Abstract

The spectral properties and the spatial structure of S-polarized surface electromagnetic waves propagating near the interface of an inhomogeneous solid plasma are examined by means of an exact analytical solution of Maxwell equations for a smooth density profile, characterized by two free parameters. The drastic differences between these waves and traditionally considered P-polarized surface plasmons are emphasized. The spectral parameters, the depth of localization, and the energy flux of such waves are shown to depend essentially upon the profile of carrier density in the plasma.

© 1999 Optical Society of America

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References

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  1. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York 1982).
  2. H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1986).
  3. E. Burstein and C. DeMartini, eds., Polaritons (Pergamon, New York, 1994).
  4. T. Tsang, T. Shrinivasan-Rao, and J. Fischer, Phys. Rev. B 43, 8870 (1991).
    [CrossRef]
  5. H. Monard, Ph.D. dissertation (University of Paris VI, Paris, 1996).
  6. P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).
  7. J. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
  8. Surface Phonons and Polaritons, A. A. Maradudin and R. F. Wallis, eds., Vol. 3 of Handbook of Surfaces and Interfaces (Garland STPM, New York, 1980).
  9. E. Kretschmann, J. Phys. (France) 241, 313 (1971).

1997 (1)

P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).

1991 (1)

T. Tsang, T. Shrinivasan-Rao, and J. Fischer, Phys. Rev. B 43, 8870 (1991).
[CrossRef]

1971 (1)

E. Kretschmann, J. Phys. (France) 241, 313 (1971).

Fischer, J.

T. Tsang, T. Shrinivasan-Rao, and J. Fischer, Phys. Rev. B 43, 8870 (1991).
[CrossRef]

Kretschmann, E.

E. Kretschmann, J. Phys. (France) 241, 313 (1971).

Kupersztych, J.

P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).

Monchicourt, P.

P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).

Raynaud, M.

P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).

Saringar, H.

P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).

Shrinivasan-Rao, T.

T. Tsang, T. Shrinivasan-Rao, and J. Fischer, Phys. Rev. B 43, 8870 (1991).
[CrossRef]

Tsang, T.

T. Tsang, T. Shrinivasan-Rao, and J. Fischer, Phys. Rev. B 43, 8870 (1991).
[CrossRef]

J. Phys. (France) (1)

E. Kretschmann, J. Phys. (France) 241, 313 (1971).

J. Phys. C (1)

P. Monchicourt, M. Raynaud, H. Saringar, and J. Kupersztych, J. Phys. C 9, 5765 (1997).

Phys. Rev. B (1)

T. Tsang, T. Shrinivasan-Rao, and J. Fischer, Phys. Rev. B 43, 8870 (1991).
[CrossRef]

Other (6)

H. Monard, Ph.D. dissertation (University of Paris VI, Paris, 1996).

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York 1982).

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1986).

E. Burstein and C. DeMartini, eds., Polaritons (Pergamon, New York, 1994).

J. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

Surface Phonons and Polaritons, A. A. Maradudin and R. F. Wallis, eds., Vol. 3 of Handbook of Surfaces and Interfaces (Garland STPM, New York, 1980).

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Figures (5)

Fig. 1
Fig. 1

Profiles of the normalized carrier densities N(z)/N0 [Eq. (3)] plotted versus the normalized coordinate z/a for the different values of parameter b.

Fig. 2
Fig. 2

Spectra of S-polarized surface waves kS(ω) for the model of an inhomogeneous semiconductor (n-type InSb), N0=3×1016 cm-3, L=12, meff=10-2 m0, and a=10-4 cm; the spectral curves are labeled by the values of parameter b. The dashed line represents the dispersion of light in vacuum.

Fig. 3
Fig. 3

Spatial structure of the components of an S-polarized surface wave; the normalized amplitudes ex [Eq. (26), solid curve] and hy [Eq. (27), dashed-dotted curve] are plotted versus the dimensionless depth z/a. The plots are calculated for the solid plasma parameters used in Fig. 2. The curves (1) to (4) relate to the frequencies ω equal to 5.64, 4.98, 4.47, and 3.94 (×1013 rad s-1) and to values of b equal to -0.4, -0.53, -0.72, and -1.1, respectively.

Fig. 4
Fig. 4

Ratio of energy fluxes S [Eq. (29)] in the surface S-polarized EM waves, traveling over and under the interface of an inhomogeneous solid plasma. The energy fluxes are calculated for the values of the parameters used in Fig. 2; the numbers near the curves show the relevant values of parameter b.

Fig. 5
Fig. 5

Coupling of surface S-polarized EM waves with optical waves incident from the free space by means of a transparent prism.

Equations (42)

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Ey=-A0cϕt,Hx=-A0ϕz,Hz=A0ϕx.
2ϕz2+2ϕx2-(z)c22ϕt2=0.
N(z)=N01-1b+F2(z)b.
F(z)0,F(z)|z=0=1.
(z)=L1-ωp2ω21-1b+F2(z)b.
ωp2=4πe2N0Lmeff,
ϕ=f(z)exp[i(ksx-ωt)],
2fz2-kS2f+ω2Lc21-ωp2ω21-1b+F2(z)bf=0.
Q=fF,η=0z F(z1)dz1,η(0)=0.
2Qη2+Q(L/c2)[ω2-ωp2(1-b-1)]-kS2F2-Lωp2c2b-12F2Fη2+14F2Fη2=0.
F(z)=(1+z/a)-1.
N(z)=N01-1b+1b(1+za-1)2.
lim N(z)|za=N0(1-b-1),
u=exp(ηa-1)=1+za-1,
2Qu2+1uQu+-p2-q2u2Q=0,
p2=(kSa)2-La2c2[ω2-ωp2(1-b-1)],
q2=Lωp2a2c2b+14.
p2>0,q20,
ϕ=u1/2Kq(pu)exp[i(kSx-ωt)].
Ey=iA0ωcϕ;Hz=iA0kSϕ;
Hx=-A0a12u+1Kq(pu)Kq(pu)uKq(pu)u1/2.
ϕ1=exp[i(kSx-ωt)+z/l],
Ey=iA1ωcϕ1,Hz=iA1kSϕ1,Hx=-A1lϕ1;
kS2=ω2c2+1l2.
al=12+1Kq(p)Kq(pu)uu=1.
-12<q0.
e(z)=u1/2Kq(pu)Kq(p),
h(z)=u-1Kq(pu)+2Kq(pu)uu1/2Kq(p)+2Kq(pu)uu=1.
P=c4π[EH].
S=Px,mPx,v=2yθq(p)Kq2(p),
θq(p)=1uKq2(pu)du,y=akS2-ω2c2.
ϕ=1+za Hq(1)p11+zaexp[i(kx-ωt)].
Hq(1)(x)=2πx expix-πq2-π4,
ω2>(kSc)2L+ωp2(1-1/b).
n sin γ=nS(ω).
F(η)=u-1=1+ηa,F(z)=1+2za-1/2,
T=Qu-1/2.
2Tu2+1uTu+T-d2-g2u2=0,
g2=p2+1,d2=Lωp2a2c2b,
T=Kq(d1+2za-1).
Φ=1+2za-1Kq(d1+2za-1)exp[i(kx-ωt)].
F=exp(-za-1)=u=1-ηa.

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