Abstract

Soliton collisions in birefringent optical fibers have been investigated numerically. It is found that soliton collisions can be divided into three kinds of behavior depending on the value of the linear birefringence. Both soliton mixing and soliton center-frequency shifts have been studied in detail. A new kind of soliton state has been found. The Čerenkov emission generated by soliton collision has also been found numerically.

© 1994 Optical Society of America

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  1. K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
    [CrossRef] [PubMed]
  2. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegemen, Opt. Lett. 13, 871 (1988).
    [CrossRef] [PubMed]
  3. M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
    [CrossRef] [PubMed]
  4. C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef] [PubMed]
  5. C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
    [CrossRef]
  6. Y. S. Kivshar, J. Opt. Soc. Am. B 7, 2204 (1990).
    [CrossRef]
  7. B. A. Malomed, Phys. Rev. A 43, 410 (1991).
    [CrossRef] [PubMed]
  8. M. N. Islam, C. E. Soccolich, and D. A. B. Miller, Opt. Lett. 15, 909 (1990).
    [CrossRef] [PubMed]
  9. M. N. Islam, C. R. Menyuk, C.-J. Chen, and C. E. Soccolich, Opt. Lett. 16, 214 (1991).
    [CrossRef] [PubMed]
  10. Y. Kodama, Phys. Lett. A 123, 276 (1987).
    [CrossRef]
  11. Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
    [CrossRef]
  12. L. M. Kovachev, Opt. Quantum Electron. 23, 1091 (1991).
    [CrossRef]
  13. Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, Opt. Lett. 17, 1265 (1992).
    [CrossRef] [PubMed]
  14. B. A. Malomed and S. Wabnitz, Opt. Lett. 16, 1388 (1991).
    [CrossRef] [PubMed]
  15. X. D. Cao and C. J. McKinstrie, J. Opt. Soc. Am. B 10, 1202 (1993).
    [CrossRef]
  16. E. Caglioti, B. Crosignani, and P. Di Porto, Phys. Rev. A 38, 4036 (1988).
    [CrossRef] [PubMed]

Blow, K. J.

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

Caglioti, E.

E. Caglioti, B. Crosignani, and P. Di Porto, Phys. Rev. A 38, 4036 (1988).
[CrossRef] [PubMed]

Cao, X. D.

X. D. Cao and C. J. McKinstrie, J. Opt. Soc. Am. B 10, 1202 (1993).
[CrossRef]

Chen, C.-J.

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, Opt. Lett. 17, 1265 (1992).
[CrossRef] [PubMed]

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

Crosignani, B.

E. Caglioti, B. Crosignani, and P. Di Porto, Phys. Rev. A 38, 4036 (1988).
[CrossRef] [PubMed]

Doran, N. J.

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

Islam, M. N.

M. N. Islam, C. E. Soccolich, and D. A. B. Miller, Opt. Lett. 15, 909 (1990).
[CrossRef] [PubMed]

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

Kivshar, Y. S.

Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

Y. S. Kivshar, J. Opt. Soc. Am. B 7, 2204 (1990).
[CrossRef]

Kodama, Y.

Y. Kodama, Phys. Lett. A 123, 276 (1987).
[CrossRef]

Kovachev, L. M.

L. M. Kovachev, Opt. Quantum Electron. 23, 1091 (1991).
[CrossRef]

Malomed, B. A.

B. A. Malomed and S. Wabnitz, Opt. Lett. 16, 1388 (1991).
[CrossRef] [PubMed]

Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

B. A. Malomed, Phys. Rev. A 43, 410 (1991).
[CrossRef] [PubMed]

McKinstrie, C. J.

X. D. Cao and C. J. McKinstrie, J. Opt. Soc. Am. B 10, 1202 (1993).
[CrossRef]

Menyuk, C. R.

C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef] [PubMed]

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

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

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, Opt. Lett. 17, 1265 (1992).
[CrossRef] [PubMed]

Miller, D. A. B.

M. N. Islam, C. E. Soccolich, and D. A. B. Miller, Opt. Lett. 15, 909 (1990).
[CrossRef] [PubMed]

Porto, P. Di

E. Caglioti, B. Crosignani, and P. Di Porto, Phys. Rev. A 38, 4036 (1988).
[CrossRef] [PubMed]

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Soccolich, C. E.

