Abstract

A quasi-optic model for the treatment of a planar dielectric waveguide having a substrate with material dispersion is presented. An application of the lowest-order waveguide mode to the development of an optical sensor for monitoring the thermal degradation of a film thickness is indicated.

© 1998 Optical Society of America

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References

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  1. K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
    [CrossRef]
  2. S. R. Seshadri, “Ray model for a planar anisotropic dielectric waveguide,” J. Opt. Soc. Am. A 15, 972–977 (1998).
    [CrossRef]
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984), pp. 624–627.
  4. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 253–256.
  5. S. R. Seshadri, “Leaky surface polariton,” J. Appl. Phys. 59, 1187–1195 (1986).
    [CrossRef]

1998

1997

K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
[CrossRef]

1986

S. R. Seshadri, “Leaky surface polariton,” J. Appl. Phys. 59, 1187–1195 (1986).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984), pp. 624–627.

Knoll, W.

K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 253–256.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 253–256.

Mittler-Neher, S.

K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
[CrossRef]

Muller, K. G.

K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
[CrossRef]

Seshadri, S. R.

Veith, M.

K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984), pp. 624–627.

J. Appl. Phys.

K. G. Muller, M. Veith, S. Mittler-Neher, W. Knoll, “Plasmon surface polariton coupling with dielectric gratings and the thermal decomposition of these dielectric gratings,” J. Appl. Phys. 82, 4172–4176 (1997).
[CrossRef]

S. R. Seshadri, “Leaky surface polariton,” J. Appl. Phys. 59, 1187–1195 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984), pp. 624–627.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 253–256.

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Figures (3)

Fig. 1
Fig. 1

Zigzag ray model for the guided wave supported by the dielectric film waveguide with a substrate of dispersive free-electron metal. Dielectric cover, μ0, 0c; dielectric film, μ0, 0f; metal, μ0, 0˜m.

Fig. 2
Fig. 2

Dielectric film thickness 2a (in nm) as a function of the angle of incidence θin (in degrees) of the light beam for 8°<θin<48°. Here c=1; f=(1.642)2; m=-18; λ0=632.8 nm; Λ0=710.1 nm.

Fig. 3
Fig. 3

Dielectric film thickness 2a (in nm) as a function of the angle of incidence θin (in degrees) of the light beam for 8.8°<θin<10.8°. Physical parameters are the same as in Fig. 2. (a) Theory and (b) result deduced from experiment and obtained from Figs. 8 and 9 of Ref. 1.

Equations (74)

