Abstract

By use of the stimulated Raman process, optical solitons can be amplified and reshaped while they propagate through a glass fiber. When an appropriate level is chosen for the pump power (10–100 mW for 10-psec solitons), the solitons can be reshaped adiabatically. The method allows the separation between two repeaters (amplifiers) to be decided by the fiber loss rather than by the fiber dispersion.

© 1983 Optical Society of America

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References

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  1. A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers," Appl. Phys. Lett. 23, 142 (1973); L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fiber," Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  2. Y. Kodama and A. Hasegawa, "Amplification and reshaping of optical solitons in glass fiber—II," Opt. Lett. 7, 339 (1982).
    [Crossref] [PubMed]
  3. Y. R. Shen and N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. A 137, C1787 (1965).
  4. R. H. Stolen and E. P. Ippen, "Raman gain in glass optical wave guides," Appl. Phys. Lett. 22, 276 (1973).
    [Crossref]
  5. J. Stone, A. R. Chraplyvy, and C. A. Burrus, "Gas-inglass — a new Raman-gain medium: molecular hydrogen in solid-silica optical fibers," Opt. Lett. 7, 297 (1982); A. R. Chraplyvy, J. Stone, and C. A. Burrus, "Optical gain exceeding 35 dB at 1.56 µm due to stimulated Raman scattering by molecular D2 in a solid silica optical fiber," Opt. Lett. 8, 415 (1983).
    [Crossref] [PubMed]
  6. The Raman gain per unit distance γR (m-1) is related to g through γR = gP/S, where P is the pump power in watts, S is the fiber cross section in square meters, and g is in units of meters per watt. For S of 20 µm2 and g = 5×10-12 cm/W, γR becomes 2.5×10-3P (W) m-1. For the same cross section β|E|2 gives 12 ×10-3P (W) m-1;. Hence α≃0.2β.
  7. A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fiber," Proc. IEEE 69, 1145 (1981).
    [Crossref]
  8. A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
    [Crossref]

1981 (1)

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fiber," Proc. IEEE 69, 1145 (1981).
[Crossref]

1980 (1)

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[Crossref]

1973 (2)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers," Appl. Phys. Lett. 23, 142 (1973); L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fiber," Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical wave guides," Appl. Phys. Lett. 22, 276 (1973).
[Crossref]

1965 (1)

Y. R. Shen and N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. A 137, C1787 (1965).

Bloembergen, N.

Y. R. Shen and N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. A 137, C1787 (1965).

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[Crossref]

Burrus, C. A.

Chraplyvy, A. R.

Hasegawa, A.

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fiber," Proc. IEEE 69, 1145 (1981).
[Crossref]

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[Crossref]

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers," Appl. Phys. Lett. 23, 142 (1973); L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fiber," Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Y. Kodama and A. Hasegawa, "Amplification and reshaping of optical solitons in glass fiber—II," Opt. Lett. 7, 339 (1982).
[Crossref] [PubMed]

Ippen, E. P.

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical wave guides," Appl. Phys. Lett. 22, 276 (1973).
[Crossref]

Kodama, Y.

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fiber," Proc. IEEE 69, 1145 (1981).
[Crossref]

Y. Kodama and A. Hasegawa, "Amplification and reshaping of optical solitons in glass fiber—II," Opt. Lett. 7, 339 (1982).
[Crossref] [PubMed]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. A 137, C1787 (1965).

Stolen, R. H.

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical wave guides," Appl. Phys. Lett. 22, 276 (1973).
[Crossref]

Stone, J.

Tappert, F.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers," Appl. Phys. Lett. 23, 142 (1973); L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fiber," Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Appl. Phys. Lett. (2)

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical wave guides," Appl. Phys. Lett. 22, 276 (1973).
[Crossref]

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers," Appl. Phys. Lett. 23, 142 (1973); L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fiber," Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

Y. R. Shen and N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. A 137, C1787 (1965).

Other (3)

The Raman gain per unit distance γR (m-1) is related to g through γR = gP/S, where P is the pump power in watts, S is the fiber cross section in square meters, and g is in units of meters per watt. For S of 20 µm2 and g = 5×10-12 cm/W, γR becomes 2.5×10-3P (W) m-1. For the same cross section β|E|2 gives 12 ×10-3P (W) m-1;. Hence α≃0.2β.

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fiber," Proc. IEEE 69, 1145 (1981).
[Crossref]

A. Hasegawa and W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[Crossref]

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Equations (21)

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i [ E p x + ( γ p + α | E s | 2 ) E p k p E p t ] 1 2 k p 2 E p t 2 + β p | E p | 2 E p = 0 ,
i [ E s x + ( γ s α | E p | 2 ) E s k s E s t ] 1 2 k s 2 E s t 2 + β | E s | 2 E s = 0 .
α 0 . 2 β .
P 0 = 3 . 32 × 10 7 S ( μ m 2 ) λ 2 2 n / λ 2 ( ω 0 t 0 ) 2 ( W ) ,
γ s β | E s | 2
γ s 1 ( m ) 5 . 3 λ ( μ m ) S ( μ m 2 ) P 0 ( W ) .
d η d x + 2 γ s η = 4 α I p η ,
½ | E s | 2 d t = η ,
E s η sech ( η t ) e i σ
I s = ½ | E s | 2 = I 4 Δ t Δ t Δ t | E s | 2 d t 0 = 1 2 Δ t η ,
d I s R d x + 2 γ s I s R = 4 α I p I s R ,
d I s L d x 2 γ s I s L = 4 α I p I s L .
d I p d x + 2 γ p I p = 4 α I p ( I s R + I s L ) ,
d d x ln I s R + d d x ln I s L = 0 .
I s R I s L = I s 0 2 ,
I p = 1 4 α d d x ( ln I s R ) .
d d x [ ln d d x ( ln I s R ) ] + 2 γ p = 4 α ( I s R + I s 0 2 I s R ) .
2 α I p 0 γ p = 1 2 γ p I s R d I s R d x + ln ( I s R I s 0 ) + 2 α I s 0 γ p ( I s R I s 0 I s 0 I s R ) .
2 α I p 0 γ p = ln ( I M I s 0 ) + 2 α I s 0 γ p ( I M I s 0 I s 0 I M ) .
2 α I p 0 γ p = ln ( I m I s 0 ) + 2 α I s 0 γ p ( I m I s 0 I s 0 I m ) .
I p 0 I s 0 = β 2 α ( γ s β I s 0 ) ( γ p γ s ) ( γ s x 0 ) + 2 sinh ( γ s x 0 ) .

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