapping and soliton standardization in an active transmission line with a finite optical-gain bandwidth. Forces destructive to femtosecond pulse propagation, such as soliton self-frequency shift and third-order dispersion, can be completely compensated for by the bandwidth-limited optical gain. Then soliton amplitude and width (i.e., area) are fixed to a certain value that indicates an N = 1 soliton, and the soliton is standardized by trapping. The technique will be a key technology for achieving ultrahigh-bit-rate (>100 Gbit/s) optical transmission systems.

© 1991 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  6. M. Nakazawa, K. Suzuki, and Y. Kimura, “3.2–5 Gb/s, 100 km error-free soliton transmission with erbium amplifiers and repeaters,” Photon. Tech. Lett. 2, 216–219 (1990); see also K. Suzuki, M. Nakazawa, E. Yamada, and Y. Kimura, “5 Gbit/s, 250 km error-free soliton transmission with Er3+-doped fibre amplifiers and repeaters,” Electron. Lett. 26, 551–553 (1990).
    [Crossref]
  7. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986); see also J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [Crossref] [PubMed]
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    [Crossref]
  9. M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
    [Crossref] [PubMed]
  10. 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).
    [Crossref]
  11. K. J. Blow, N. J. Doran, and D. Wood, “Generation and stabilization of short soliton pulses in the amplified nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 5, 381–390 (1988).
    [Crossref]
  12. K. J. Blow, N. J. Doran, and D. Wood, “Trapping of energy into solitary waves in amplified nonlinear dispersive systems,” Opt. Lett. 12, 1011–1013 (1987).
    [Crossref] [PubMed]
  13. M. Nakazawa, Y. Kimura, and K. Suzuki, “Ultralong dispersion-shifted erbium-doped fiber amplifier and its application to soliton communication,” IEEE J. Quantum Electron. 26, 2103–2108 (1991).
    [Crossref]
  14. J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Suppl. Prog. Theor. Phys. 55, 284–306 (1974).
    [Crossref]

1991 (1)

M. Nakazawa, Y. Kimura, and K. Suzuki, “Ultralong dispersion-shifted erbium-doped fiber amplifier and its application to soliton communication,” IEEE J. Quantum Electron. 26, 2103–2108 (1991).
[Crossref]

1990 (2)

M. Nakazawa, K. Suzuki, and Y. Kimura, “3.2–5 Gb/s, 100 km error-free soliton transmission with erbium amplifiers and repeaters,” Photon. Tech. Lett. 2, 216–219 (1990); see also K. Suzuki, M. Nakazawa, E. Yamada, and Y. Kimura, “5 Gbit/s, 250 km error-free soliton transmission with Er3+-doped fibre amplifiers and repeaters,” Electron. Lett. 26, 551–553 (1990).
[Crossref]

M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
[Crossref] [PubMed]

1989 (1)

1988 (2)

1987 (2)

1986 (1)

1980 (1)

1979 (1)

1974 (1)

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Suppl. Prog. Theor. Phys. 55, 284–306 (1974).
[Crossref]

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulse in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

Blow, K. J.

Chase, E. W.

M. Stern, J. P. Heritage, and E. W. Chase, Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 56.

Doran, N. J.

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulse in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

Haus, H. A.

Heritage, J. P.

M. Stern, J. P. Heritage, and E. W. Chase, Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 56.

Kimura, Y.

M. Nakazawa, Y. Kimura, and K. Suzuki, “Ultralong dispersion-shifted erbium-doped fiber amplifier and its application to soliton communication,” IEEE J. Quantum Electron. 26, 2103–2108 (1991).
[Crossref]

M. Nakazawa, K. Suzuki, and Y. Kimura, “3.2–5 Gb/s, 100 km error-free soliton transmission with erbium amplifiers and repeaters,” Photon. Tech. Lett. 2, 216–219 (1990); see also K. Suzuki, M. Nakazawa, E. Yamada, and Y. Kimura, “5 Gbit/s, 250 km error-free soliton transmission with Er3+-doped fibre amplifiers and repeaters,” Electron. Lett. 26, 551–553 (1990).
[Crossref]

K. Suzuki, Y. Kimura, and M. Nakazawa, “Subpicosecond soliton amplification and transmission using Er3+-doped fibers pumped by InGaAsP laser diodes,” Opt. Lett. 14, 865–867 (1989).
[Crossref] [PubMed]

Kubota, H.