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

M. N. Islam, C. E. Soccolich, and D. A. B. Miller, Opt. Lett. 15, 909 (1990).
[CrossRef] [PubMed]

Stegemen, G. I.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegemen, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

Tratnik, M. V.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Trillo, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegemen, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

Wabnitz, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegemen, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

B. A. Malomed and S. Wabnitz, Opt. Lett. 16, 1388 (1991).
[CrossRef] [PubMed]

Wai, P. K. A.

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, Opt. Lett. 17, 1265 (1992).
[CrossRef] [PubMed]

Wang, Q.

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, Opt. Lett. 17, 1265 (1992).
[CrossRef] [PubMed]

Wood, D.

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

Wright, E. M.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegemen, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

Other

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegemen, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef] [PubMed]

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

Y. S. Kivshar, J. Opt. Soc. Am. B 7, 2204 (1990).
[CrossRef]

B. A. Malomed, Phys. Rev. A 43, 410 (1991).
[CrossRef] [PubMed]

M. N. Islam, C. E. Soccolich, and D. A. B. Miller, Opt. Lett. 15, 909 (1990).
[CrossRef] [PubMed]

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

Y. Kodama, Phys. Lett. A 123, 276 (1987).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

L. M. Kovachev, Opt. Quantum Electron. 23, 1091 (1991).
[CrossRef]

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, Opt. Lett. 17, 1265 (1992).
[CrossRef] [PubMed]

B. A. Malomed and S. Wabnitz, Opt. Lett. 16, 1388 (1991).
[CrossRef] [PubMed]

X. D. Cao and C. J. McKinstrie, J. Opt. Soc. Am. B 10, 1202 (1993).
[CrossRef]

E. Caglioti, B. Crosignani, and P. Di Porto, Phys. Rev. A 38, 4036 (1988).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Dependence of M on the linear birefringence δ. (a) Overall behavior. (b) Fine structure of the second interval, 0.27 < δ < 0.305.

Fig. 2
Fig. 2

Dependence of υδ of colliding solitons on the linear birefringence δ. (a) Overall behavior. (b) Fine structure of the second interval, 0.27 < δ < 0.305.

Fig. 3
Fig. 3

Dynamic behavior of soliton collision in the second interval with δ = 0.298. (a) Variation of m(z) versus propagation distance Z. (b) Variation of center of mass of one soliton versus propagation distance Z.

Fig. 4
Fig. 4

Dynamic behavior of soliton collision in the second interval with δ = 0.304. (a) Variation of m(z) versus propagation distance Z. (b) Variation of center of mass of one soliton versus propagation distance Z.

Fig. 5
Fig. 5

There is no mixing when velocities of colliding solitons are large. δ = 2.

Fig. 6
Fig. 6

New kinds of soliton generated by soliton collision. δ = 0.304. After 200 soliton periods, one of the outgoing solitons is used as the initial condition for the next simulation.

Fig. 7
Fig. 7

Čerenkov emission generated by two colliding solitons in the second interval. δ = 0.2, propagation distance Z = 200 soliton periods. (a) The trapping state is shown in the center, while the radiation is shown outside the center part. The radiation field is amplified 1000 times. (b) Radiation detected at a position far from the trapping region, t = 20.

Equations (3)

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i ( z + δ t ) A 1 + 1 2 2 t 2 A 1 + ( | A 1 | 2 + | A 2 | 2 ) A 1 = 0 , i ( z δ t ) A 2 + 1 2 2 t 2 A 2 + ( | A 2 | 2 + | A 1 | 2 ) A 2 = 0 ,
A 1 ( z = 0 , t ) = A 0 sech [ A 0 ( t + t 0 ) ] , A 2 = 0 , A 2 ( z = 0 , t ) = A 0 sech [ A 0 ( t t 0 ) ] , A 1 = 0 ,
m ( z ) = + | A 1 ( z , t ) | | A 2 ( z , t ) | d t + | A 1 ( z = 0 , t ) | 2 d t .

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