Abstract

We present a perturbative study of the mutual coupling between solitons and dispersive waves in periodically amplified links. Our analysis describes the limits of soliton transmissions operating beyond the average soliton regime.

© 1996 Optical Society of America

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References

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  1. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  2. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  3. S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
    [CrossRef]
  4. J. N. Elgin, S. M. J. Kelly, Opt. Lett. 18, 787 (1993).
    [CrossRef] [PubMed]
  5. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  6. A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 123.
  7. D. J. Kaup, A. C. Newell, Proc. R. Soc. London Ser. A 361, 413(1978).
    [CrossRef]
  8. J. N. Elgin, Phys. Rev. A 47, 331 (1993).
    [CrossRef]
  9. G. Boffetta, A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
    [CrossRef]
  10. T. Georges, B. Charbonnier, Opt. Lett. 21, 1232 (1996).
    [CrossRef] [PubMed]

1996

1993

1992

G. Boffetta, A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

1990

1978

D. J. Kaup, A. C. Newell, Proc. R. Soc. London Ser. A 361, 413(1978).
[CrossRef]

1972

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Boffetta, G.

G. Boffetta, A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

Charbonnier, B.

Elgin, J. N.

Georges, T.

Gordon, J. P.

Hasegawa, A.

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 123.

Kaup, D. J.

D. J. Kaup, A. C. Newell, Proc. R. Soc. London Ser. A 361, 413(1978).
[CrossRef]

Kelly, S. M. J.

Kodama, Y.

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 123.

Newell, A. C.

D. J. Kaup, A. C. Newell, Proc. R. Soc. London Ser. A 361, 413(1978).
[CrossRef]

Osborne, A. R.

G. Boffetta, A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Electron. Lett.

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

J. Comput. Phys.

G. Boffetta, A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

J. N. Elgin, Phys. Rev. A 47, 331 (1993).
[CrossRef]

Proc. R. Soc. London Ser. A

D. J. Kaup, A. C. Newell, Proc. R. Soc. London Ser. A 361, 413(1978).
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 123.

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Figures (3)

Fig. 1
Fig. 1

Perturbative (continuous curves) and numerical (discrete points) evolutions of the dispersive wave energy CR.

Fig. 2
Fig. 2

Same as Fig. 1 with analytical (continuous curves) results from Eq. (10) for the case ZA = 1 and from Eq. (9) for the others. The curves marked with crosses are from perturbation theory with a constant-amplitude soliton.

Fig. 3
Fig. 3

Soliton amplitude 2η and the corresponding value of the effective amplifier spacing ZAeff ≡ 4η2ZA at a fixed distance of 1000 km as a function of the amplifier spacing ZA. Continuous curves, from Eq. (9); discrete points, from numerical simulation.

Equations (12)

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i V Z + 1 2 2 V T 2 + V 2 V = i [ Γ G n = + δ ( Z n Z A ) ] V ,
i U Z + 1 2 2 U T 2 + U 2 U = i P A ( Z ) U 2 U ,
A ( Z ) = rep Z A [ exp ( 2 Γ Z ) 1 exp ( 2 Γ Z A ) 2 Γ Z A ] = n 0 a n exp ( i n κ A Z ) .
C 0 = C S + C R 4 η ( Z ) 1 π + d w log [ 1 b ( w , Z ) 2 ]
b ( w , Z ) Z = 2 i w 2 b i A ( Z ) ( w 2 + η 2 ) U ^ S * ,
η [ ( l + 1 ) Z A ] = η ( l Z A ) 1 4 π × log { 1 b ( w , l Z A ) 2 1 b [ w , ( l + 1 ) Z A ] 2 } d w ,
b [ w , ( l + 1 ) Z A ] = b ( w , l Z A ) + ( w 2 + η 2 ) U ^ exp ( 2 i w 2 Z ) × m 0 a m exp ( i D m l Z A ) exp ( i D m Z A ) 1 D m ,
b ( w , Z m ) 2 ( w 2 + η 2 ) 2 π 2 sech 2 ( π w 2 η ) Z m 2 × n Ω R a n 2 sinc ( D n Z m 2 ) 2 ,
η ( Z m ) η ( 0 ) = η ( Z m ) 1 / 2 = Z m 4 n Ω R ( n κ A 2 ) 2 a n 2 w n ( η ) U ^ ( η ) 2 .
d η d Z = 1 4 n Ω R ( n κ A 2 ) 2 a n 2 w n ( η ) U ^ ( η ) 2 .
η ( Z ) = 1 2 A n B n [ 1 exp ( B n Z ) ] ,
A n = a n 2 W n ( π κ A n 4 ) 2 sech 2 ( π W n ) , B n = A n W n [ 1 2 W n + 2 n κ A π tanh ( π W n ) ] ,

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