Abstract

We consider soliton solutions to equations describing a pair of tunnel-coupled nonlinear optical fibers with a phase-velocity mismatch between them. The analysis is based on the variational approximation, which is checked (with quite favorable results) against direct numerical solutions at selected values of the parameters. The results are presented in the form of curves demonstrating evolution of the energy in one of the soliton's components with increase of the mismatch, with the total energy of the soliton being fixed. Two bifurcations are found. One of them, which to our knowledge has not been observed in any form earlier, involves a termination, occurring at a finite value of the mismatch parameter, of the branch whose solitons have components of the opposite sign; this branch corresponds to the antisymmetric soliton in the model with no mismatch. The other, more important, bifurcation is perceived as the occurrence of a hysteresis-type behavior of another branch, whose solitons have the same signs of their components; this branch corresponds to both the symmetric and the asymmetric solitons in the model with no mismatch. The implications of this second bifurcation for the propagation of a subpicosecond soliton in a real-world dual-core fiber are also discussed.

© 1997 Optical Society of America

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References

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  1. M. Romangoli, S. Trillo, and S. Wabnitz, Opt. Quantum Electron. 24, S1237 (1992).
    [CrossRef]
  2. B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
    [CrossRef]
  3. A. W. Snyder, D. J. Mitchell, L. Poladian, D. R. Rowland, and Y. Chen, J. Opt. Soc. Am. B 8, 2102 (1991).
    [CrossRef]
  4. C. Paré and M. Florjańczyk, Phys. Rev. A 40, 4455 (1989).
    [CrossRef]
  5. N. N. Akhmediev and A. A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
    [CrossRef] [PubMed]
  6. J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
    [CrossRef]
  7. P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
    [CrossRef]
  8. I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
    [CrossRef]
  9. C. R. Menyuk and P. K. A. Wai, J. Opt. Soc. Am. B 11, 1288 (1994).
    [CrossRef]
  10. D. J. Kaup, B. A. Malomed, and R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
    [CrossRef]
  11. K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
    [CrossRef] [PubMed]
  12. A. C. Newell, Solitons in Mathematics and Physics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1985).
  13. Yu. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
    [CrossRef]

1996 (1)

B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
[CrossRef]

1994 (1)

1993 (4)

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

N. N. Akhmediev and A. A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

1992 (1)

M. Romangoli, S. Trillo, and S. Wabnitz, Opt. Quantum Electron. 24, S1237 (1992).
[CrossRef]

1991 (1)

1989 (2)

C. Paré and M. Florjańczyk, Phys. Rev. A 40, 4455 (1989).
[CrossRef]

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

1987 (1)

1981 (1)

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Akhmediev, N. N.

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

N. N. Akhmediev and A. A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Ankiewicz, A. A.

N. N. Akhmediev and A. A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Blow, K. J.

Chen, Y.

Chu, P. L.

B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

Doran, N. J.

Florjanczyk, M.

C. Paré and M. Florjańczyk, Phys. Rev. A 40, 4455 (1989).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Kaup, D. J.

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Kivshar, Yu. S.

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

Malomed, B. A.

B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

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

Menyuk, C. R.

Mitchell, D. J.

Paré, C.

C. Paré and M. Florjańczyk, Phys. Rev. A 40, 4455 (1989).
[CrossRef]

Peng, G. D.

B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

Poladian, L.

Romangoli, M.

M. Romangoli, S. Trillo, and S. Wabnitz, Opt. Quantum Electron. 24, S1237 (1992).
[CrossRef]

Rowland, D. R.

Skinner, I.

B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
[CrossRef]

Snyder, A. W.

Soto-Crespo, J. M.

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

Tasgal, R. S.

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Trillo, S.

M. Romangoli, S. Trillo, and S. Wabnitz, Opt. Quantum Electron. 24, S1237 (1992).
[CrossRef]

Wabnitz, S.

M. Romangoli, S. Trillo, and S. Wabnitz, Opt. Quantum Electron. 24, S1237 (1992).
[CrossRef]

Wai, P. K. A.

Wood, D.

IEEE J. Quantum Electron. (1)

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

M. Romangoli, S. Trillo, and S. Wabnitz, Opt. Quantum Electron. 24, S1237 (1992).
[CrossRef]

Phys. Rev. A (1)

C. Paré and M. Florjańczyk, Phys. Rev. A 40, 4455 (1989).
[CrossRef]

Phys. Rev. E (3)

B. A. Malomed, I. Skinner, G. D. Peng, and P. L. Chu, Phys. Rev. E 53, 4084 (1996).
[CrossRef]

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

N. N. Akhmediev and A. A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Other (1)

A. C. Newell, Solitons in Mathematics and Physics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1985).

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Figures (6)

Fig. 1
Fig. 1

Plots of the relative share (a) of the soliton energy in the u component, and (b) of the soliton's normalized propagation constant, (Q/λ), versus the normalized phase-velocity mismatch (κ/λ), as obtained by numerical solution of the algebraic equations (9)–(12) at the soliton's energy E=1.0. Solid curve, branch 1; dashed curve, branch 2; dotted–dashed curve, branch 3. In (b), the dotted curves correspond to the curves (Q/λ)=±(κ/λ)2+1.

Fig. 2
Fig. 2

Same as in Fig. 1 for E=2.0.

Fig. 3
Fig. 3

Same as in the previous figures, but for E=3.5. Note that branch 3 is not shown.

Fig. 4
Fig. 4

Critical value of mismatch, κ0, at which the lower part of branch 1 terminates, versus the soliton energy.

Fig. 5
Fig. 5

Numerically found solutions versus the variational approximation at E=2.0: (a) a localized solution corresponding to branch 1 in Fig. 2, (b) a delocalized solution corresponding to branch 2 in Fig. 2.

Fig. 6
Fig. 6

Amplitude of the oscillating tails of the delocalized solutions of branch 2 as a function of Q for fixed V(0); E=2.0.

Equations (24)

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iuz+κu+12uττ+|u|2u=-λv,
ivz-κv+12vττ+|v|2v=-λu,
λ1/8
E=2/π-dτ(|u|2+|v|2),
u(z, τ)=exp(iQz)U(τ),v(z, τ)=exp(iQz)V(τ),
-(Q-κ)U+12U+U3+λV=0,
-(Q+κ)V+12V+V3+λU=0,
L=14[(U)2+(V)2]+12[(Q-κ)U2+(Q+κ)V2]-14(U4+V4)-λUV.
U(τ)=A1 exp(-w12τ2),V(τ)=A2 exp(-w22τ2),
A13+8λw13(w12+w22)-3/2A2
=[-2w12+22(Q-κ)]A1,
A23+8λw23(w12+w22)-3/2A1
=[-2w22+22(Q+κ)]A2,
A13+2λw1(w12+w22)-1/2A2
=[w12/2+2(Q-κ)]A1,
A23+2λw2(w12+w22)-1/2A1
=[w22/2+2(Q+κ)]A2
E=A12w1+A22w2.
E0=4λ,E13.83λ.
E02.38,E12.28.
Q±κ2+λ2=±κ2+1/8±κ,
u(2κ)vforu>0,v>0,
u-12κvforu>0,v<0.
α2=2(Q±κ2+λ2).

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