Abstract

Novel exact solutions suggest the possibility of clean and efficient nonlinear compression of chirped solitary waves with appropriate tailoring of the gain or dispersion as a function of distance and with optional phase modulation. A numerical simulation with 20-fold compression is reported. Numerical tests reveal the robustness of the technique to perturbations of the initial condition or to the tailored gain/dispersion.

© 1996 Optical Society of America

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References

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1994

1993

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

1992

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

1991

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 2347 (1991).
[CrossRef]

1989

1988

B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
[CrossRef]

1984

1983

1982

Ahmed, K. A.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

Ashkin, A.

Botineau, J.

Chernikov, S. V.

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 2347 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
[CrossRef] [PubMed]

Chusseau, L.

Delaveque, E.

Dianov, E. M.

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 2347 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
[CrossRef] [PubMed]

Gordon, J. P.

Kolner, B. H.

B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
[CrossRef]

Laming, R. I.

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

Lee, P.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

Liu, H. F.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

Mamyshev, P. V.

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 2347 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
[CrossRef] [PubMed]

Mollenauer, L. F.

Ogawa, Y.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

Onodera, N.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

Payne, D. N.

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

Prokhorov, A. M.

Richardson, D. J.

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

Shank, C. V.

Stolen, R. H.

Tomlinson, W. J.

Tucker, R. S.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

Appl. Phys. Lett.

B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
[CrossRef]

Electron. Lett.

K. A. Ahmed, H. F. Liu, N. Onodera, P. Lee, R. S. Tucker, Y. Ogawa, Electron. Lett. 29, 57 (1993).
[CrossRef]

S. V. Chernikov, D. J. Richardson, R. I. Laming, E. M. Dianov, D. N. Payne, Electron. Lett. 28, 1210 (1992).
[CrossRef]

IEEE J. Quantum Electron.

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 2347 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

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Figures (2)

Fig. 1
Fig. 1

Twentyfold compression and four-hundredfold peak power amplification of a chirped solitary wave. Short-dashed curve, initial condition; long-dashed curve, z = 0.05; solid curve, z = 0.1.

Fig. 2
Fig. 2

Comparisons of the logarithm of power of ideally compressed nonlinear chirped solitary waves of the form of Eq. (6) with α0 = 0.95 (dashed curves) with compressed pulses under perturbations: (a) the input pulse power multiplied by 1.44, (b) the input pulse has a sinusoidal rather than a quadratic phase profile, (c) the input pulse is ideal but the ideal gain as a function of distance is approximated stepwise with five steps (see text).

Equations (15)

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i u z + 1 2 u t t + u 2 u - i α ( z ) 2 u - M ( z ) t 2 u = 0 ,
u ( z , t ) = exp [ i ϕ ( z , t ) ] A exp [ 0 z α ( z ) d z ] × sech { A exp [ 0 z α ( z ) d z ] t } , ϕ ( z , t ) = ϕ 0 - α t 2 2 + A 2 2 0 z exp [ 2 0 z α ( z ) d z ] d z
M ( z ) = ½ ( α z - α 2 ) .
α = 1 α 0 - 1 - z .
u ( z , t ) = exp [ i ϕ ( z , t ) ] ( A α α 0 ) sech ( A α t α 0 ) , ϕ ( z , t ) = ϕ 0 - α 2 [ t 2 - ( A α 0 ) 2 ] .
u ( 0 , t ) = exp ( - i α 0 t 2 2 ) sech ( t ) ,
k 2 ( z ) β ( ξ ) ,
z = - 1 t 0 2 0 ξ β ( ξ ) d ξ .
k 2 = β 0 ( 1 - α 0 z ) + b ( 1 - α 0 z ) ln ( 1 - α 0 z ) ,
b = 2 Γ t 0 2 α 0 .
β = β 0 exp { - 2 Γ ξ - [ 1 - exp ( - 2 Γ ξ ) ] / 2 Γ ξ s } ,
ξ = - t 0 2 / β 0 α 0 .
α 0 z = 1 - exp { [ exp ( - 2 Γ ξ ) - 1 ] / 2 Γ ξ s } .
β = β 0 exp ( - ξ / ξ s ) .
α 0 z = 1 - exp ( - ξ / ξ s ) .

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