M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
[Crossref] [PubMed]

Kurokawa, K.

M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
[Crossref] [PubMed]

Marcuse, D.

Mitschke, F. M.

Miyagi, M.

Mollenauer, L. F.

Nakazawa, M.

M. Nakazawa, Y. Kimura, and K. Suzuki, “Ultralong dispersion-shifted erbium-doped fiber amplifier and its application to soliton communication,” IEEE J. Quantum Electron. 26, 2103–2108 (1991).
[Crossref]

M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
[Crossref] [PubMed]

M. Nakazawa, K. Suzuki, and Y. Kimura, “3.2–5 Gb/s, 100 km error-free soliton transmission with erbium amplifiers and repeaters,” Photon. Tech. Lett. 2, 216–219 (1990); see also K. Suzuki, M. Nakazawa, E. Yamada, and Y. Kimura, “5 Gbit/s, 250 km error-free soliton transmission with Er3+-doped fibre amplifiers and repeaters,” Electron. Lett. 26, 551–553 (1990).
[Crossref]

K. Suzuki, Y. Kimura, and M. Nakazawa, “Subpicosecond soliton amplification and transmission using Er3+-doped fibers pumped by InGaAsP laser diodes,” Opt. Lett. 14, 865–867 (1989).
[Crossref] [PubMed]

H. A. Haus and M. Nakazawa, “Theory of the fiber Raman soliton laser,” J. Opt. Soc. Am. B 4, 652–660 (1987).
[Crossref]

Nishida, S.

Satsuma, J.

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Suppl. Prog. Theor. Phys. 55, 284–306 (1974).
[Crossref]

Stern, M.

M. Stern, J. P. Heritage, and E. W. Chase, Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 56.

Suzuki, K.

M. Nakazawa, Y. Kimura, and K. Suzuki, “Ultralong dispersion-shifted erbium-doped fiber amplifier and its application to soliton communication,” IEEE J. Quantum Electron. 26, 2103–2108 (1991).
[Crossref]

M. Nakazawa, K. Suzuki, and Y. Kimura, “3.2–5 Gb/s, 100 km error-free soliton transmission with erbium amplifiers and repeaters,” Photon. Tech. Lett. 2, 216–219 (1990); see also K. Suzuki, M. Nakazawa, E. Yamada, and Y. Kimura, “5 Gbit/s, 250 km error-free soliton transmission with Er3+-doped fibre amplifiers and repeaters,” Electron. Lett. 26, 551–553 (1990).
[Crossref]

K. Suzuki, Y. Kimura, and M. Nakazawa, “Subpicosecond soliton amplification and transmission using Er3+-doped fibers pumped by InGaAsP laser diodes,” Opt. Lett. 14, 865–867 (1989).
[Crossref] [PubMed]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulse in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

Wood, D.

Yajima, N.

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Suppl. Prog. Theor. Phys. 55, 284–306 (1974).
[Crossref]

Yamada, E.

M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulse in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Nakazawa, Y. Kimura, and K. Suzuki, “Ultralong dispersion-shifted erbium-doped fiber amplifier and its application to soliton communication,” IEEE J. Quantum Electron. 26, 2103–2108 (1991).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Lett. (3)

Photon. Tech. Lett. (1)

M. Nakazawa, K. Suzuki, and Y. Kimura, “3.2–5 Gb/s, 100 km error-free soliton transmission with erbium amplifiers and repeaters,” Photon. Tech. Lett. 2, 216–219 (1990); see also K. Suzuki, M. Nakazawa, E. Yamada, and Y. Kimura, “5 Gbit/s, 250 km error-free soliton transmission with Er3+-doped fibre amplifiers and repeaters,” Electron. Lett. 26, 551–553 (1990).
[Crossref]

