Abstract

We investigate a symmetric layered structure that consists of a slab containing Lorentz oscillators bounded on both sides by thin metal films. We show that the absorption and the dispersion introduced by the Lorentz oscillators can drastically affect the coupled surface plasmon resonances, leading to a suppression or shift of the resonances. The frequency dependence of the reflectivity can show a splitting for larger densities of oscillators. The splitting is explained in terms of backbending in the dispersion of the long- and the short-range modes and their overlap because of resonance broadening.

© 1992 Optical Society of America

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References

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  1. See, for example, H. Raether, in Physics of Thin Films, G. Hass, M. H. Francombe, eds.(Academic, New York, 1977), Vol. 9, pp. 145–261.
  2. For surface plasmons in layered media see, for example, G. Kovacs, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 142–200.
  3. For a review of dispersion characteristics of the surface modes at the interface between two media see, for example, P. Halevi, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 249–304.See also D. N. Mirlin, in Surface Polaritons, V. M. Agranovich, D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 3–67.
  4. For linear properties see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
    [CrossRef]
  5. For nonlinear properties see M. B. Pande, S. Dutta Gupta, Opt. Lett. 15, 944 (1990);Pramana J. Phys. 37, 357 (1991).
    [CrossRef] [PubMed]
  6. See, for example, D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
    [CrossRef]
  7. A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

1990 (2)

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

For nonlinear properties see M. B. Pande, S. Dutta Gupta, Opt. Lett. 15, 944 (1990);Pramana J. Phys. 37, 357 (1991).
[CrossRef] [PubMed]

1988 (1)

For linear properties see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

1981 (1)

See, for example, D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

Born, M.

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

Carmichael, H. J.

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

Dutta Gupta, S.

Gauthier, D. J.

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

Halevi, P.

For a review of dispersion characteristics of the surface modes at the interface between two media see, for example, P. Halevi, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 249–304.See also D. N. Mirlin, in Surface Polaritons, V. M. Agranovich, D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 3–67.

Kovacs, G.

For surface plasmons in layered media see, for example, G. Kovacs, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 142–200.

Morin, S. E.

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

Mossberg, T. W.

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

Pande, M. B.

Raether, H.

See, for example, H. Raether, in Physics of Thin Films, G. Hass, M. H. Francombe, eds.(Academic, New York, 1977), Vol. 9, pp. 145–261.

Sambles, J. R.

For linear properties see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

Sarid, D.

See, for example, D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

Welford, K. R.

For linear properties 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).

Wu, Q.

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

Zhu, Y.

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

For linear properties see K. R. Welford, J. R. Sambles, J. Mod. Opt. 35, 1467 (1988).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

See, for example, D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

A somewhat similar phenomenon was observed by several groups;see Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, T. W. Mossberg, Phys. Rev. Lett. 64, 2499 (1990);M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989);For a theoretical treatment see G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985);Phys. Rev. Lett. 53, 1732 (1984);J. J. Sanchez-Mondragon, N. B. Narozhny, J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[CrossRef] [PubMed]

Other (4)

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

See, for example, H. Raether, in Physics of Thin Films, G. Hass, M. H. Francombe, eds.(Academic, New York, 1977), Vol. 9, pp. 145–261.

For surface plasmons in layered media see, for example, G. Kovacs, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 142–200.

For a review of dispersion characteristics of the surface modes at the interface between two media see, for example, P. Halevi, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 249–304.See also D. N. Mirlin, in Surface Polaritons, V. M. Agranovich, D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 3–67.

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Figures (6)

Fig. 1
Fig. 1

Intensity reflection coefficient R as a function of angle of incidence ϑ (in degrees) for (a) Δ/δ = 0 and αd of (curve 1) 0, (curve 2) 0.02, and (curve 3) 0.3. (b) αd = 0.4 and Δ/δ is (curve 1) −10, (curve 2) −2, (curve 3) 0, (curve 4) 2, and (curve 5) 10. Other parameters are c/f0 = 1.06 μm, d1 = 0.045 μm, d = 3 μm, δ = 107 s−1, εi = 6.145, and ε1 = −67.03 + 2.44i. (c) Schematic view of the layered structure.

Fig. 2
Fig. 2

Intensity reflection coefficient R as a function of normalized detuning Δ/δ for (a) ϑ = 23.85°, (b) ϑ = 24.058°, and (c) ϑ = 23.995°. Curves 1, 2, and 3 in (a) and (b) are for αd of 0.001, 0.1, and 0.5, respectively; in (c) curves 1, 2, and 3 for αd of 0.01, 0.2, and 0.5, respectively. Other parameters are as in Fig. 1.

Fig. 3
Fig. 3

(a) ϑ′ and (b) ϑ″ as functions of detuning Δ/δ for αd = 0.05. The solid (dashed) curves are for the left, i.e., short-range (right, i.e., long-range) mode. Other parameters are as in Fig. 1.

Fig. 4
Fig. 4

Same as in Fig. 3 except αd = 0.5.

Fig. 5
Fig. 5

Field profiles |H2| and |Ey| in the layered structure corresponding to (a) the dip in curve 1 in Fig. 2(c) (Δ/δ = 0.0599, αd = 0.01, ϑ = 23.995°), (b) the left dip in curve 3 in Fig. 2(c) (Δ/δ = −1.32, αd = 0.5, ϑ = 23.995°), and (c) the right dip in curve 3 in Fig. 2(c) (Δ/δ = 2.94, αd = 0.5, ϑ = 23.995°). Other parameters are as in Fig. 1. Layers 1 and 3 represent the metal layers; layers 2 are the dielectric layers. Each layer width has been normalized to unity.

Fig. 6
Fig. 6

Intensity transmission coefficient T as a function of Δ/δ for (a) ϑ = 23.85°, (b) ϑ = 24.058°, and (c) ϑ = 23.995° for varying αd. Labeling of the curves is as in Fig. 2.

Equations (7)

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ɛ ( Δ δ ) = 1 + α k i 2 ( Δ / δ ) 1 + ( 2 Δ / δ ) 2 ,
k d 1 = ( 2 π f 0 / c ) d 1 + π ( Δ / δ ) ( Δ f 1 / δ ) ,
k d = ( 2 π f 0 / c ) d + π ( Δ / δ ) / ( Δ f / δ ) ,
Δ f 1 / δ = c / ( 2 d 1 δ ) , Δ f / δ = c / ( 2 d δ ) .
( m 11 + P f m 12 ) p i + ( m 21 + p f m 22 ) = 0 .
p f = p i = [ ɛ i ( k y / k ) 2 ] 1 / 2 / ɛ i ,
k y = ( 2 π f / c ) ɛ i sin ϑ ,

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