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2x2+2z2+ω2μ00˜vHyv(x, z)=0,
Exv(x, z)=1iω0˜vzHyv(x, z),
Ezv(x, z)=-1iω0˜vxHyv(x, z),
˜m=m+δ2imi=1-ωp2ω2+δ2iωp2ω2νω.
Hyv(x, z)iscontinuous,
1˜vxHyv(x, z)iscontinuous.
kfj=(ω2μ00f-βj2)1/2
tan θj=vgzjvgxj=βjkfj.
Hyc(x, z)=N0jA0j exp[-αcj(x-a)]exp(iβjz)
forx>a,
Hyf(x, z)=N0j{B0j exp[-ikfj(x-a)]+C0j exp[ikfj(x-a)]}exp(iβjz)
for|x|<a,
αvj=(βj2-ω2μ00v)1/2,forv=c, m.
Hym(x, z)=1-δ2iω2μ00mix2αmj×N0jD0j exp[αmj(x+a)]exp(iβjz)
forx<-a.
B0j=C0j exp(-i2ϕcj),
2 cos ϕcj exp(-iϕcj)C0j=A0j,
tan ϕvj=fαvjkfjvforv=c, m.
C0j exp(-i2kfja)=B0j exp(i2kfja)exp(-i2ϕmj)-δ2 cos ϕmj×exp(-iϕmj)fmikfjm2αmj×αmj2+12ω2μ00mD0j,
2 cos ϕmj exp[-i(2kfja-ϕmj)]C0j=D0j+δ2terms.
zv j=2ϕv jβjforv=c, m,
tv j=-2ϕv jωforv=c, m.
zv j=2βjkfj1αv jqv jforv=c, m,
qv j=βj2ω2μ001f+1v-1forv=c, m,
tc j=βjωzc j,
tm j=βjωzm j-2ϕm jmmω,
mω=2ωp2ω3,
-2ϕm jm=2fkf j(αm j2+12ω2μ00m)(f2αm j2+m2kf j2)αm j.
ZB j=zc j+zm j+4a tan θj.
TB j=tc j+tm j+4a tan θj/vg z j.
ZB j=2βjkf j(2aeff, j)=2 tan θj2a+1αc jqc j+1αm jqm j,
TB j=2ωμ00fkf j2a+βj2ω2μ00f1αc jqc j+1αm jqm j-2ϕm jmmω.
B0j(z)=C0j(z-ZB j)exp(-i2ϕc j),
C0j(z)=C0j(z-ZB j)exp[iD(ω, βj)]-δ2 cos ϕm j exp[i(2kf ja-ϕm j)]×fkf jmim2αm jαm j2+12ω2μ00mD0 j(z),
D(ω, βj)=4kf ja-2ϕc j-2ϕm j.
D(ω, βj)=2π(j-1),
ZB j=-D(ω, βj)βj,
TB j=D(ω, βj)ω,
Vgj=-D/βjD/ω,
Hyc(x, z)=N0 jA0 j exp[-αc j(x-a)]exp(iβjz)
forx>a,
Hyf(x, z)=N0 jA0 jcos[kf j(x-a)+ϕc j]cos ϕc jexp(iβjz)
for|x|<a,
Hym(x, z)=N0 jA0 jcos ϕm jcos ϕc j(-1)(j-1)×exp[αm j(x+a)]exp(iβjz)
forx<-a.
N0 j=8ω0f cos2 ϕm jwkf jZB j1/2.
C0 j(z-ZB j)=C0 j(z)-δ2ZB jC0 j(z)z,
zA0 j(z)+αg jA0 j(z)=0,
αg j=2 cos2 ϕm jZB jfkf jmim2αm jαm j2+12ω2μ00m.
α˜m j=(βj2-ω2μ00˜m)1/2.
tan ϕ˜m j=fα˜m jkf j˜m.
D(ω, β˜j, ˜m)=4akf j-2ϕc j-2ϕ˜m j=2π(j-1),
αg j=miZB jDm=-miZB j2ϕm jm.
P=|A0 j|2.
whv=14μ0|Hyv(x, z)|2forv=c, f, m,
wev=140v[|Exv(x, z)|2+|Ezv(x, z)|2]forv=c, f.
wem=140ω(ωm)[|Exm(x, z)|2+|Ezm(x, z)|2].
wem=wem1+wem2,
wem1=140m[|Exm(x, z)|2+|Ezm(x, z)|2],
wem2=140ωω(m)[|Exm(x, z)|2+|Ezm(x, z)|2].
W+=-2ϕm jm mωPZB j.
W0=2ωμ00fkf j2a+βj2ω2μ00f×1αc jqc j+1αm jqm j PZB j.
W=TB jZB jP.
PD=-Pz=2αg jP.
αg j=PD2P.
pdis(x)=12ω0mi[|Exm(x, z)|2+|Ezm(x, z)|2].
PD=w--apdis(x)dx,
PD=mi-2ϕm jm 2PZB j=νW+.
2akk j=ϕc j-|ϕm j|.
ω(μ00c)1/2 sin θin=βj-K.
βj02=ω2μ00c(ωp2-ω2)(1+c)[ωp2(1+c)-1-ω2]fora0.
(2a)tr=1fω(μ00)1/2|m|(f-m)1/2-c(f-c)1/2.
αf j=-ikf j=(βj2-ω2μ00f)1/2.
exp(-4aαf j)=1-fαm jαf j|m|1+fαc jαf jc1+fαm jαf j|m|1-fαc jαf jc.

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