Abstract

Properties of a leaky quasi-waveguide formed by a thin film of refractive index smaller than the substrate are described. By exciting these leaky waves through the substrate, we have demonstrated a convenient and accurate method of measuring both the refractive index and thickness of thin films. Experimental results are given for polystyrene, with a demonstrated accuracy comparable with both that of prism coupling into a waveguiding film and with ellipsometry.

© 1983 Optical Society of America

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References

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  1. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  2. R. Ulrich, R. Torge, Appl. Opt. 12, 2901 (1973).
    [CrossRef] [PubMed]
  3. K. Tanaka, Appl. Phys. Lett. 34, 672 (1979).
    [CrossRef]
  4. P. P. Herrmann, Appl. Opt. 19, 3261 (1980).
    [CrossRef] [PubMed]
  5. R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
    [CrossRef]
  6. R. Th. Kersten, Opt. Commun. 13, 327 (1975).
    [CrossRef]
  7. A. C. Adams, D. P. Schinke, C. D. Capio, J. Electrochem. Soc. 126, 1539 (1979).
    [CrossRef]
  8. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 31–34.
  9. C. Vassallo, J. Opt. Soc. Am. 69, 311 (1979).
    [CrossRef]
  10. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).
  11. T. W. Hou, C. J. Mogab, Appl. Opt. 20, 3184 (1981).
    [CrossRef] [PubMed]
  12. The main sources of error come from the measurement of angles. For example, for propagation constant N we have ΔN=∂N∂αΔα+∂β∂ϵΔϵ. Here Δα and Δ∊ are the experimental deviation of the incident angles and the angle of prism, respectively. In our experiment Δα ≈ Δ∊ ≈ 1 min, so that ΔN = 0.0003 is the same order of magnitude as the rms error of N̅ in Table I.

1981

1980

1979

K. Tanaka, Appl. Phys. Lett. 34, 672 (1979).
[CrossRef]

A. C. Adams, D. P. Schinke, C. D. Capio, J. Electrochem. Soc. 126, 1539 (1979).
[CrossRef]

C. Vassallo, J. Opt. Soc. Am. 69, 311 (1979).
[CrossRef]

1975

R. Th. Kersten, Opt. Commun. 13, 327 (1975).
[CrossRef]

1973

1969

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Adams, A. C.

A. C. Adams, D. P. Schinke, C. D. Capio, J. Electrochem. Soc. 126, 1539 (1979).
[CrossRef]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

Capio, C. D.

A. C. Adams, D. P. Schinke, C. D. Capio, J. Electrochem. Soc. 126, 1539 (1979).
[CrossRef]

Herrmann, P. P.

Hou, T. W.

Kersten, R. Th.

R. Th. Kersten, Opt. Commun. 13, 327 (1975).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 31–34.

Martin, R. J.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Mogab, C. J.

Prettl, W.

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

Schinke, D. P.

A. C. Adams, D. P. Schinke, C. D. Capio, J. Electrochem. Soc. 126, 1539 (1979).
[CrossRef]

Tanaka, K.

K. Tanaka, Appl. Phys. Lett. 34, 672 (1979).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Torge, R.

Ulrich, R.

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

R. Ulrich, R. Torge, Appl. Opt. 12, 2901 (1973).
[CrossRef] [PubMed]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Vassallo, C.

Appl. Opt.

Appl. Phys.

R. Ulrich, W. Prettl, Appl. Phys. 1, 55 (1973).
[CrossRef]

Appl. Phys. Lett.

K. Tanaka, Appl. Phys. Lett. 34, 672 (1979).
[CrossRef]

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

J. Electrochem. Soc.

A. C. Adams, D. P. Schinke, C. D. Capio, J. Electrochem. Soc. 126, 1539 (1979).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

R. Th. Kersten, Opt. Commun. 13, 327 (1975).
[CrossRef]

Other

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 31–34.

The main sources of error come from the measurement of angles. For example, for propagation constant N we have ΔN=∂N∂αΔα+∂β∂ϵΔϵ. Here Δα and Δ∊ are the experimental deviation of the incident angles and the angle of prism, respectively. In our experiment Δα ≈ Δ∊ ≈ 1 min, so that ΔN = 0.0003 is the same order of magnitude as the rms error of N̅ in Table I.

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Figures (3)

Fig. 1
Fig. 1

Zigzag path of a ray in a three-layer dielectric slab structure. The substrate n2 is shown with a larger refractive index than the quasi-waveguiding layer n1. Light is shown totally internally reflected at the cladding boundary.

Fig. 2
Fig. 2

Experimental setup and photograph of quasi-waveguide m-lines.

Fig. 3
Fig. 3

Discrete leaky-wave incident angles and their reflection coefficients for (a) the quasi-waveguide we used in our experiment, n1 = 1.58, n2 = 1.72, n3 = 1, d = 6.44 μm and (b) a real waveguide, n1 = 1.54, n2 = 1.52, n3 = 1, d = 8 μm.

Tables (1)

Tables Icon

Table I Measurement and Analysis of Quasi-Waveguide

Equations (14)

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2 Kd + ϕ 12 + ϕ 13 = 2 m π ,
K 2 = n 1 2 k 2 N 2 k 2 .
ϕ 12 = 2 tan 1 [ ( n 1 n 2 ) ρ N 2 n 2 2 k / K ] ,
ϕ 13 = 2 tan 1 [ ( n 1 n 3 ρ N 2 n 3 2 k / K ] .
ϕ 12 = π , ϕ 13 = 2 tan 1 [ ( n 1 n e ) ρ N 2 n 3 2 k / K ] ,
n 1 2 N i 2 n 1 2 N j 2 = ( m i + ½ ) π + tan 1 N i 2 n 3 2 n 1 2 N i 2 ( m j + ½ ) π + tan 1 N j 2 n 3 2 n 1 2 N j 2 .
n 1 2 N i 2 n 1 2 N j 2 = ( m i + 1 ) π n 1 2 N i 2 N i 2 n 3 2 ( m j + 1 ) π n 1 2 N j 2 N j 2 n 3 2 .
n 1 2 = N i 2 + ( m i + 1 ) 2 ( m j + 1 ) 2 ( m i + 1 ) 2 ( N i 2 N j 2 ) .
d = λ 4 π n 1 2 N 2 [ ( 2 m + 1 ) π + 2 tan 1 N 2 n 3 2 n 1 2 N 2 ] .
d = λ 2 [ ( m j + 1 ) 2 ( m i + 1 ) 2 N i 2 N j 2 1 π N i 2 n 3 2 ] .
σ ( n , d ) = i M [ N ̅ i N i ( n , d ) ] 2 ,
d = 2 λ r ( 1 r ) n 2 2 n 1 2 λ / 2 π n 1 2 1 .
d λ H n 1 2 n 2 2 n 1 2 where H = ( 1 + r 1 r ) 2 n 2 4 n 1 4
L m = ( n 1 n 2 ) ρ 4 n 1 ( n 2 2 n 1 2 ) ½ λ 2 ( m + 1 ) 2 W eff 3 ,

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