Abstract

The effects on propagation in directional couplers made of non-Kerr-law material are examined. Many unstable modes can exist at one input power level, in contrast to only one for Kerr-law material. Special design features are possible by tailoring the dependence of the refractive index on intensity.

© 1990 Optical Society of America

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References

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  1. G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
    [CrossRef]
  2. G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
    [CrossRef]
  3. E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
    [CrossRef]
  4. E. Caglioti, S. Trillo, S. Wabnitz, G. I. Stegeman, J. Opt. Soc. Am. B 5, 472 (1988).
    [CrossRef]
  5. G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
    [CrossRef]
  6. G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
    [CrossRef]
  7. L. Thylen, E. M. Wright, G. I. Stegeman, J. Opt. Soc. Am. B 5, 467 (1988).
    [CrossRef]
  8. D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989); A. W. Snyder, D. J. Mitchell, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1989), paper PD2.
    [CrossRef] [PubMed]
  9. A. W. Snyder, D. J. Mitchell, Opt. Lett. 14, 1146 (1989).
    [CrossRef] [PubMed]
  10. R. Ulrich, A. Simon, Appl. Opt. 18, 2241 (1979).
    [CrossRef] [PubMed]
  11. B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 8, 4512 (1985).
    [CrossRef]
  12. A. W. Snyder, D. J. Mitchell, Y. Chen, L. Poladian, D. Rowland, “Nonlinear fiber amplifiers and switches: order and chaos,” submitted to J. Opt. Soc. Am. B.

1989 (2)

1988 (3)

1987 (4)

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
[CrossRef]

1985 (1)

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 8, 4512 (1985).
[CrossRef]

1979 (1)

Caglioti, E.

E. Caglioti, S. Trillo, S. Wabnitz, G. I. Stegeman, J. Opt. Soc. Am. B 5, 472 (1988).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
[CrossRef]

Chen, Y.

A. W. Snyder, D. J. Mitchell, Y. Chen, L. Poladian, D. Rowland, “Nonlinear fiber amplifiers and switches: order and chaos,” submitted to J. Opt. Soc. Am. B.

Cullen, T.

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

Daino, B.

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 8, 4512 (1985).
[CrossRef]

Finlayson, N.

G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

Gregori, G.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 8, 4512 (1985).
[CrossRef]

Ironside, C. N.

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
[CrossRef]

Mitchell, D. J.

Poladian, L.

A. W. Snyder, D. J. Mitchell, Y. Chen, L. Poladian, D. Rowland, “Nonlinear fiber amplifiers and switches: order and chaos,” submitted to J. Opt. Soc. Am. B.

Rowland, D.

A. W. Snyder, D. J. Mitchell, Y. Chen, L. Poladian, D. Rowland, “Nonlinear fiber amplifiers and switches: order and chaos,” submitted to J. Opt. Soc. Am. B.

Seaton, C. T.

G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

Simon, A.

Snyder, A. W.

Stegeman, G. I.

G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

L. Thylen, E. M. Wright, G. I. Stegeman, J. Opt. Soc. Am. B 5, 467 (1988).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, G. I. Stegeman, J. Opt. Soc. Am. B 5, 472 (1988).
[CrossRef]

G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
[CrossRef]

Thylen, L.

Trillo, S.

E. Caglioti, S. Trillo, S. Wabnitz, G. I. Stegeman, J. Opt. Soc. Am. B 5, 472 (1988).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
[CrossRef]

Ulrich, R.

Wabnitz, S.

E. Caglioti, S. Trillo, S. Wabnitz, G. I. Stegeman, J. Opt. Soc. Am. B 5, 472 (1988).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
[CrossRef]

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 8, 4512 (1985).
[CrossRef]

Walker, A. C.

G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

Wright, E. M.

L. Thylen, E. M. Wright, G. I. Stegeman, J. Opt. Soc. Am. B 5, 467 (1988).
[CrossRef]

G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

Zanoni, R.

G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. Cullen, A. C. Walker, Appl. Phys. Lett. 50, 1035 (1987).
[CrossRef]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[CrossRef]

IEEE J. Lightwave Technol. (1)

G. I. Stegeman, R. Zanoni, N. Finlayson, E. M. Wright, C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

J. Appl. Phys. (1)

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 8, 4512 (1985).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

G. I. Stegeman, E. Caglioti, S. Trillo, S. Wabnitz, Opt. Commun. 63, 281 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, A. C. Walker, C. N. Ironside, Opt. Commun. 61, 277 (1987).
[CrossRef]

Opt. Lett. (2)

Other (1)

A. W. Snyder, D. J. Mitchell, Y. Chen, L. Poladian, D. Rowland, “Nonlinear fiber amplifiers and switches: order and chaos,” submitted to J. Opt. Soc. Am. B.

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Figures (5)

Fig. 1
Fig. 1

Twin-core nonlinear coupler structure.

Fig. 2
Fig. 2

Mode diagram for Kerr-law nonlinear medium, (a) Refractive-index dependence on power Pi, in core i (i = 1, 2). (b) Mode diagram in which the solid curve denotes stable modes and the dashed vertical line denotes an unstable mode, (c) Phase-space trajectories corresponding to certain power levels, where ϕ1ϕ2 is the phase difference between two cores, (d) Power flow along the axis of core 1 for certain power levels.

Fig. 3
Fig. 3

Mode diagram for a power-law nonlinear medium. (a)Power-induced propagation-constant change in core i. (b) Mode diagram in which the dashed curves denote the unstable modes. At a characteristic power below Pb or above Pb′, the qualitative features are similar to those of a Kerr-law nonlinear medium. However, for a characteristic power P ranging from Pb to Pb′, the structure supports two unstable modes associated with unequal power distribution in two cores, and the even mode is still stable. Only at P > Pb′ does the even mode become unstable, (c) Phase-space trajectories. The interesting characteristic in this case that at Pb < P < Pb′, the separatrix is associated with two unstable singular points, (d) Power flow along the axis of core 1.

Fig. 4
Fig. 4

Mode diagram for a theoretical rapid change index induced by power, (a) Power-induced propagation-constant change in core i, in which a rapid change in index near P′ and P″ has been idealized by two step jumps, (b) Mode diagram, (c) Phase-space trajectories.

Fig. 5
Fig. 5

Mode diagrams for various models of saturation, where 2C = β+β. (a) Power-induced propagation-constant change in core i. (b) Mode diagram, (c) Phase-space trajectories, (d) Power flow along the axis in core 1.

Equations (5)

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

β i ( P i ° ) = β ¯ + δ β i ( P i ° ) .
P 1 ° P 2 ° 2 ( P 1 ° P 2 ° ) 1 / 2 = β 1 ( P 1 ° ) β 2 ( P 2 ° ) β + β
P P < 1 + f 1 1 + f 2 f 2 ,
f 1 = { β β β + β + [ 1 + ( β β β + β ) 2 ] 1 / 2 } 2
f 2 = { β β β + β + [ 1 + ( β β β + β ) 2 ] 1 / 2 } 2 .

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