Abstract

We give an approximate analytical solution to the coupled nonlinear Schrödinger equations that govern the soliton switching in a nonlinear fiber coupler. We have derived, in simple analytical form, the switching condition by which solitons can be switched from one core to another. The analytical result has been checked against the numerical results, and it is found that there is close agreement.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  2. D. R. Heatley, E. M. Wright, J. Ehrlich, G. I. Stegeman, Opt. Lett. 13, 419 (1988).
    [CrossRef] [PubMed]
  3. G. D. Peng, A. Ankiewicz, Int. J. Nonlinear Opt. Phys. 1, 135 (1992).
    [CrossRef]
  4. C. C. Yang, Opt. Lett. 16, 1641 (1991).
    [CrossRef] [PubMed]
  5. J. Wilson, G. I. Stegeman, E. M. Wright, Opt. Lett. 16, 1653 (1991).
    [CrossRef] [PubMed]
  6. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
    [CrossRef] [PubMed]
  7. F. Kh. Abdullaev, R. M. Abrarov, S. A. Darmanyan, Opt. Lett. 14, 131 (1989).
    [CrossRef] [PubMed]
  8. Y. S. Kivshar, B. A. Malomed, Opt. Lett. 14, 1365 (1989).
    [CrossRef] [PubMed]
  9. C. Paré, M. Florjanczyk, Phys. Rev. A 41, 6287 (1990).
    [CrossRef] [PubMed]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 5.
  11. A. D. Bonderson, D. Anderson, M. Lisak, Phys. Scr. 20, 479 (1979); D. Anderson, M. Lisak, T. Reichel, J. Opt. Soc. Am. B 5, 207 (1988); T. Ueda, W. L. Kath, Phys. Rev. A 42, 563 (1990).
    [CrossRef] [PubMed]

1992 (1)

G. D. Peng, A. Ankiewicz, Int. J. Nonlinear Opt. Phys. 1, 135 (1992).
[CrossRef]

1991 (2)

1990 (1)

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

1989 (2)

1988 (2)

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

1979 (1)

A. D. Bonderson, D. Anderson, M. Lisak, Phys. Scr. 20, 479 (1979); D. Anderson, M. Lisak, T. Reichel, J. Opt. Soc. Am. B 5, 207 (1988); T. Ueda, W. L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Abdullaev, F. Kh.

Abrarov, R. M.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 5.

Anderson, D.

A. D. Bonderson, D. Anderson, M. Lisak, Phys. Scr. 20, 479 (1979); D. Anderson, M. Lisak, T. Reichel, J. Opt. Soc. Am. B 5, 207 (1988); T. Ueda, W. L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Ankiewicz, A.

G. D. Peng, A. Ankiewicz, Int. J. Nonlinear Opt. Phys. 1, 135 (1992).
[CrossRef]

Bonderson, A. D.

A. D. Bonderson, D. Anderson, M. Lisak, Phys. Scr. 20, 479 (1979); D. Anderson, M. Lisak, T. Reichel, J. Opt. Soc. Am. B 5, 207 (1988); T. Ueda, W. L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Darmanyan, S. A.

Ehrlich, J.

Florjanczyk, M.

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

Heatley, D. R.

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Kivshar, Y. S.

Lisak, M.

A. D. Bonderson, D. Anderson, M. Lisak, Phys. Scr. 20, 479 (1979); D. Anderson, M. Lisak, T. Reichel, J. Opt. Soc. Am. B 5, 207 (1988); T. Ueda, W. L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Malomed, B. A.

Paré, C.

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

Peng, G. D.

G. D. Peng, A. Ankiewicz, Int. J. Nonlinear Opt. Phys. 1, 135 (1992).
[CrossRef]

Stegeman, G. I.

Trillo, S.

Wabnitz, S.

Wilson, J.

Wright, E. M.

Yang, C. C.

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

G. D. Peng, A. Ankiewicz, Int. J. Nonlinear Opt. Phys. 1, 135 (1992).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (1)

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

Phys. Scr. (1)

A. D. Bonderson, D. Anderson, M. Lisak, Phys. Scr. 20, 479 (1979); D. Anderson, M. Lisak, T. Reichel, J. Opt. Soc. Am. B 5, 207 (1988); T. Ueda, W. L. Kath, Phys. Rev. A 42, 563 (1990).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 5.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Switching behavior of the soliton in a nonlinear coupler. Here the normalized peak power in core 1 is defined by P1 = |u(ξ, 0)|2/K and Pth is given by Eq. (16).

Fig. 2
Fig. 2

Numerical simulation of soliton propagation in a nonlinear coupler with m < 1. (Here K = 1 and, at input ξ = 0, a2 = η and P1 = a4 = 2.)

Fig. 3
Fig. 3

Numerical simulation of soliton propagation in a nonlinear coupler with m > 1. (Here K = 1 and, at input ξ = 0, a2 = η and P1 = a4 = 8.)

Equations (19)

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

i u ξ + 1 2 2 u τ 2 + | u | 2 u + K ν = 0 ,
i ν ξ + 1 2 2 ν τ 2 + | ν | 2 ν + K u = 0 ,
L = + L d τ ,
L = i 1 2 u * u ξ + i 1 2 ν * ν ξ 1 4 | u τ | 2 1 4 | ν τ | 2 + 1 4 | u | 4 + 1 4 | ν | 4 + K u ν * + c . c .
u ( ξ , τ ) = a η sech ( η τ ) cos θ exp ( i ϕ + i ψ + i q τ 2 ) ,
ν ( ξ , τ ) = a η sech ( η τ ) sin θ exp ( i ϕ i ψ i q τ 2 ) ,
L = 2 a 2 cos ( 2 θ ) ψ ξ 1 3 a 4 η sin 2 ( 2 θ ) + 2 K a 2 sin ( 2 θ ) cos ( 2 ψ ) .
sin ( 2 θ ) [ θ ξ + K sin ( 2 ψ ) ] = 0 .
sin ( 2 θ ) = 0
θ ξ = K sin ( 2 ψ ) .
sin ( 2 θ ) ψ ξ = 1 3 a 2 η sin ( 2 θ ) cos ( 2 θ ) K cos ( 2 θ ) cos ( 2 ψ ) .
H = 1 6 a 2 η sin 2 ( 2 θ ) + K sin ( 2 θ ) cos ( 2 ψ ) .
cos ( 2 ψ ) = a 2 η 6 K sin ( 2 θ ) .
θ ξ = K 1 m sin 2 2 θ ,
m = ( a 2 η 6 K ) 2 .
sin 2 θ = sn ( 2 K ξ | m ) for m 1 ,
sin 2 θ = 1 m sn ( 2 K m ξ | 1 / m ) for m > 1 .
sin ( 2 θ ) = tanh ( 2 K ξ ) .
P th = ( a 2 η K ) th = 6 .

Metrics