Abstract

A simple analytical approach based on a variational formalism is applied to an analysis of the switching dynamics of solitons in fiber nonlinear directional couplers. It is demonstrated that soliton switching may be described by a simplified Hamiltonian model that displays three different regimes of soliton dynamics, depending on the universal parameter, which is the ratio of the squared intensity ν2 to the coupling parameter κ. It follows from the analysis presented that perfect soliton switching may be achieved only for the case ν2/κ < π/2.

© 1993 Optical Society of America

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  1. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
    [Crossref] [PubMed]
  2. J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
    [Crossref]
  3. A. B. Aceves, S. Wabnitz, Opt. Lett. 17, 25 (1992).
    [Crossref] [PubMed]
  4. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 158 (1982).
  5. A. A. Mayer, Sov. J. Quantum Electron. 12, 1490 (1982); A. A. Mayer, Sov. J. Quantum Electron. 14, 101 (1984).
    [Crossref]
  6. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  7. F. Kh. Abdullaev, R. M. Abrarov, S. A. Darmanyan, Opt. Lett. 14, 131 (1989).
    [Crossref] [PubMed]
  8. Yu. S. Kivshar, B. A. Malomed, Opt. Lett. 14, 1365 (1989).
    [Crossref] [PubMed]
  9. C. Paré, M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
    [Crossref] [PubMed]
  10. P. A Bélanger, C. Paré, Phys. Rev. A 41, 5254 (1990).
    [Crossref] [PubMed]
  11. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [Crossref]
  12. D. Anderson, Yu. S. Kivshar, M. Lisak, Phys. Scr. 43, 273 (1991).
    [Crossref]
  13. Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
    [Crossref]

1992 (1)

1991 (2)

J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
[Crossref]

D. Anderson, Yu. S. Kivshar, M. Lisak, Phys. Scr. 43, 273 (1991).
[Crossref]

1990 (2)

C. Paré, M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[Crossref] [PubMed]

P. A Bélanger, C. Paré, Phys. Rev. A 41, 5254 (1990).
[Crossref] [PubMed]

1989 (3)

1988 (1)

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

1982 (2)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 158 (1982).

A. A. Mayer, Sov. J. Quantum Electron. 12, 1490 (1982); A. A. Mayer, Sov. J. Quantum Electron. 14, 101 (1984).
[Crossref]

1980 (1)

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

Abdullaev, F. Kh.

Abrarov, R. M.

Aceves, A. B.

Anderson, D.

D. Anderson, Yu. S. Kivshar, M. Lisak, Phys. Scr. 43, 273 (1991).
[Crossref]

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

Bélanger, P. A

P. A Bélanger, C. Paré, Phys. Rev. A 41, 5254 (1990).
[Crossref] [PubMed]

Darmanyan, S. A.

Florjanczyk, M.

C. Paré, M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[Crossref] [PubMed]

Gordon, J. P.

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

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 158 (1982).

Kivshar, Yu. S.

D. Anderson, Yu. S. Kivshar, M. Lisak, Phys. Scr. 43, 273 (1991).
[Crossref]

Yu. S. Kivshar, B. A. Malomed, Opt. Lett. 14, 1365 (1989).
[Crossref] [PubMed]

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

Lisak, M.

D. Anderson, Yu. S. Kivshar, M. Lisak, Phys. Scr. 43, 273 (1991).
[Crossref]

Malomed, B. A.

Yu. S. Kivshar, B. A. Malomed, Opt. Lett. 14, 1365 (1989).
[Crossref] [PubMed]

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

Mayer, A. A.

A. A. Mayer, Sov. J. Quantum Electron. 12, 1490 (1982); A. A. Mayer, Sov. J. Quantum Electron. 14, 101 (1984).
[Crossref]

Mollenauer, L. F.

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

Paré, C.

C. Paré, M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[Crossref] [PubMed]

P. A Bélanger, C. Paré, Phys. Rev. A 41, 5254 (1990).
[Crossref] [PubMed]

Soto-Crespo, J. M.

J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
[Crossref]

Stegeman, G. I.

Stolen, R. H.

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

Trillo, S.

Wabnitz, S.

Wright, E. M.

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 158 (1982).

J. Appl. Phys. (1)

J. M. Soto-Crespo, E. M. Wright, J. Appl. Phys. 70, 7240 (1991).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (3)

C. Paré, M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[Crossref] [PubMed]

P. A Bélanger, C. Paré, Phys. Rev. A 41, 5254 (1990).
[Crossref] [PubMed]

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

Phys. Rev. Lett. (1)

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

Phys. Scr. (1)

D. Anderson, Yu. S. Kivshar, M. Lisak, Phys. Scr. 43, 273 (1991).
[Crossref]

Rev. Mod. Phys. (1)

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

Sov. J. Quantum Electron. (1)

A. A. Mayer, Sov. J. Quantum Electron. 12, 1490 (1982); A. A. Mayer, Sov. J. Quantum Electron. 14, 101 (1984).
[Crossref]

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Figures (1)

Fig. 1
Fig. 1

Different regimes of the soliton dynamics described by the system of Eqs. (9) and (10) depending on the normalized parameter α = ν2/κ: (a) α < π/2; (b) π/2 < α < αcr, where αcr = 4/3[1 + (π2/12)] ≈ 2.43; (c) α > αcr. Perfect soliton switching is possible only for the case illustrated in (a).

Equations (15)

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i u x + 1 2 2 u t 2 + | u | 2 u = κ υ ,
i υ x + 1 2 2 υ t 2 + | υ | 2 υ = κ u ,
u = ν 1 exp ( i ϕ 1 ) cosh ( ν 1 t ) , υ = ν 2 exp ( i ϕ 2 ) cosh ( ν 2 t ) ,
L 1 = i 2 ( u * u x u u * x ) 1 2 | u t | 2 + 1 2 | u | 4 ,
L int = κ ( υ u * + υ * u ) .
L = 2 ν 1 d ϕ 1 d x 2 ν 2 d ϕ 2 d x + 1 3 ( ν 1 3 + ν 2 3 ) + 2 κ ν 1 ν 2 cos ϕ d x cosh ( ν 1 x ) cosh ( ν 2 x ) ,
I 1 = d t ( | u | 2 + | υ | 2 ) = 2 ( ν 1 + ν 2 ) .
Δ = ν 1 ν 2 ν 1 + ν 2 , | Δ | 1 ,
d Δ d τ = ( 1 Δ 2 ) I ( Δ ) sin ϕ ,
d ϕ d τ = α Δ + d d Δ [ ( 1 Δ 2 ) I ( Δ ) ] cos ϕ .
I ( Δ ) = 0 d x cosh 2 x + sinh 2 ( Δ x ) ,
α = ν 2 / κ .
H = 1 2 α Δ 2 ( 1 Δ 2 ) I ( Δ ) cos ϕ ,
Δ 2 = 1 , cos ϕ = 2 α / π
sin ϕ = 0 , Δ = 0 or σ α = 2 I ( Δ ) + ( Δ 1 Δ ) I ( Δ ) ,

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