Abstract

Optical solitons can be transmitted through a low-loss fiber to a distance exceeding 6 × 103 without a conventional repeater if they are amplified periodically at appropriate distances. An example of a numerical simulation for a 2-gigabit/sec system is presented with solitons having peak power of 11.2 mW, a width of 34.2 psec in a monomode fiber with a cross-sectional area of 20 μm2, a loss rate of 0.2 dB/km at λ = 1.5 μm, and amplifiers with 2-dB power gain spaced at every 10 km.

© 1982 Optical Society of America

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References

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  1. The first theoretical prediction of the optical soliton in glass fiber was made by A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973), and the first experimental verification was obtained by C. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  2. A. Hasegawa, Y. Kodama, “Signal transmissions by optical solitons in monomode fiber,” Proc. IEEE 69, 1145 (1981).
    [Crossref]
  3. A. Hasegawa, Y. Kodama, “Amplification and reshaping of optical solitons in glass fiber–I,” Opt. Lett. 7, 285 (1982).
    [Crossref] [PubMed]
  4. V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].
  5. Note that this distance is the same as that required for repeaters in a high-bit-rate linear system in which the bit rate is limited by the dispersion (rather than by the fiber loss).

1982 (1)

1981 (1)

A. Hasegawa, Y. Kodama, “Signal transmissions by optical solitons in monomode fiber,” Proc. IEEE 69, 1145 (1981).
[Crossref]

1973 (1)

The first theoretical prediction of the optical soliton in glass fiber was made by A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973), and the first experimental verification was obtained by C. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

1971 (1)

V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Hasegawa, A.

A. Hasegawa, Y. Kodama, “Amplification and reshaping of optical solitons in glass fiber–I,” Opt. Lett. 7, 285 (1982).
[Crossref] [PubMed]

A. Hasegawa, Y. Kodama, “Signal transmissions by optical solitons in monomode fiber,” Proc. IEEE 69, 1145 (1981).
[Crossref]

The first theoretical prediction of the optical soliton in glass fiber was made by A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973), and the first experimental verification was obtained by C. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Kodama, Y.

A. Hasegawa, Y. Kodama, “Amplification and reshaping of optical solitons in glass fiber–I,” Opt. Lett. 7, 285 (1982).
[Crossref] [PubMed]

A. Hasegawa, Y. Kodama, “Signal transmissions by optical solitons in monomode fiber,” Proc. IEEE 69, 1145 (1981).
[Crossref]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Tappert, F.

The first theoretical prediction of the optical soliton in glass fiber was made by A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973), and the first experimental verification was obtained by C. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Appl. Phys. Lett. (1)

The first theoretical prediction of the optical soliton in glass fiber was made by A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973), and the first experimental verification was obtained by C. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Opt. Lett. (1)

Proc. IEEE (1)

A. Hasegawa, Y. Kodama, “Signal transmissions by optical solitons in monomode fiber,” Proc. IEEE 69, 1145 (1981).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Other (1)

Note that this distance is the same as that required for repeaters in a high-bit-rate linear system in which the bit rate is limited by the dispersion (rather than by the fiber loss).

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Figures (3)

Fig. 1
Fig. 1

Panoramic display of soliton structures at multiples of 540 km [540 × (n − 1) km]. A unit of periodic pulse series of on–on–off is shown to demonstrate the stationarity of the pulse shapes as well as the lack of interference between two solitons.

Fig. 2
Fig. 2

Two sets of solitons (solid line) separated by eight times their widths at 2700 km from the source. The dashed line shows the initial shape. The figure is an expansion of Fig. 1 at n = 6. Nominal parameters are λ = 1.5 μm and γ = 0.2 dB/km and an amplifier spacing of 9.99 km.

Fig. 3
Fig. 3

Same as Fig. 2 but at 5940 km, showing almost no deterioration in the pulse quality.

Equations (23)

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Γ | q | 2 .
i q ξ + 1 2 2 q τ 2 + | q | 2 q = i Γ q + i β 3 q τ 3 ,
ξ = 10 9 x / λ ,
τ = 10 4 . 5 ( λ k ) 1 / 2 ( t x υ g ) ,
q = 10 4 . 5 ( π n 2 ) 1 / 2 ϕ ,
Γ = 10 9 λ γ ,
β = 1 6 k k 10 4 . 5 ( λ k ) 1 / 2 .
k = k ω = n c ( 1 λ n n λ ) ,
k = 2 k ω 2 = λ 2 π c 2 ( λ 2 2 n λ 2 ) ,
k = 3 k ω 3 = λ 2 4 π 2 c 3 λ ( λ 3 2 n λ 2 ) ,
q ( τ , ξ ) = q ˆ ( τ , ξ ) ( 1 + β { 2 η 2 τ 3 η × tanh [ η ( τ 2 β σ ) ] } + i 2 Γ τ 2 ) exp ( i σ ) + O ( Γ 2 , β 2 , Γ β ) | τ | O ( Γ 1 / 2 ) ,
q ˆ ( τ , ξ ) = η sech [ η ( τ 2 β σ ) ] , η = q 0 exp ( 2 Γ ξ ) ,
σ = q 0 2 8 Γ [ 1 exp ( 4 Γ ξ ) ] .
Γ = 0 . 0346 ,
β = 0 . 0019 ,
S ( ξ , τ ) = i [ exp ( Γ ξ 0 ) 1 ] n = 1 N δ ( ξ n ξ 0 ) q ( ξ , τ ) .
S ( ξ , τ ) i Γ ξ 0 n = 1 N δ ( ξ n ξ 0 ) q ( ξ , τ ) i Γ δ ( x ξ ) q ( ξ , τ ) d x as ξ 0 0 = i Γ q ( ξ , τ ) .
η sech η τ a η sech η τ ,
A = ( 2 a 1 ) η .
Δ E = a 2 η 2 sech 2 η τ d τ A 2 sech 2 A τ d τ = 2 η ( a 1 ) 2 .
ξ 0 < τ 0 2 = q 0 2 ,
x 0 < t 0 2 / k ,
a = exp ( T ξ 0 ) .

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