Abstract

We study the inelastic collisions between orthogonally polarized solitons in a birefringent optical fiber. We show that if the collision is sufficiently slow, one soliton may be destroyed by the other, or the two solitons may fuse into a breatherlike solitary pulse. We derive a simple analytical estimate for this soliton decay, based on a condition of spatial resonance between the two solitons, and confirm this prediction by numerical simulations. Breakup of colliding solitons with different polarizations may set a fundamental lower bound to the soliton time width in soliton transmissions.

© 1991 Optical Society of America

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References

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  1. Y. Kodama, Phys. Lett. A 123, 276 (1987).
    [Crossref]
  2. Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
    [Crossref]
  3. B. Crosignani, A. Cutolo, P. Di Porto, J. Opt. Soc. Am. 72, 1136 (1982).
    [Crossref]
  4. C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
    [Crossref]
  5. S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989).
    [Crossref]
  6. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974);V. E. Zakharov, E. I. Schulman, Physica D 4, 270 (1982).
    [Crossref]
  7. C. R. Menyuk, Opt. Lett. 12, 614 (1987);J. Opt. Soc. Am. B 5, 392 (1988).
    [Crossref] [PubMed]
  8. M. N. Islam, C. D. Poole, J. P. Gordon, Opt. Lett. 14, 1011 (1989);M. N. Islam, Opt. Lett. 14, 1257 (1989);M. N. Islam, Opt. Lett. 15, 417 (1990);M. N. Islam, C. E. Soccolich, D. A. B. Miller, Opt. Lett. 15, 909 (1990).
    [Crossref] [PubMed]
  9. C. J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 15, 477 (1990);M. N. Islam, C. R. Menyuk, C. J. Chen, C. E. Soccolich, Opt. Lett. 16, 214 (1991).
    [Crossref] [PubMed]
  10. J. D. Moores, K. Bergman, H. A. Haus, E. P. Ippen, Opt. Lett. 16, 138 (1991);J. Opt. Soc. Am. B 8, 594 (1991).
    [Crossref] [PubMed]
  11. M. Eguchi, K. Hayata, M. Koshiba, Opt. Lett. 16, 82 (1991).
    [Crossref] [PubMed]
  12. Y. Sakai, R. J. Hawkins, S. Friberg, Opt. Lett. 15, 239 (1990).
    [Crossref] [PubMed]
  13. Inelastic slow soliton collisions owing to cross-phase modulation between different-wavelength solitons were reported by V. V. Afanasjev, E. M. Dianov, V. Serkin, IEEE J. Quantum Electron. 25, 2656 (1989). However, it appears that inelastic collisions in this case are just an artifact of approximating the integrable single-field NLS equation with two non-integrable coupled NLS equations.
    [Crossref]

1991 (2)

1990 (2)

1989 (5)

M. N. Islam, C. D. Poole, J. P. Gordon, Opt. Lett. 14, 1011 (1989);M. N. Islam, Opt. Lett. 14, 1257 (1989);M. N. Islam, Opt. Lett. 15, 417 (1990);M. N. Islam, C. E. Soccolich, D. A. B. Miller, Opt. Lett. 15, 909 (1990).
[Crossref] [PubMed]

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

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

Inelastic slow soliton collisions owing to cross-phase modulation between different-wavelength solitons were reported by V. V. Afanasjev, E. M. Dianov, V. Serkin, IEEE J. Quantum Electron. 25, 2656 (1989). However, it appears that inelastic collisions in this case are just an artifact of approximating the integrable single-field NLS equation with two non-integrable coupled NLS equations.
[Crossref]

S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989).
[Crossref]

1987 (2)

1982 (1)

1974 (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974);V. E. Zakharov, E. I. Schulman, Physica D 4, 270 (1982).
[Crossref]

Afanasjev, V. V.

Inelastic slow soliton collisions owing to cross-phase modulation between different-wavelength solitons were reported by V. V. Afanasjev, E. M. Dianov, V. Serkin, IEEE J. Quantum Electron. 25, 2656 (1989). However, it appears that inelastic collisions in this case are just an artifact of approximating the integrable single-field NLS equation with two non-integrable coupled NLS equations.
[Crossref]

Bergman, K.

Chen, C. J.

Crosignani, B.

Cutolo, A.

Di Porto, P.

Dianov, E. M.

