Abstract

An analytical investigation is made of the asymptotic propagation properties of pulses evolving from nonsoliton initial conditions in an optical-fiber communication system. Explicit analytical results are obtained for the characteristic parameters of the asymptotically emerging soliton as well as of the accompanying decaying nonsoliton part. The importance of the dispersively decaying part of the pulse for a soliton-based optical-fiber communication system is especially emphasized.

© 1988 Optical Society of America

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References

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  1. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  2. H. E. Lassen, F. Mengel, B. Tromborg, N. C. Albertsen, P. L. Christiansen, Opt. Lett. 10, 34 (1985).
    [CrossRef] [PubMed]
  3. C. Desem, P. L. Chu, Opt. Lett. 11, 248 (1986).
    [CrossRef]
  4. K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986).
    [CrossRef]
  5. D. Anderson, M. Lisak, P. Anderson, Opt. Lett. 10, 134 (1985).
    [CrossRef] [PubMed]
  6. S. Novikov, S. V. Manakov, Theory of Solitons (Consultants Bureau, New York, 1984).
  7. Z. V. Lewis, Phys. Lett. A 112, 99 (1985).
    [CrossRef]
  8. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  9. D. Anderson, M. Lisak, Opt. Lett. 11, 569 (1986).
    [CrossRef] [PubMed]
  10. J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1984).
    [CrossRef]

1986 (3)

1985 (3)

1984 (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1984).
[CrossRef]

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Albertsen, N. C.

Anderson, D.

Anderson, P.

Blow, K. J.

K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986).
[CrossRef]

Christiansen, P. L.

Chu, P. L.

Desem, C.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Lassen, H. E.

Lewis, Z. V.

Z. V. Lewis, Phys. Lett. A 112, 99 (1985).
[CrossRef]

Lisak, M.

Manakov, S. V.

S. Novikov, S. V. Manakov, Theory of Solitons (Consultants Bureau, New York, 1984).

Mengel, F.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Novikov, S.

S. Novikov, S. V. Manakov, Theory of Solitons (Consultants Bureau, New York, 1984).

Satsuma, J.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1984).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Tromborg, B.

Wood, D.

K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986).
[CrossRef]

Yajima, N.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1984).
[CrossRef]

Opt. Commun. (1)

K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (1)

Z. V. Lewis, Phys. Lett. A 112, 99 (1985).
[CrossRef]

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Prog. Theor. Phys. Suppl. (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1984).
[CrossRef]

Other (1)

S. Novikov, S. V. Manakov, Theory of Solitons (Consultants Bureau, New York, 1984).

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Figures (2)

Fig. 1
Fig. 1

Asymptotic soliton amplitude as a function of initial frequency chirp: dashed curves, formula (18); solid curves, according to numerical results from Ref. 3.

Fig. 2
Fig. 2

Critical frequency chirp at which the soliton property is lost versus initial amplitude: solid curve, Eq. (19); × and □, numerical results from Refs. 3 and 4, respectively.

Equations (31)

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ψ τ 2 + 1 2 2 ψ τ 2 + ψ 2 ψ = 0 ,
ψ ( 0 , τ ) = N sech τ exp ( i ϕ 0 τ 2 ) ,
δ L d x d τ = 0 ,
L = i ( ψ ψ * x - ψ * ψ x ) + | ψ τ | 2 - ψ 4 .
ψ T = A ( x ) sech [ τ a ( x ) ] exp [ i b ( x ) τ 2 ] .
δ L d x = 0 ,
L = - + L ( ψ T ) d τ .
1 2 ( d a d x ) 2 + π ( a ) = 0 ,
π ( a ) = 2 π 2 ( 1 a 2 - 1 ) - 4 N 2 π 2 ( 1 a - 1 ) - 2 ϕ 0 2 .
b ( x ) = 1 2 d d x ln a ( x ) , A 2 = N 2 a ( x ) , d d x arg A = - 1 3 a 2 + 5 6 N 2 a .
a ( x ) ~ 2 [ ϕ 0 2 + 1 π 2 ( 1 - 2 N 2 ) ] 1 / 2 x .
A ( x , τ ) 2 = N 2 2 ϕ 0 x sech 2 τ 2 ϕ 0 x ,
σ RMS 2 = - + τ 2 ψ ( x , τ ) 2 d τ / - + ψ ( x , τ ) 2 d τ ,
σ RMS 2 ( x ) / σ RMS 2 ( 0 ) = a 2 = 4 [ ϕ 0 2 + 1 π 2 ( 1 - 2 N 2 ) ] x 2 .
σ RMS 2 ( x ) / σ RMS 2 ( 0 ) ~ - + | ψ ( 0 , τ ) τ | 2 d τ / - + τ 2 ψ ( 0 , τ ) 2 d τ = 4 ( ϕ 0 2 + 1 π 2 ) x 2 .
a min , max = N 2 ± ( N 4 + 1 + π 2 ϕ 0 2 - 2 N 2 ) 1 / 2 2 N 2 - 1 - π 2 ϕ 0 2 .
η = ( 2 N 2 - 1 - π 2 ϕ 0 2 ) 1 / 2 .
η ( 2 N 2 - 1 ) [ 1 - π 2 ϕ 0 2 2 ( 2 N 2 - 1 ) ] .
η = ( 2 N - 1 ) [ 1 - ϕ 2 ϕ * 2 ( 2 N - 1 ) 2 ] ,
ϕ c = ϕ * ( 2 N - 1 ) .
ψ = ψ s + ψ r ,
ψ s ( x , τ ) = η sech η τ exp ( i η 2 x / 2 ) A s exp ( i θ s ) ,
A r = f ( τ / x ) x .
A r = A k x sech τ k x ,
ψ r ( x , τ ) = A k x sech τ k x exp ( i τ 2 / 2 x ) .
- + ψ ( x , τ ) 2 d τ = constant , - + ( | ψ ( x , τ ) 2 τ | - ψ ( x , τ ) 4 ) d τ = constant .
A 2 = N 2 - η , k 2 = 4 N 2 π 2 1 + π 2 ϕ 0 2 - 2 N 2 + η 3 / N 2 N 2 - η ,
Δ = energy of asymptotic soliton energy of initial pulse = η N 2 .
σ RMS 2 ( x ) / σ RMS 2 ( 0 ) = A 2 k 2 N 2 x 2 ,
α = 2 π [ 1 + π 2 ϕ 0 2 - 2 N 2 + η 3 ( N , ϕ 0 ) N 2 ] 1 / 2 .
S peak intensity of soliton peak intensity of dispersive background = η 2 A 2 / k x = η 2 N ( N 2 - η ) 3 / 2 α x .

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