Abstract

A pair of weakly interacting optical fibers, which are described by two nonlinear Schrödinger equations with linear coupling terms, is considered in the framework of perturbation theory. It is shown that the interaction of optical solitons in this system is inelastic and that they may form a bound state (bisoliton). The stability and internal oscillations of the bisoliton are also investigated.

© 1989 Optical Society of America

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References

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  1. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  2. A. A. Maier, Kvantovaya Elektron. (Moscow) 9, 2296 (1982);Kvantovaya Elektron. (Moscow) 11, 157 (1984);Kvantovaya Elektron. (Moscow) 13, 1360 (1986);Kvantovaya Elektron. (Moscow) 14, 1596 (1987).
  3. D. Marcuse, Theory of Optical Dielectric Waveguides (Academic, New York, 1974).
  4. B. S. Azimov, A. P. Sukhorukov, D. V. Trukhov, Izv. Akad. Nauk SSSR Ser. Fiz. 52, 587 (1988).
  5. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
    [Crossref] [PubMed]
  6. D. N. Christodoulidis, R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [Crossref]
  7. S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, V. E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Consultants Bureau, New York, 1984).
  8. B. A. Malomed, Wave Motion 9, 401 (1987).
    [Crossref]
  9. Yu. S. Kivshar, B. A. Malomed, Phys. Rev. B 37, 9325 (1988).
    [Crossref]
  10. B. A. Malomed, Phys. Scr. 38, 66 (1988).
    [Crossref]
  11. K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
    [Crossref] [PubMed]
  12. Yu. S. Kivshar, B. A. Malomed, J. Phys. 19, L967 (1986).
  13. C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
    [Crossref]
  14. P. K. Wai, C. R. Menyuk, Y. C. Lee, H. H. Chen, Opt. Lett. 11, 464 (1986).
    [Crossref] [PubMed]
  15. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [Crossref]
  16. C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr medium,” preprint UMBC-EER (University of Maryland, College Park, Md., 1989).
  17. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  18. A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
    [Crossref]

1988 (5)

B. S. Azimov, A. P. Sukhorukov, D. V. Trukhov, Izv. Akad. Nauk SSSR Ser. Fiz. 52, 587 (1988).

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[Crossref] [PubMed]

D. N. Christodoulidis, R. I. Joseph, Opt. Lett. 13, 53 (1988).
[Crossref]

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. B 37, 9325 (1988).
[Crossref]

B. A. Malomed, Phys. Scr. 38, 66 (1988).
[Crossref]

1987 (4)

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

B. A. Malomed, Wave Motion 9, 401 (1987).
[Crossref]

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[Crossref]

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

1986 (2)

1983 (1)

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
[Crossref]

1982 (1)

A. A. Maier, Kvantovaya Elektron. (Moscow) 9, 2296 (1982);Kvantovaya Elektron. (Moscow) 11, 157 (1984);Kvantovaya Elektron. (Moscow) 13, 1360 (1986);Kvantovaya Elektron. (Moscow) 14, 1596 (1987).

1980 (1)

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

1974 (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Azimov, B. S.

B. S. Azimov, A. P. Sukhorukov, D. V. Trukhov, Izv. Akad. Nauk SSSR Ser. Fiz. 52, 587 (1988).

Blow, K. J.

Chen, H. H.

Christodoulidis, D. N.

Doran, N. J.

Gordon, J. P.

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

Hasegawa, A.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

Haus, H. A.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
[Crossref]

Ippen, E. P.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
[Crossref]

Joseph, R. I.

Kivshar, Yu. S.

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. B 37, 9325 (1988).
[Crossref]

Yu. S. Kivshar, B. A. Malomed, J. Phys. 19, L967 (1986).

Kodama, Y.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

Lattes, A.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
[Crossref]

Lee, Y. C.

Leonberger, F. J.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
[Crossref]

Maier, A. A.

A. A. Maier, Kvantovaya Elektron. (Moscow) 9, 2296 (1982);Kvantovaya Elektron. (Moscow) 11, 157 (1984);Kvantovaya Elektron. (Moscow) 13, 1360 (1986);Kvantovaya Elektron. (Moscow) 14, 1596 (1987).

Malomed, B. A.

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. B 37, 9325 (1988).
[Crossref]

B. A. Malomed, Phys. Scr. 38, 66 (1988).
[Crossref]

B. A. Malomed, Wave Motion 9, 401 (1987).
[Crossref]

Yu. S. Kivshar, B. A. Malomed, J. Phys. 19, L967 (1986).

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, V. E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Consultants Bureau, New York, 1984).

Marcuse, D.

D. Marcuse, Theory of Optical Dielectric Waveguides (Academic, New York, 1974).

Menyuk, C. R.