Inelastic slow soliton collisions owing to cross-phase modulation between different-wavelength solitons were reported by V. V. Afanasjev, E. M. Dianov, V. Serkin, IEEE J. Quantum Electron. 25, 2656 (1989). However, it appears that inelastic collisions in this case are just an artifact of approximating the integrable single-field NLS equation with two non-integrable coupled NLS equations.
[Crossref]

Eguchi, M.

Friberg, S.

Gordon, J. P.

Haus, H. A.

Hawkins, R. J.

Hayata, K.

Ippen, E. P.

Islam, M. N.

Kivshar, Yu. S.

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Kodama, Y.

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

Koshiba, M.

Malomed, B. A.

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974);V. E. Zakharov, E. I. Schulman, Physica D 4, 270 (1982).
[Crossref]

Menyuk, C. R.

Moores, J. D.

Poole, C. D.

Sakai, Y.

Serkin, V.

Inelastic slow soliton collisions owing to cross-phase modulation between different-wavelength solitons were reported by V. V. Afanasjev, E. M. Dianov, V. Serkin, IEEE J. Quantum Electron. 25, 2656 (1989). However, it appears that inelastic collisions in this case are just an artifact of approximating the integrable single-field NLS equation with two non-integrable coupled NLS equations.
[Crossref]

Trillo, S.

Wabnitz, S.

Wai, P. K. A.

IEEE J. Quantum Electron. (2)

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

Inelastic slow soliton collisions owing to cross-phase modulation between different-wavelength solitons were reported by V. V. Afanasjev, E. M. Dianov, V. Serkin, IEEE J. Quantum Electron. 25, 2656 (1989). However, it appears that inelastic collisions in this case are just an artifact of approximating the integrable single-field NLS equation with two non-integrable coupled NLS equations.
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Opt. Lett. (6)

Phys. Lett. A (1)

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

Rev. Mod. Phys. (1)

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Sov. Phys. JETP (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974);V. E. Zakharov, E. I. Schulman, Physica D 4, 270 (1982).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Fast collision of equal solitons. Here δ = 0.8 and η2/η1 = 1.

Fig. 2
Fig. 2

Slow collision: soliton reflection and annihilation. Here δ = 0.5 and (a) η2/η1 = 2, (b) η2/η1 = 1.25, (c) η2/η1 = 1.142 (resonance).

Fig. 3
Fig. 3

Soliton fusion in breatherlike vector soliton. Here δ = 0.1 and η2/η1 = 1.

Equations (11)

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i α 1 z + i 1 V 1 α 1 t + α 2 2 α 1 t 2 + R [ | α 1 | 2 + ( 1 σ ) | α 2 | 2 ] a 1 = 0 , i α 2 z + i 1 V 2 α 2 t + α 2 2 α 2 t 2 + R [ ( 1 σ ) | α 1 | 2 + | α 2 | 2 ] a 2 = 0 .
( t z / V ) / t 0 τ , z | α | / t 0 2 = z / z 0 ξ , α 1 , 2 R t 0 2 / | α | exp ( ± Δ t α Δ 2 z 2 α ) u , υ ,
i u ξ + 1 2 2 u τ 2 + ( | u | 2 + | υ | 2 ) u = σ | υ | 2 u , i υ ξ + 1 2 2 υ τ 2 + ( | υ | 2 + | u | 2 ) υ = σ | u | 2 υ .
u 1 ( ξ = 0 , τ ) = η 1 sech [ η 1 ( τ + τ 0 ) ] exp [ i δ ( τ + τ 0 ) ] , υ 1 ( ξ = 0 , τ ) = 0 ; u 1 ( ξ = 0 , τ ) = 0 , υ 2 ( ξ = 0 , τ ) η 2 sech ( η 2 τ ) .
u 1 = η 1 sech [ η 1 ( τ + τ 0 δ ξ ) ] exp [ i δ ( τ + τ 0 ) + ξ 2 ( η 1 2 δ 2 ) ] , υ 1 0 .
i u ξ + 1 2 2 u τ 2 + η 2 2 ( 1 σ ) sech 2 ( η 2 τ ) u = 0 .
1 2 ψ n + η 2 2 ( 1 σ ) sech 2 ( η 2 τ ) Ψ = Ω Ψ .
Ω n = η 2 2 8 [ 1 + 8 ( 1 σ ) ( 2 n + 1 ) ] 2 , n = 0 , 1 , 2 ,
ψ 0 = sech ( η 2 τ ) ,
η 1 2 δ 2 = η 2 2 4 [ 1 + 8 ( 1 σ ) 1 ] 2 .
2 ( n x n y ) t 0 | α | c = 2 δ = 1 .

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