Abstract

The surface modes of metal-clad four-layer waveguides were theoretically analyzed. We showed that the long-range surface modes can be excited in such waveguides. The long-range surface modes were experimentally studied with the angle scanning attenuated-total-reflection method; the dependence of wave vector and loss of these modes on the waveguide parameters were measured. Experimental results were in good agreement with theoretical calculations.

© 1986 Optical Society of America

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References

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  1. D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
    [CrossRef]
  2. R. T. Deck, D. Sarid, “Enhancement of Second-Harmonic Generation by Coupling to Long-Range Surface Plasmons,” J. Opt. Soc. Am. 72, 1613 (1982).
    [CrossRef]
  3. A. Otto, W. Sohler, “Modification of the Total Reflection Modes in a Dielectric Film by One Metal Boundary,” Opt. Commun. 3, 254 (1971).
    [CrossRef]
  4. I. P. Kaminow, W. L. Mammel, H. P. Weber, “Metal-Clad Optical Waveguides: Analytical and Experimental Study,” Appl. Opt. 13, 396 (1974).
    [CrossRef] [PubMed]
  5. A. Otto, “Spectroscopy of Surface Polaritons by Attenuated Total Reflection,” in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p. 677.
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  7. W. P. Chen, J. M. Chen, “Use of Surface Plasma Waves for Determination of the Thickness and Optical Constants of Thin Metallic Films,” J. Opt. Soc. Am. 71, 189 (1981).
    [CrossRef]
  8. J. C. Quail, J. G. Rako, H. J. Simon, “Long-Range Surface-Plasmon Modes in Silver and Aluminum Films,” Opt. Lett. 8, 377 (1983).
    [CrossRef] [PubMed]
  9. P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  10. D. Sarid, “Recovery of the Refractive-Index Profile of an Optical Waveguide from the Measured Coupling Angles,” Appl. Opt. 19, 1606 (1980).
    [CrossRef] [PubMed]
  11. A. N. Kaul et al., “Inverse WKB Method for Refractive Index Profile Estimation of Monomode Graded Index Planar Optical Waveguides,” Opt. Commun. 48, 313 (1984).
    [CrossRef]

1984 (1)

A. N. Kaul et al., “Inverse WKB Method for Refractive Index Profile Estimation of Monomode Graded Index Planar Optical Waveguides,” Opt. Commun. 48, 313 (1984).
[CrossRef]

1983 (1)

1982 (1)

1981 (2)

1980 (1)

1974 (1)

1972 (1)

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1971 (1)

A. Otto, W. Sohler, “Modification of the Total Reflection Modes in a Dielectric Film by One Metal Boundary,” Opt. Commun. 3, 254 (1971).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Chen, J. M.

Chen, W. P.

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Deck, R. T.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kaminow, I. P.

Kaul, A. N.

A. N. Kaul et al., “Inverse WKB Method for Refractive Index Profile Estimation of Monomode Graded Index Planar Optical Waveguides,” Opt. Commun. 48, 313 (1984).
[CrossRef]

Mammel, W. L.

Otto, A.

A. Otto, W. Sohler, “Modification of the Total Reflection Modes in a Dielectric Film by One Metal Boundary,” Opt. Commun. 3, 254 (1971).
[CrossRef]

A. Otto, “Spectroscopy of Surface Polaritons by Attenuated Total Reflection,” in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p. 677.

Quail, J. C.

Rako, J. G.

Sarid, D.

Simon, H. J.

Sohler, W.

A. Otto, W. Sohler, “Modification of the Total Reflection Modes in a Dielectric Film by One Metal Boundary,” Opt. Commun. 3, 254 (1971).
[CrossRef]

Weber, H. P.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Opt. Commun. (2)

A. Otto, W. Sohler, “Modification of the Total Reflection Modes in a Dielectric Film by One Metal Boundary,” Opt. Commun. 3, 254 (1971).
[CrossRef]

A. N. Kaul et al., “Inverse WKB Method for Refractive Index Profile Estimation of Monomode Graded Index Planar Optical Waveguides,” Opt. Commun. 48, 313 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

Other (2)

A. Otto, “Spectroscopy of Surface Polaritons by Attenuated Total Reflection,” in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p. 677.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

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Figures (8)

Fig. 1
Fig. 1

Geometry of the metal-clad four-layer waveguide.

Fig. 2
Fig. 2

Effective index K/(ω/c) of the TM0 mode vs thickness t of the metal film (theoretical curves): ɛ2 = −18; ɛ3 = 1.592; s = 10000 Å; λ = 6328 Å.

Fig. 3
Fig. 3

Geometry of the prism-coupled metal-clad four-layer optical waveguide with graded-index profile.

Fig. 4
Fig. 4

K/(ω/c) of the TM0 mode vs thickness t of the metal film of the prism-coupled graded-index waveguide (theoretical curves): ɛ2 = −18 + i0.47; ɛ 3 ( z ) = n 3 ( z ) = 1.5120 + 0.0780 [ 1 - ( z / 20000 ) - 2 ( z / 20000 ) 2 ]; ɛ4 = 1.51202; np = 1.7997; λ = 6328 Å.

Fig. 5
Fig. 5

Index of matching liquid and thickness of metal film vs the angular halfwidth ΔK/(ω/c) of the ATR resonance dip.

Fig. 6
Fig. 6

Angle scanning ATR curve of the LRSPM: ɛ1 = 1.562; L = 7300 Å; t = 144 Å; ----, experimental values; —, theoretical values.

