Abstract

We present a linear stability analysis of two-dimensional continuous waves and one-dimensional temporal solitons in nonlinear-optical fiber arrays. Guided by this analysis, we use numerical integrations of the governing equations to show that these arrays are all-optical switching devices. Light injected into the N-fiber array is temporally compressed and spatially localized into a few fibers on output.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. B. Benjamin, J. E. Feir, J. Fluid Mech. 27, 417 (1967).
    [CrossRef]
  2. V. E. Zakharov, J. Appl. Mech. Tech. Phys. 2, 190 (1968).
  3. K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  4. K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
    [CrossRef]
  5. S. Trillo, S. Wabnitz, Opt. Lett. 16, 986 (1991).
    [CrossRef] [PubMed]
  6. S. Trillo, S. Wabnitz, Opt. Lett. 16, 1566 (1991).
    [CrossRef] [PubMed]
  7. Yu. S. Kivshar, M. Peyrard, Phys. Rev. A 46, 3198 (1992).
    [CrossRef] [PubMed]
  8. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  9. C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
    [CrossRef]
  10. L. J. Bernstein, Opt. Commun. 94, 406 (1992).
    [CrossRef]
  11. P. E. Langridge, W. J. Firth, Opt. Quantum Electron. 24, 1315 (1992).
    [CrossRef]
  12. M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
    [CrossRef]
  13. Yu. S. Kivshar, Phys. Lett. A 173, 172 (1993).
    [CrossRef]
  14. A. B. Aceves, C. De Angelis, A. M. Rubenchik, S. K. Turitsyn, Opt. Lett. 19, 329 (1994).
    [CrossRef] [PubMed]
  15. G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), pp. 40–41.
  16. D. B. Mortimore, J. A. Arkwright, Appl. Opt. 29, 1814 (1991).
    [CrossRef]
  17. R. Courant, D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1953), Vol. 1, Chap. 6.
  18. L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Addison-Wesley, Reading, Mass., 1958), pp. 73–74.
  19. G. Hadley, Opt. Lett. 16, 624 (1991).
    [CrossRef] [PubMed]

1994 (1)

1993 (2)

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

Yu. S. Kivshar, Phys. Lett. A 173, 172 (1993).
[CrossRef]

1992 (4)

Yu. S. Kivshar, M. Peyrard, Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

L. J. Bernstein, Opt. Commun. 94, 406 (1992).
[CrossRef]

P. E. Langridge, W. J. Firth, Opt. Quantum Electron. 24, 1315 (1992).
[CrossRef]

1991 (4)

1988 (1)

1986 (2)

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

1968 (1)

V. E. Zakharov, J. Appl. Mech. Tech. Phys. 2, 190 (1968).

1967 (1)

T. B. Benjamin, J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Aceves, A. B.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), pp. 40–41.

Arkwright, J. A.

Benjamin, T. B.

T. B. Benjamin, J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Bernstein, L. J.

L. J. Bernstein, Opt. Commun. 94, 406 (1992).
[CrossRef]

Christodoulides, D. N.

Courant, R.

R. Courant, D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1953), Vol. 1, Chap. 6.

De Angelis, C.

Feir, J. E.

T. B. Benjamin, J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Firth, W. J.

P. E. Langridge, W. J. Firth, Opt. Quantum Electron. 24, 1315 (1992).
[CrossRef]

Hadley, G.

Hasegawa, A.

K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Hilbert, D.

R. Courant, D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1953), Vol. 1, Chap. 6.

Jewell, J. L.

K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Joseph, R. I.

Kivshar, Yu. S.

Yu. S. Kivshar, Phys. Lett. A 173, 172 (1993).
[CrossRef]

Yu. S. Kivshar, M. Peyrard, Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Addison-Wesley, Reading, Mass., 1958), pp. 73–74.

Langridge, P. E.

P. E. Langridge, W. J. Firth, Opt. Quantum Electron. 24, 1315 (1992).
[CrossRef]

Lederer, F.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Addison-Wesley, Reading, Mass., 1958), pp. 73–74.

Molina, M. I.

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

Mortimore, D. B.

Muschall, R.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

Peyrard, M.

Yu. S. Kivshar, M. Peyrard, Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

Rubenchik, A. M.

Schmidt-Hattenberger, C.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Tomita, A.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tomita, K

K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Trillo, S.

Trutschel, U.

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

Tsironis, G. P.

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

Turitsyn, S. K.

Wabnitz, S.

Zakharov, V. E.

V. E. Zakharov, J. Appl. Mech. Tech. Phys. 2, 190 (1968).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Tai, K Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

J. Appl. Mech. Tech. Phys. (1)

V. E. Zakharov, J. Appl. Mech. Tech. Phys. 2, 190 (1968).

J. Fluid Mech. (1)

T. B. Benjamin, J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Opt. Commun. (2)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, F. Lederer, Opt. Commun. 89, 473 (1992).
[CrossRef]

L. J. Bernstein, Opt. Commun. 94, 406 (1992).
[CrossRef]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

P. E. Langridge, W. J. Firth, Opt. Quantum Electron. 24, 1315 (1992).
[CrossRef]

Phys. Lett. A (1)

Yu. S. Kivshar, Phys. Lett. A 173, 172 (1993).
[CrossRef]

Phys. Rev. A (1)

Yu. S. Kivshar, M. Peyrard, Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Physica D (1)

M. I. Molina, G. P. Tsironis, Physica D 65, 267 (1993).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), pp. 40–41.

R. Courant, D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1953), Vol. 1, Chap. 6.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Addison-Wesley, Reading, Mass., 1958), pp. 73–74.

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

Numerical integration of Eq. (1), with the initial condition ψn(0, t) = 1 + cos[(2π/7)n], = 0.01, n = 1,…, 7 in an array of seven fibers. Here the spatiotemporal evolution refers to ψ7(z, t).

Fig. 2
Fig. 2

Numerical integration of Eq. (1), with the initial condition ψn(0, t) = λn sech(λnt), λ(n) = 1 + cos[(2π/7)n], = 0.01, n = 1,…,7. Here the spatiotemporal evolution refers to ψ7(z, t).

Fig. 3
Fig. 3

Final state intensity in Fig. 2 (dots) for (a) the first fiber and (b) the second fiber compared with the analytical solution in Ref. 14 (solid curves).

Equations (7)

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

i z ψ n + κ ( ψ n + 1 + ψ n - 1 - 2 ψ n ) + β 2 t t ψ n + ψ n 2 ψ n = 0 ,             n = 1 , 2 , , N ,
d v d z - L 1 u - 4 κ sin 2 ( s / 2 ) u = 0 , - d u d z - L 0 v - 4 κ sin 2 ( s / 2 ) v = 0 ,
p 2 = - [ 4 κ sin 2 ( s / 2 ) + ( β / 2 ) ω 2 ] { λ 2 - [ 4 κ sin 2 ( s / 2 ) + ( β / 2 ) ω 2 ] } .
4 κ sin 2 ( s / 2 ) + ( β / 2 ) ω 2 < λ 2 .
0 < 4 κ sin 2 ( s / 2 ) + ( β / 2 ) ω 2 < λ 2 .
p 2 = min { Ψ L 1 + 4 κ sin 2 ( s / 2 ) Ψ Ψ [ L 0 + 4 κ sin 2 ( s / 2 ) ] ( - 1 ) Ψ } ,
4 κ sin 2 ( s / 2 ) < 3 λ 2 2 .

Metrics