Abstract

An analytical solution is obtained for solitary pulse propagation in an amplified nonlinear dispersive system. For a homogeneously broadened gain medium, this solitary pulse has a hyperbolic secant amplitude and a hyperbolic tangent instantaneous frequency variation. The pulse is a gain-guided pulse in either the positive or the negative dispersion regime as well as in the self-focusing or self-defocusing regime. A dark solitary pulse that has a hyperbolic tangent amplitude and a similar instantaneous frequency variation is also obtained.

© 1989 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  2. L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
    [CrossRef] [PubMed]
  3. K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 1011 (1987); J. Opt. Soc. Am. B 5, 381 (1988).
    [CrossRef] [PubMed]
  4. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  5. A. Höök, D. Anderson, M. Lisak, Opt. Lett. 13, 1114 (1988), and references therein.
    [CrossRef] [PubMed]
  6. K. Nozaki, N. Bekki, Phys. Rev. Lett. 51, 2171 (1983); J. Phys. Soc. Jpn. 53, 1581 (1984); N. Bekki, K. Nozaki, Phys. Lett. A 110, 133 (1985).
    [CrossRef]
  7. R. Hirota, in Solitons, R. K. Bullough, P. J. Candrey, eds., Vol. 17 of Topics in Current Physics (Springer-Verlag, New York, 1980).
    [CrossRef]

1988 (2)

1987 (1)

1983 (1)

K. Nozaki, N. Bekki, Phys. Rev. Lett. 51, 2171 (1983); J. Phys. Soc. Jpn. 53, 1581 (1984); N. Bekki, K. Nozaki, Phys. Lett. A 110, 133 (1985).
[CrossRef]

1973 (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Anderson, D.

Bekki, N.

K. Nozaki, N. Bekki, Phys. Rev. Lett. 51, 2171 (1983); J. Phys. Soc. Jpn. 53, 1581 (1984); N. Bekki, K. Nozaki, Phys. Lett. A 110, 133 (1985).
[CrossRef]

Blow, K. J.

Doran, N. J.

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Hirota, R.

R. Hirota, in Solitons, R. K. Bullough, P. J. Candrey, eds., Vol. 17 of Topics in Current Physics (Springer-Verlag, New York, 1980).
[CrossRef]

Höök, A.

Lisak, M.

Mollenauer, L. F.

Nozaki, K.

K. Nozaki, N. Bekki, Phys. Rev. Lett. 51, 2171 (1983); J. Phys. Soc. Jpn. 53, 1581 (1984); N. Bekki, K. Nozaki, Phys. Lett. A 110, 133 (1985).
[CrossRef]

Siegman, A. E.

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

Smith, K.

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Wood, D.

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

K. Nozaki, N. Bekki, Phys. Rev. Lett. 51, 2171 (1983); J. Phys. Soc. Jpn. 53, 1581 (1984); N. Bekki, K. Nozaki, Phys. Lett. A 110, 133 (1985).
[CrossRef]

Other (2)

R. Hirota, in Solitons, R. K. Bullough, P. J. Candrey, eds., Vol. 17 of Topics in Current Physics (Springer-Verlag, New York, 1980).
[CrossRef]

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

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Figures (3)

Fig. 1
Fig. 1

Chirp parameter β from Eq. (6a) as a function of the relative dispersion D for n2 > 0 (solid curve) and n2 < 0 (dashed curve).

Fig. 2
Fig. 2

Relative width G / α T 0 of the pulse described by Eq. (6b) as a function of the relative dispersion D for n2 > 0 (solid curve) and n2 < 0 (dashed curve).

Fig. 3
Fig. 3

Relative intensity number N [see Eq. (6c)] as a function of the relative dispersion for n2 > 0.

Equations (16)

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G ( ω ) exp { gz [ 1 i T 0 ( ω ω 0 ) T 0 2 ( ω ω 0 ) 2 ] } ,
E ( t , z ) exp [ i ( ω 0 t k 0 z ) ] V ( τ , z )
τ = t ( k 0 + g T 0 ) z .
( k 0 2 ig T 0 2 ) V ττ + 2 i V z 2 i ( g γ ) V n 2 k 0 | V | 2 V = 0 ,
V = V 0 sech ( ατ ) exp { i [ Γ z + β ln cosh ( ατ ) ] } ,
β 2 3 2 = 0 ,
D = k 0 2 g T 0 2 ; α 2 T 0 2 ( β 2 + 1 ) = 3 G ,
G = g γ g ; β 2 + 3 β D = 2 ( 1 N ) ,
N = n 2 k 0 | V 0 | 2 2 k 0 α 2
Γ = Γ 0 ( 1 β 2 2 β D ) ,
ω ( τ ) = ω 0 + ( βα ) tanh ( ατ ) .
α T 0 = 3 G
V = V tanh ( ατ ) exp { i [ Γ z + β ln cosh ( ατ ) ] } ,
α 2 T 0 2 β 2 = G ,
β 2 + 3 β D = 2 ( 1 + N ) ,
Γ = Γ 0 ( 1 3 2 β D ) ,

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