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[Crossref]

P. K. Wai, C. R. Menyuk, Y. C. Lee, H. H. Chen, Opt. Lett. 11, 464 (1986).
[Crossref] [PubMed]

C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr medium,” preprint UMBC-EER (University of Maryland, College Park, Md., 1989).

Mollenauer, L. F.

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

Novikov, S. P.

S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, V. E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Consultants Bureau, New York, 1984).

Pitaevsky, L. P.

S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, V. E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Consultants Bureau, New York, 1984).

Stegeman, G. I.

Stolen, R. H.

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

Sukhorukov, A. P.

B. S. Azimov, A. P. Sukhorukov, D. V. Trukhov, Izv. Akad. Nauk SSSR Ser. Fiz. 52, 587 (1988).

Trillo, S.

Trukhov, D. V.

B. S. Azimov, A. P. Sukhorukov, D. V. Trukhov, Izv. Akad. Nauk SSSR Ser. Fiz. 52, 587 (1988).

Wabnitz, S.

Wai, P. K.

Wood, D.

Wright, E. M.

Zakharov, V. E.

S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, V. E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Consultants Bureau, New York, 1984).

IEEE J. Quantum Electron. (3)

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[Crossref]

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 1718 (1983).
[Crossref]

Izv. Akad. Nauk SSSR Ser. Fiz. (1)

B. S. Azimov, A. P. Sukhorukov, D. V. Trukhov, Izv. Akad. Nauk SSSR Ser. Fiz. 52, 587 (1988).

J. Phys. (1)

Yu. S. Kivshar, B. A. Malomed, J. Phys. 19, L967 (1986).

Kvantovaya Elektron. (Moscow) (1)

A. A. Maier, Kvantovaya Elektron. (Moscow) 9, 2296 (1982);Kvantovaya Elektron. (Moscow) 11, 157 (1984);Kvantovaya Elektron. (Moscow) 13, 1360 (1986);Kvantovaya Elektron. (Moscow) 14, 1596 (1987).

Opt. Lett. (4)

Phys. Rev. B (1)

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. B 37, 9325 (1988).
[Crossref]

Phys. Rev. Lett. (1)

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

Phys. Scr. (1)

B. A. Malomed, Phys. Scr. 38, 66 (1988).
[Crossref]

Sov. Phys. JETP (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Wave Motion (1)

B. A. Malomed, Wave Motion 9, 401 (1987).
[Crossref]

Other (3)

D. Marcuse, Theory of Optical Dielectric Waveguides (Academic, New York, 1974).

S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, V. E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Consultants Bureau, New York, 1984).

C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr medium,” preprint UMBC-EER (University of Maryland, College Park, Md., 1989).

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Equations (17)

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

i u 1 x + 2 u 1 t 2 + 2 | u 1 | 2 u 1 = α u 2 ,
i u 2 x + 2 u 2 t 2 + 2 | u 2 | 2 u 2 = α u 1 ,
I 1 = + d t ( | u 1 | 2 + | u 2 | 2 ) ,
I 2 = + d t [ | u 1 t | 2 + | u 2 t | 2 | u 1 | 4 | u 2 | 4 + α Re ( u 1 u 2 * ) ] .
H int α Re + d t u 1 u 2 * ,
u j ( x , t ) = 2 i η j exp ( i V j t / 2 i ϕ ̂ j ) cosh [ 2 η j ( t τ j ) ] ,
θ ̂ = 1 8 η d ϕ ̂ d x , V = 1 4 η d τ d x ,
d 2 τ d x 2 = 32 α η 2 ( tanh τ τ ) ( cosh τ / sinh 2 τ ) cos ϕ ̂ ,
d 2 ϕ ̂ d x 2 = 32 α η 2 ( τ / sinh τ ) sin ϕ ̂ .
U = 32 α η 2 ( τ / sinh τ ) cos ϕ ̂ .
τ = 0 , sin ϕ ̂ = 0.
ω ϕ 2 = 32 α η 2 ,
ω τ 2 = ( 32 / 3 ) α η 2 cos ϕ ̂ .
d 2 ϕ ̂ d x 2 = 32 α η 2 sin ϕ ̂ .
Δ η 1 = Δ η 2 Δ η = α π 2 sin [ ϕ ̂ 1 ( 0 ) ϕ ̂ 2 ( 0 ) ] 16 V cosh 2 ( π V / 8 η ) ,
Δ V 1 = Δ V 2 = ( V / η ) Δ η .
Δ ( I 1 ) j = 4 Δ η j , Δ ( I 2 ) j = ( 16 3 η j 2 + V j 2 ) Δ η j + 1 2 η j V j Δ V j .

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