Abstract

The interaction forces between two dark solitons are numerically investigated. It is found that dark solitons are less affected than bright solitons by their respective interaction forces. An empirical expression for the separation of two solitons as a function of initial separation and traveling distance is deduced, which agrees well with numerical results.

© 1989 Optical Society of America

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References

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  1. L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 437 (1985);see also A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [CrossRef]
  2. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  3. A. Hasegawa, Opt. Lett. 8, 650 (1983).
    [CrossRef] [PubMed]
  4. L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
    [CrossRef] [PubMed]
  5. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  6. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  7. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
    [CrossRef] [PubMed]
  8. W. Zhao, E. Bourkoff, Opt. Lett. 14, 703 (1989).
    [CrossRef] [PubMed]
  9. W. Zhao, E. Bourkoff, Opt. Lett. 14, 808 (1989).
    [CrossRef] [PubMed]
  10. W. Zhao, E. Bourkoff, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper ThT9.
  11. C. Desem, P. L. Chu, Inst. Electr. Eng. Proc. Pt. J 134, 145 (1987).

1989 (2)

1988 (2)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
[CrossRef] [PubMed]

1987 (1)

C. Desem, P. L. Chu, Inst. Electr. Eng. Proc. Pt. J 134, 145 (1987).

1985 (1)

L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 437 (1985);see also A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

1983 (2)

1973 (2)

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Bourkoff, E.

W. Zhao, E. Bourkoff, Opt. Lett. 14, 703 (1989).
[CrossRef] [PubMed]

W. Zhao, E. Bourkoff, Opt. Lett. 14, 808 (1989).
[CrossRef] [PubMed]

W. Zhao, E. Bourkoff, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper ThT9.

Chu, P. L.

C. Desem, P. L. Chu, Inst. Electr. Eng. Proc. Pt. J 134, 145 (1987).

Desem, C.

C. Desem, P. L. Chu, Inst. Electr. Eng. Proc. Pt. J 134, 145 (1987).

Gordon, J. P.

Hasegawa, A.

A. Hasegawa, Opt. Lett. 8, 650 (1983).
[CrossRef] [PubMed]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

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

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Leaird, D. E.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
[CrossRef] [PubMed]

L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 437 (1985);see also A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Smith, K.

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

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

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Weiner, A. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Zhao, W.

W. Zhao, E. Bourkoff, Opt. Lett. 14, 703 (1989).
[CrossRef] [PubMed]

W. Zhao, E. Bourkoff, Opt. Lett. 14, 808 (1989).
[CrossRef] [PubMed]

W. Zhao, E. Bourkoff, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper ThT9.

Appl. Phys. Lett. (2)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

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

Inst. Electr. Eng. Proc. Pt. J (1)

C. Desem, P. L. Chu, Inst. Electr. Eng. Proc. Pt. J 134, 145 (1987).

Opt. Lett. (5)

Philos. Trans. R. Soc. London Ser. A (1)

L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 437 (1985);see also A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Other (1)

W. Zhao, E. Bourkoff, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper ThT9.

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Figures (3)

Fig. 1
Fig. 1

Pulse shapes of a pair of (a) dark and (b) bright solitons after propagating a distance of (a) ξ = 96 and (b) ξ = 8 in fibres. The initial separation is q0 = 3 for both cases. The dotted curves correspond to the input pulse shapes.

Fig. 2
Fig. 2

Pulse shapes of a pair of dark solitons with initial separation of q0 = 2 after propagating a distance of (a) ξ = 16 and (b) ξ = 96. The dotted curves correspond to the input pulse shapes.

Fig. 3
Fig. 3

Relative increase of pulse separation as a function of propagation distance for initial separations of q0 = 1.5 [curve (a)], q0 = 2 [curve (b)], and q0 = 2.5 [curve (c)]. The solid curves are obtained with the empirical expression [Eq. (4)]; the dashed curves denote the numerical solution of the nonlinear Schrodinger equation.

Equations (6)

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u ( 0 , τ ) = sech ( τ q 0 ) + r sech [ r ( τ + q 0 ) ] exp ( i θ ) ,
exp [ 2 ( q q 0 ) ] = ½ { 1 + cos [ 4 ξ exp ( q 0 ) ] } .
π sinh ( 2 q 0 ) cosh ( q 0 ) [ 2 q 0 + sinh ( 2 q 0 ) ] .
u ( 0 , τ ) = tanh ( τ + q 0 ) ,
u ( 0 , τ ) = tanh ( τ q 0 ) ,
exp [ 2 ( q q 0 ) ] = ½ { 1 + exp [ 4 ξ exp ( 2 q 0 ) ] } .

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