Abstract

We theoretically examine the interaction between two solitons in a double-mode optical fiber. The bound state between two solitons of different modes is investigated, including both dark and bright solitons. It is shown that interaction between dark solitons as well as between bright solitons is always attractive, but the interaction between bright and dark solitons may be repulsive. Analytical results are in agreement with numerical ones.

© 1989 Optical Society of America

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  1. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  2. B. Hermansson, D. Yevick, Electron. Lett. 19, 570 (1983).
    [CrossRef]
  3. P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
    [CrossRef]
  4. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  5. P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985);Opt. Lett. 12, 349 (1987).
    [CrossRef] [PubMed]
  6. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23510 (1987).
    [CrossRef]
  7. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
    [CrossRef] [PubMed]
  8. Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
    [CrossRef] [PubMed]
  9. D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
    [CrossRef] [PubMed]
  10. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
    [CrossRef] [PubMed]
  11. A. Hasegawa, Opt. Lett. 6, 62 (1981).
  12. B. Crosignani, P. Di Porto, Opt. Lett. 6, 329 (1981).
    [CrossRef] [PubMed]
  13. E. Caglioti, B. Crosignani, P. Di Porto, Phys. Rev. A 38, 4036 (1988).
    [CrossRef] [PubMed]
  14. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 871 (1988).
    [CrossRef] [PubMed]
  15. V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).
  16. S. A. Gredeskul, Yu. S. Kivshar, Phys. Rev. Lett. 62, 977 (1989).
    [CrossRef] [PubMed]
  17. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [CrossRef] [PubMed]
  18. D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
    [CrossRef]

1989 (1)

S. A. Gredeskul, Yu. S. Kivshar, Phys. Rev. Lett. 62, 977 (1989).
[CrossRef] [PubMed]

1988 (7)

D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 53 (1988).
[CrossRef] [PubMed]

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[CrossRef]

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

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

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).

D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

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

1987 (3)

1985 (2)

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985);Opt. Lett. 12, 349 (1987).
[CrossRef] [PubMed]

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

1983 (2)

J. P. Gordon, Opt. Lett. 8, 596 (1983).
[CrossRef] [PubMed]

B. Hermansson, D. Yevick, Electron. Lett. 19, 570 (1983).
[CrossRef]

1981 (2)

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Afanasyev, V. V.

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).

Caglioti, E.

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

Christodoulides, D. N.

Chu, P. L.

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985);Opt. Lett. 12, 349 (1987).
[CrossRef] [PubMed]

Crosignani, B.

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

B. Crosignani, P. Di Porto, Opt. Lett. 6, 329 (1981).
[CrossRef] [PubMed]

Desem, C.

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985);Opt. Lett. 12, 349 (1987).
[CrossRef] [PubMed]

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

Di Porto, P.

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

B. Crosignani, P. Di Porto, Opt. Lett. 6, 329 (1981).
[CrossRef] [PubMed]

Dianov, E. M.

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).

Gordon, J. P.

J. P. Gordon, Opt. Lett. 8, 596 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Gredeskul, S. A.

S. A. Gredeskul, Yu. S. Kivshar, Phys. Rev. Lett. 62, 977 (1989).
[CrossRef] [PubMed]

Grischkowsky, D.

D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Guiliani, G.

D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Halas, K.

D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Hasegawa, A.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23510 (1987).
[CrossRef]

A. Hasegawa, Opt. Lett. 6, 62 (1981).

Hawkins, R. J.

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

Hermansson, B.

B. Hermansson, D. Yevick, Electron. Lett. 19, 570 (1983).
[CrossRef]

Joseph, R. I.

Kirschner, E. M.

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

Kivshar, Yu. S.

S. A. Gredeskul, Yu. S. Kivshar, Phys. Rev. Lett. 62, 977 (1989).
[CrossRef] [PubMed]

Kodama, Y.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23510 (1987).
[CrossRef]

Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
[CrossRef] [PubMed]

Krökel, D.

D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Mitschke, F. M.

Mollenauer, L. F.

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Nozaki, K.

Prokhorov, A. M.

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).

Serkin, V. N.

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).

Stegeman, G. I.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Thurston, R. N.

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

Trillo, S.

Wabnitz, S.

Weiner, A. M.

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

Wright, E. M.

Yevick, D.

B. Hermansson, D. Yevick, Electron. Lett. 19, 570 (1983).
[CrossRef]

Electron. Lett. (3)

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985);Opt. Lett. 12, 349 (1987).
[CrossRef] [PubMed]

B. Hermansson, D. Yevick, Electron. Lett. 19, 570 (1983).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23510 (1987).
[CrossRef]

Opt. Lett. (7)

Phys. Lett. A (1)

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (4)

D. Krökel, K. Halas, G. Guiliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

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

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

S. A. Gredeskul, Yu. S. Kivshar, Phys. Rev. Lett. 62, 977 (1989).
[CrossRef] [PubMed]

Pis'ma Zh. Eksp. Teor. Fiz. (1)

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, Pis'ma Zh. Eksp. Teor. Fiz. 48, 588 (1988).

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Figures (3)

Fig. 1
Fig. 1

Dynamics of coupled dark and bright solitons of different optical modes for R11 = R22 = 3 and R12 = R21 = 1 ( = 2/3). The pulse intensities in both modes are shown together. (a) The initial shift is zero; (b) the initial shift is 0.1.

Fig. 2
Fig. 2

The same as in Fig. 1 but for the opposite case: R11 = R22 = 18 and R21 = R12 = 20 ( ≈ 2.2). The initial shift is 0.5.

Fig. 3
Fig. 3

Oscillating motion of two bright solitons of different modes for R11 = R22 = 1.75 and R12 = R21 = 0.25 ( = 2/7).

Equations (11)

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

i υ z + σ υ υ t t + ( R 11 | υ | 2 + R 12 | u | 2 ) υ = 0 , i u z + σ u u t t + ( R 21 | υ | 2 + R 22 | u | 2 ) u = 0 ,
υ = ( 2 / R 11 ) 1 / 2 e i α z V ( z , t ) , u = ( 2 / R 22 ) 1 / 2 e i β z U ( z , t )
i V z + σ υ V t t + ( 2 | V | 2 + 1 | U | 2 + α ) V = 0 , i U z + σ υ U t t + ( 2 | U | 2 + 2 | V | 2 + β ) U = 0.
H int = d t ( | U | 2 | V | 2 + α | V | 2 + β | U | 2 + γ ) .
V = A e i η 2 z sech ( η t ) , U = A tanh ( η t ) ,
η 2 = A 2 ( 1 / 2 ) ,
H int ( b d ) = H 0 + H 1 cosh Δ sinh 3 Δ ( Δ tanh Δ ) ,
V = A tanh ( η t ) , U = A e i η 2 z sech ( η t ) ,
η 2 = A 2 ( / 2 1 )
V = U = ( η / 1 + / 2 ) e i η 2 z sech ( η t ) ,
V = U = ( η / 1 + / 2 ) tanh ( η t ) ,

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