Fig. 7
Fig. 7

Index of matching liquid vs effective index K/(ω/c) of the LRSPM branch of the TM0 mode: ○, experimental values; –, theoretical values.

Fig. 8
Fig. 8

Experimental results of the angular width of the LRSPM vs the thickness of the silver film: ○, experimental values; —, theoretical values.

Equations (28)

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E x = { B 1 exp ( α 1 z ) ( - < z 0 ) A 2 exp ( - α 2 z ) + B 2 exp ( α 2 z ) ( 0 z < t ) A 3 exp ( - α 3 z ) + B 3 exp ( α 3 z ) ( t z < t + s ) A 4 exp ( - α 4 z ) ( t + s z < + ) ,
H y = { i ω ɛ 1 c α 1 B 1 exp ( α 1 z ) ( - < z 0 ) i ω ɛ 2 c α 2 [ B 2 exp ( α 2 z ) - A 2 exp ( - α 2 z ) ] ( 0 z < t ) i ω ɛ 3 c α 3 [ B 3 exp ( α 3 z ) - A 3 exp ( - α 3 z ) ] ( t z < t + s ) - i ω ɛ 4 c α 4 A 4 exp ( - α 4 z ) ( t + s z < + ) ,
α j = K 2 - ω 2 c 2 ɛ j ,             j = 1 , 2 , 3 , 4 ;
α 3 s = arctan ( ɛ 3 α 4 ɛ 4 α 3 ) - arctan { ɛ 3 α 2 ɛ 2 α 3 × 1 - exp [ - 2 α 2 t + 2 arc t h ( ɛ 2 α 1 ɛ 1 α 2 ) ] 1 + exp [ - 2 α 2 t + 2 arc t h ( ɛ 2 α 1 ɛ 1 α 2 ) ] } + m π             ( m = 0 , 1 , 2 , ) ,
α 3 = ω 2 c 2 ɛ 3 - K 2 ,
α 3 s = - arc t h ( ɛ 4 α 3 ɛ 3 α 4 ) + arc t h { ɛ 2 α 3 ɛ 3 α 2 × 1 + exp [ - 2 α 2 t + 2 arc t h ( ɛ 2 α 1 ɛ 1 α 2 ) ] 1 - exp [ - 2 α 2 t + 2 arc t h ( ɛ 2 α 1 ɛ 1 α 2 ) ] } - i m π             ( m = 0 , 1 , 2 , ) ,
ɛ 4 α 3 ɛ 3 α 4 < 1.
t = 1 2 α 2 ln [ ( 1 + B ) ( A + 1 ) ( 1 - B ) ( A - 1 ) ] ,
A = ɛ 3 α 2 ɛ 2 α 3 t h [ α 3 s + arc t h ( ɛ 4 α 3 ɛ 3 α 4 ) ] ,
B = ɛ 2 α 1 ɛ 1 α 2 ,
K 1 = ω c ɛ 2 ɛ 1 ɛ 2 - ɛ 1 ,
B = ɛ 2 α 1 ɛ 1 α 2 = 1 ;
ω c ɛ 2 ɛ 4 ɛ 2 - ɛ 4 K 2 < ω c ɛ 2 ɛ 3 ɛ 2 - ɛ 3 ,
A = ɛ 3 α 2 ɛ 2 α 3 t h [ α 3 s + arc t h ( ɛ 4 α 3 ɛ 3 α 4 ) ] = 1.
A ɛ 3 ɛ 2 < 1 ,             B ɛ 2 ɛ 1 > 1 ,
t = 1 2 α 2 ln [ ( 1 + B ) ( 1 + C ) ( 1 - B ) ( 1 - C ) ] ,
C = - ɛ 2 α 3 ɛ 3 α 2 tan [ α 3 s - arctan ( ɛ 3 α 4 ɛ 4 α 3 ) ] .
( 1 + B ) ( 1 + C ) = ( 1 - B ) ( 1 - C ) .
K = ω c ɛ 3
t c = 1 2 α 2 ln [ ( 1 + B ) ( 1 + D ) ( 1 - B ) ( 1 - D ) ] ,
D = ɛ 2 ω c ɛ 3 + ɛ 2 [ ɛ 3 s + ɛ 4 ω c ɛ 3 - ɛ 4 ] .
min ( K 1 , K 2 ) < K < max ( K 1 , K 2 ) .
B 2 A 2 = ɛ 2 α 1 ɛ 1 α 2 - 1 ɛ 2 α 1 ɛ 1 α 2 + 1 .
ɛ 2 α 1 ɛ 1 α 2 = 1 ,
R = r 2 , r = [ m 11 + m 12 ( α 4 / ɛ 4 k 0 ) ] ( α p / ɛ p k 0 ) - [ m 21 - m 22 ( α 4 / ɛ 4 k 0 ) ] [ m 11 + m 12 ( α 4 / ɛ 4 k 0 ) ] ( α p / ɛ p k 0 ) + [ m 21 - m 22 ( α 4 / ɛ 4 k 0 ) ] } ,
α 4 = k 0 2 ɛ 4 - K 2 , α p = k 0 2 ɛ p - K 2 , K = n p k 0 sin θ , k 0 = ω / c ,             ɛ p = n p 2 ,
M = M 1 M 2 M 3 = M 1 M 2 M 31 M 32 M 3 l = | m 11 m 12 m 21 m 22 | ,
n 3 ( z ) = 1.5120 + 0.0780 [ 1 - z 20000 - 2 ( z 20000 ) 2 ] ,

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