Abstract

We calculate the power-dependent propagation constant of a surface-plasma wave as a function of the thickness of the metal film on which it propagates when the metal film is bounded by a nonlinear semiconductor. In the case of a Cu film bounded by InSb at a wavelength of ∼5 μm and a temperature of 5 K, we find that the effect of the nonlinearity on the propagation constant is enhanced by a factor of 10 as the metal thickness decreases from 120 to 15 nm.

© 1982 Optical Society of America

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References

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  1. A. Miller, D. A. B. Miller, and S. D. Smith, “Dynamic nonlinear optical processes in semiconductors,” Adv. Phys. 30, 697–800 (1981).
    [Crossref]
  2. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
    [Crossref]
  3. S. W. Koch and H. Haug, “Two photon generation of excitonic molecules and optical bistability,” Phys. Rev. Lett. 46, 450–452 (1981).
    [Crossref]
  4. D. Sarid, “Analysis of bistability in a ring-channel waveguide,” Opt. Lett. 6, 552–553 (1981).
    [Crossref] [PubMed]
  5. D. Sarid and M. Sargent, “Tunable nonlinear directional coupler,” J. Opt. Soc. Am. 72, 835–838 (1982).
    [Crossref]
  6. D. Sarid, “The nonlinear propagation constant of a surface-plasma wave,” Appl. Phys. Lett. 39, 889–891 (1981).
    [Crossref]
  7. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Res. Lett. 47, 1927–1930 (1981).
    [Crossref]

1982 (1)

1981 (5)

D. Sarid, “The nonlinear propagation constant of a surface-plasma wave,” Appl. Phys. Lett. 39, 889–891 (1981).
[Crossref]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Res. Lett. 47, 1927–1930 (1981).
[Crossref]

A. Miller, D. A. B. Miller, and S. D. Smith, “Dynamic nonlinear optical processes in semiconductors,” Adv. Phys. 30, 697–800 (1981).
[Crossref]

S. W. Koch and H. Haug, “Two photon generation of excitonic molecules and optical bistability,” Phys. Rev. Lett. 46, 450–452 (1981).
[Crossref]

D. Sarid, “Analysis of bistability in a ring-channel waveguide,” Opt. Lett. 6, 552–553 (1981).
[Crossref] [PubMed]

1979 (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Gossard, A. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Haug, H.

S. W. Koch and H. Haug, “Two photon generation of excitonic molecules and optical bistability,” Phys. Rev. Lett. 46, 450–452 (1981).
[Crossref]

Koch, S. W.

S. W. Koch and H. Haug, “Two photon generation of excitonic molecules and optical bistability,” Phys. Rev. Lett. 46, 450–452 (1981).
[Crossref]

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Miller, A.

A. Miller, D. A. B. Miller, and S. D. Smith, “Dynamic nonlinear optical processes in semiconductors,” Adv. Phys. 30, 697–800 (1981).
[Crossref]

Miller, D. A. B.

A. Miller, D. A. B. Miller, and S. D. Smith, “Dynamic nonlinear optical processes in semiconductors,” Adv. Phys. 30, 697–800 (1981).
[Crossref]

Passner, A.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Sargent, M.

Sarid, D.

D. Sarid and M. Sargent, “Tunable nonlinear directional coupler,” J. Opt. Soc. Am. 72, 835–838 (1982).
[Crossref]

D. Sarid, “The nonlinear propagation constant of a surface-plasma wave,” Appl. Phys. Lett. 39, 889–891 (1981).
[Crossref]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Res. Lett. 47, 1927–1930 (1981).
[Crossref]

D. Sarid, “Analysis of bistability in a ring-channel waveguide,” Opt. Lett. 6, 552–553 (1981).
[Crossref] [PubMed]

Smith, S. D.

A. Miller, D. A. B. Miller, and S. D. Smith, “Dynamic nonlinear optical processes in semiconductors,” Adv. Phys. 30, 697–800 (1981).
[Crossref]

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Wiegmann, W.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

Adv. Phys. (1)

A. Miller, D. A. B. Miller, and S. D. Smith, “Dynamic nonlinear optical processes in semiconductors,” Adv. Phys. 30, 697–800 (1981).
[Crossref]

Appl. Phys. Lett. (2)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
[Crossref]

D. Sarid, “The nonlinear propagation constant of a surface-plasma wave,” Appl. Phys. Lett. 39, 889–891 (1981).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Phys. Res. Lett. (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Res. Lett. 47, 1927–1930 (1981).
[Crossref]

Phys. Rev. Lett. (1)

S. W. Koch and H. Haug, “Two photon generation of excitonic molecules and optical bistability,” Phys. Rev. Lett. 46, 450–452 (1981).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

The geometry of the long-range surface-plasma wave propagating on a thin metal film that is bounded by a nonlinear semiconductor.

Fig. 2
Fig. 2

The real part of β as a function of the metal-film thickness t. Note the splitting of the degenerate mode into two branches.

Fig. 3
Fig. 3

The imaginary part of β as a function of the metal-film thickness. As in Fig. 2, one observes the splitting of the degenerate mode into a short- and a long-range SPW.

Fig. 4
Fig. 4

The scaled power n2,IP/Wλ as a function of the metal-film thickness. One observes that the branch belonging to the LRSPW obtains a minimum at 15 nm.

Equations (22)

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n ( P ) = n + n 2 , E | E | 2 ,
n ( P ) = n + n 2 , I I ,
tan [ ( B / B ) ln | k | ] + k / k = 0
t = ln | k | / 2 K B ,
k = ( k 10 i ) ( k 12 i ) / ( k 10 + i ) ( k 12 + i ) ,
k 10 = A / n 0 2 B ,
k 12 = C / n 2 2 B ,
A 2 = β 2 n 0 2 ,
B 2 = β 2 ,
C 2 = β 2 n 2 2 .
E z ( x ) = ( i A D / n 2 2 c 0 ) e KAx
E x ( x ) = ( β D / n 2 2 c 0 ) e KAx ,
| D | 2 = 2 K c 0 A n 2 2 P / β ( 1 + A 2 / B 2 ) W ,
Δ β = ( c 0 W / 2 P ) n ( x , z ) n 2 , E ( x , z ) | E ( x , z ) | 4 d x ,
Δ β = ( β c 2 0 2 W / 4 P ) n ( x , z ) n 2 , I ( x , z ) | E ( x , z ) | 4 d x .
| E | 4 = ( 2 K / c 0 ) 2 ξ ( β A P / n 2 2 W ) 2 exp ( 4 K A x ) ,
ξ = [ ( 1 + A 2 / B 2 ) / ( 1 A 2 / B 2 ) ] 2 .
Δ β = ( K / c 0 ) ξ ( B 2 A / n 2 3 W ) n 2 , E P
Δ β = ( K / 2 W ) ξ ( B / n 2 ) 3 A n 2 , I P ,
P ( z ) = P 0 e α z .
0 L K Δ β ( z ) d z = π / 2 .
n 2 , I P 0 / W λ = ( n 2 / B ) 3 [ e / ( e 1 ) ξ ] β / A .