Phys. Rev. Lett. (1)

M. Nakazawa, K. Kurokawa, H. Kubota, and E. Yamada, “Observation of the trapping of an optical soliton by adiabatic gain narrowing and its escape,” Phys. Rev. Lett. 65, 1881–1884 (1990).
[Crossref] [PubMed]

Suppl. Prog. Theor. Phys. (1)

J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Suppl. Prog. Theor. Phys. 55, 284–306 (1974).
[Crossref]

Other (1)

M. Stern, J. P. Heritage, and E. W. Chase, Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 56.

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Figures (10)

Fig. 1
Fig. 1

Femtosecond soliton trapping in a bandwidth-limited gain medium: (a) solitons (nontrapped) escaping by means of the SSFS; (b) soliton trapped with the aid of a gain bandwidth limitation.

Fig. 2
Fig. 2

Femtosecond soliton trapping in a bandwidth-limited gain: (a) solitons escaping by means of the SSFS and the third-order dispersion Dλ; (b) solitons trapped by the gain bandwidth limitation.

Fig. 3
Fig. 3

Changes in the spectrum of the soliton pulse caused by adiabatic trapping in the presence of the SSFS: (a) nontrapped condition; (b) trapped condition, in which the SSFS of the soliton pulse is stopped by gain with a finite bandwidth. (a) and (b) Correspond to Figs. 1(a) and 1(b), respectively.

Fig. 4
Fig. 4

Changes in the spectrum of the soliton pulse caused by trapping in the presence of the SSFS and Dλ: (a) nontrapped condition; (b) trapped condition. (a) and (b) Correspond to Figs. 2(a) and 2(b), respectively.

Fig. 5
Fig. 5

Transient changes in the soliton pulse width and the amplitude to the fully trapped state as a function of propagation distance: (a) soliton pulse width versus distance; (b) soliton amplitude versus distance. When the gain increases, soliton trapping occurs strongly, and a steady-state propagation of the trapped soliton is realized.

Fig. 6
Fig. 6

Pulse area change (amplitude times width) as a function of propagation distance. The parameters are gain coefficients of 1–3 dB/km.

Fig. 7
Fig. 7

Soliton spectra for gain coefficients of (a) 2 and (b) 3 dB/km as a function of propagation distance. An asymmetric profile occurs on the shorter-wavelength part, since the spectral components are located at the peak of the gain profile. The larger gain coefficient gives rise to the larger modification in the spectrum.

Fig. 8
Fig. 8

Changes in soliton pulse width (1/2η) and frequency (ξ) as a function of distance, obtained from the perturbation theory: (a) soliton pulse width versus distance; (b) frequency shift by the SSFS versus distance. Soliton trapping and standardization can be clearly seen.

Fig. 9
Fig. 9

Propagation characteristics of a pair of N = 1 subpicosecond solitons: (a) waveform changes as a function of propagation distance for a soliton pulse width of 0.8 ps and a separation of 10 ps; (b) changes in each soliton pulse width and pulse separation as a function of propagation distance.

Fig. 10
Fig. 10

Propagation characteristics of a pair of N = 1 femtosecond solitons: (a) waveform changes for a soliton pulse width of 0.3 ps and a separation of 2 ps; (b) changes in each soliton pulse width and pulse separation as a function of propagation distance.

Equations (3)

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( - i ) u q = 1 2 2 u τ 2 - i 1 6 k ( 3 ) k ( 2 ) τ 0 3 u τ 3 + u 2 u - i G [ u + 1 ( ω g τ 0 ) 2 2 u τ 2 ] + i Γ - τ n τ 0 u u 2 τ .
d ( 2 η ) d q = 2 η [ 2 G - 4 G 3 ( ω g τ 0 ) 2 ( 2 η ) 2 - 4 G ( ω g τ 0 ) 2 ( 2 ξ ) 2 ] ,
d ξ d q = - [ 4 G 3 ( ω g τ 0 ) 2 ( 2 η ) 2 ( 2 ξ ) + 8 15 ( τ n τ 0 ) ( 2 η ) 4 ] .

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