Abstract

The shadows generated by the interaction of a pair of solitons in a birefringent optical fiber are studied numerically. The amplitudes, widths, and shapes of the shadows are calculated.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. N. Islam, C. E. Soccolich, D. A. B. Miller, Opt. Lett. 15, 909 (1990).
    [CrossRef] [PubMed]
  2. M. N. Islam, C. R. Menyuk, C.-J. Chen, C. E. Soccolich, Opt. Lett. 16, 214 (1991).
    [CrossRef] [PubMed]
  3. C.-J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 15, 477 (1990).
    [CrossRef] [PubMed]
  4. C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
    [CrossRef]
  5. G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980), pp. 34–38.
  6. B. A. Malomed, in Proceedings of the Workshop on Optical Solitons, F. Kh. Abdullaev, ed. (World Scientific, Singapore, 1989), pp. 81–103.
  7. C. R. Menyuk, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WF2.
  8. T. Ueda, W L. Kath, Phys. Rev. A 42, 563 (1990).
    [CrossRef] [PubMed]

1991 (1)

1990 (3)

1989 (1)

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

Chen, C.-J.

Islam, M. N.

Kath, W L.

T. Ueda, W L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Lamb, G. L.

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980), pp. 34–38.

Malomed, B. A.

B. A. Malomed, in Proceedings of the Workshop on Optical Solitons, F. Kh. Abdullaev, ed. (World Scientific, Singapore, 1989), pp. 81–103.

Menyuk, C. R.

M. N. Islam, C. R. Menyuk, C.-J. Chen, C. E. Soccolich, Opt. Lett. 16, 214 (1991).
[CrossRef] [PubMed]

C.-J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 15, 477 (1990).
[CrossRef] [PubMed]

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

C. R. Menyuk, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WF2.

Miller, D. A. B.

Soccolich, C. E.

Ueda, T.

T. Ueda, W L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Wai, P. K. A.

IEEE J. Quantum Electron. (1)

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

T. Ueda, W L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Other (3)

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980), pp. 34–38.

B. A. Malomed, in Proceedings of the Workshop on Optical Solitons, F. Kh. Abdullaev, ed. (World Scientific, Singapore, 1989), pp. 81–103.

C. R. Menyuk, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WF2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Soliton and its shadow and (b) the shadow and its approximation shown at a distance of 50 soliton periods with A0 = 1 and s0 = 0. The u polarization is shown as a solid curve, the υ polarization is shown as a dashed curve, and the approximation is shown as a dashed–dotted curve.

Fig. 2
Fig. 2

Amplitudes of the shadows versus initial separation with A0 = 1. The points correspond to the curves in Fig. 4.

Fig. 3
Fig. 3

Asymptotic behavior of colliding solitons as functions of A0 and s0. There is a region in which solitons always self-trap, a region in which solitons always pass through each other, and a transition region.

Fig. 4
Fig. 4

Amplitudes of the shadows versus the initial amplitudes of the solitons. The solid curves are for s0 ≤ 0, and the dashed curves are for s0 > 0. The flat part of the curves indicates the transition regions, beyond which bound states form. The curves correspond to the points in Fig. 2.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

i u ξ + i δ u s + 1 2 2 u s 2 + ( | u | 2 + B | υ | 2 ) u = 0 , i υ ξ i δ υ s + 1 2 2 υ s 2 + ( B | υ | 2 + | υ | 2 ) υ = 0 ,
ϕ = A shadow { sech [ A soliton ( s s p ) ] } ( 1 + 8 B 1 ) / 2 ,

Metrics