Abstract

We present the exact numerical results for optical multistability with surface plasmons coupled through a dielectric slab with isotropic Kerr-type nonlinearity. We show the possibility of having multivalued output with both the long- and short-range modes and discuss the field profiles in the nonlinear medium. Moreover, we show the existence of nonlinearity-induced resonances in the structure that are missing in the linear theory.

© 1990 Optical Society of America

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References

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  1. For a detailed study of the linear properties of such structures, see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
    [CrossRef]
  2. For a review on the coupling of surface plasmons, see, e.g., H. Raether, Physics of Thin Films (Academic, New York, 1977), Vol. 9, pp. 145–261.
  3. S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
    [CrossRef]
  4. D. Sarid, R. T. Deck, J. J. Fasano, J. Opt. Soc. Am. 72, 1345 (1982);D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, J. J. Fasano, Appl. Opt. 21, 3993 (1982);J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983);R. K. Hickernell, D. Sarid, J. Opt. Soc. Am. B 3, 1059 (1986).
    [CrossRef] [PubMed]
  5. R. Dragila, B. Luther-Davies, S. Vukovic, Phys. Rev. Lett. 55, 1117 (1985).
    [CrossRef] [PubMed]
  6. R. W. Gruhlkhe, D. G. Hall, Appl. Phys. Lett. 53, 1041 (1988);R. W. Gruhlkhe, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
    [CrossRef]
  7. K. M. Leung, Phys. Rev. A 32, 5093 (1985);A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
    [CrossRef] [PubMed]
  8. G. S. Agarwal, S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
    [CrossRef]
  9. A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

1988 (2)

For a detailed study of the linear properties of such structures, see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

R. W. Gruhlkhe, D. G. Hall, Appl. Phys. Lett. 53, 1041 (1988);R. W. Gruhlkhe, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
[CrossRef]

1987 (2)

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).

1986 (1)

G. S. Agarwal, S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

1985 (2)

R. Dragila, B. Luther-Davies, S. Vukovic, Phys. Rev. Lett. 55, 1117 (1985).
[CrossRef] [PubMed]

K. M. Leung, Phys. Rev. A 32, 5093 (1985);A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

1982 (1)

Agarwal, G. S.

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

G. S. Agarwal, S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

Boardman, A. D.

A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

Deck, R. T.

Dragila, R.

R. Dragila, B. Luther-Davies, S. Vukovic, Phys. Rev. Lett. 55, 1117 (1985).
[CrossRef] [PubMed]

Fasano, J. J.

Gruhlkhe, R. W.

R. W. Gruhlkhe, D. G. Hall, Appl. Phys. Lett. 53, 1041 (1988);R. W. Gruhlkhe, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
[CrossRef]

Gupta, S. Dutta

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

G. S. Agarwal, S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

Hall, D. G.

R. W. Gruhlkhe, D. G. Hall, Appl. Phys. Lett. 53, 1041 (1988);R. W. Gruhlkhe, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
[CrossRef]

Leung, K. M.

K. M. Leung, Phys. Rev. A 32, 5093 (1985);A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

Luther-Davies, B.

R. Dragila, B. Luther-Davies, S. Vukovic, Phys. Rev. Lett. 55, 1117 (1985).
[CrossRef] [PubMed]

Raether, H.

For a review on the coupling of surface plasmons, see, e.g., H. Raether, Physics of Thin Films (Academic, New York, 1977), Vol. 9, pp. 145–261.

Sambles, J. R.

For a detailed study of the linear properties of such structures, see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

Sarid, D.

Shivarova, A.

A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).

Stegeman, G. I.

A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).

Twardowski, T.

A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).

Varada, G. V.

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

Vukovic, S.

R. Dragila, B. Luther-Davies, S. Vukovic, Phys. Rev. Lett. 55, 1117 (1985).
[CrossRef] [PubMed]

Welford, K. R.

For a detailed study of the linear properties of such structures, see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

Appl. Phys. Lett. (1)

R. W. Gruhlkhe, D. G. Hall, Appl. Phys. Lett. 53, 1041 (1988);R. W. Gruhlkhe, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
[CrossRef]

IEEE Proc. (1)

A. D. Boardman, T. Twardowski, A. Shivarova, G. I. Stegeman, IEEE Proc. 134, 152 (1987).

J. Mod. Opt. (1)

For a detailed study of the linear properties of such structures, see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. A (1)

K. M. Leung, Phys. Rev. A 32, 5093 (1985);A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

Phys. Rev. B (2)

G. S. Agarwal, S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dragila, B. Luther-Davies, S. Vukovic, Phys. Rev. Lett. 55, 1117 (1985).
[CrossRef] [PubMed]

Other (2)

For a review on the coupling of surface plasmons, see, e.g., H. Raether, Physics of Thin Films (Academic, New York, 1977), Vol. 9, pp. 145–261.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

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Figures (3)

Fig. 1
Fig. 1

Bottom: linear reflection coefficient R as a function of the angle of incidence θ for d2 = 4 μm (curve 1), 1.8 μm (curve 2), and 1 μm (curve 3). Other parameters are λ = 1.06 μm, d1 = 0.045 μm, i,= f = 6.145, 1 = −67.03 + i2.44, and 20 = 2.54. Top: schematic view of the layered structure.

Fig. 2
Fig. 2

(a) Reflection coefficient R as a function of the input intensity Ui for d2 = 1 μm. The left (right) curve is for the LR (SR) mode for an angle of incidence θ = 41.8° (40.5°). Field distributions (b) |y| and (c) |Ẽx| in the central dielectric layer for d2 = 1 μm; curve 1 (curve 2) shows the distribution for the linear (nonlinear) resonant case with θ = 39.861°, Ui = 8.747 × 10−3, and Uf = 1.705 × 10−3 (θ = 40.5°, Ui = 8.747 × 10−3, and Uf = 1.717 × 10−3). Other parameters are as in Fig. 1.

Fig. 3
Fig. 3

(a) Reflection coefficient R as a function of input intensity Ui for d2 = 1.8 μm and θ = 41.3°. (b) Angular dependence of R for the same value of d2 and for various output intensities: Uf = 1.0 × 10−17 (curve 1), Uf = 5.0 × 10−5 (curve 2), and Uf = 1.0 × 10−4 (curve 3). Other parameters are as in Fig. 1.

Equations (6)

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E ˜ ˙ x = D E ˜ y ,
E ˜ ˙ x = D E ˜ y ,
E ˜ ˙ y = ( A 1 A 2 B 2 ) 1 × [ A 2 ( C E ˜ x + F E ˜ y ) B ( C E ˜ x + F E ˜ y ) ] ,
E ˜ ˙ y = ( A 1 A 2 B 2 ) 1 × [ B ( C E ˜ x + F E ˜ y ) + A 1 ( C E ˜ x + F E ˜ y ) ] ,
A 1 = 2 + 2 E ˜ y 2 , A 2 = n + 2 E ˜ y 2 , B = 2 E ˜ y E ˜ y , C = 2 η , D = ( η 2 / η ) F = 2 D ( E ˜ x E ˜ y E ˜ x E ˜ y ) ,
E ˜ x 0 = E ˜ x 0 + , E ˜ x 0 = η H ˜ x 0 + / ( 20 + | E ˜ x 0 | 2 + | E ˜ y 0 | 2 ) .

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