Abstract

A convenient and accurate method for determining the birefringence of a thin dielectric film is presented. In this technique, the film is deposited directly onto the base of a prism, thus forming a leaky waveguide, and a converging laser beam is coupled into the film to excite simultaneously many leaky modes. We present an error analysis to evaluate the effect of each source of uncertainty on the value of the birefringence.

© 1984 Optical Society of America

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References

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  1. P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Light Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  2. R. Th. Kersten, “The Prism-Film Coupler as a Precision Instrument Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
    [CrossRef]
  3. W. D. Westwood, J. S. Wei, “Guided Optics Techniques for Investigation of Films,” Can. J. Phys. 57, 1247 (1979).
    [CrossRef]
  4. R. Th. Kersten, “A New Method for Measuring Refractive Index Thickness of Liquid and Deposited Solid Thin Films,” Opt. Commun. 13, 327 (1975).
    [CrossRef]
  5. T.-N. Ding, E. Garmire, “Measuring Refractive Index and Thickness of Thin Films: A New Technique,” Appl. Opt. 22, 3177 (1983).
    [CrossRef] [PubMed]
  6. G. Leclerc, A. Yelon, “Temperature Dependence of Birefringence of Atactic Polystyrene: The Liquid–Liquid Transition,” J. Macromol. Sci. Phys. 22 (5 and 6), 861 (1983).
    [CrossRef]
  7. J. S. Wei, W. D. Westwood, “A New Method for Determining Thin-Film Refractive Index and Thickness Using Guided Optical Waves,” Appl. Phys. Lett. 32, 819 (1978).
    [CrossRef]
  8. W. M. Prest, D. J. Luca, “The Origin of the Optical Anisotropy of Solvent Cast Polymeric Films,” J. Appl. Phys. 50, 6077 (1979).
    [CrossRef]
  9. W. M. Prest, D. J. Luca, “The Alignment of Polymers During the Solvent-Coating Process,” J. Appl. Phys. 51, 5170 (1980).
    [CrossRef]
  10. Y. Cohen, S. Reich, “Ordering Phenomena in Thin Polystyrene Films,” J. Polym. Sci. Phys. Ed. 19, 599 (1981).
    [CrossRef]
  11. S. T. Kirsch, “Determining the Refractive Index and Thickness of Thin Films from Prism Coupler Measurements,” Appl. Opt. 20, 2085 (1981).
    [CrossRef] [PubMed]

1983 (2)

T.-N. Ding, E. Garmire, “Measuring Refractive Index and Thickness of Thin Films: A New Technique,” Appl. Opt. 22, 3177 (1983).
[CrossRef] [PubMed]

G. Leclerc, A. Yelon, “Temperature Dependence of Birefringence of Atactic Polystyrene: The Liquid–Liquid Transition,” J. Macromol. Sci. Phys. 22 (5 and 6), 861 (1983).
[CrossRef]

1981 (2)

Y. Cohen, S. Reich, “Ordering Phenomena in Thin Polystyrene Films,” J. Polym. Sci. Phys. Ed. 19, 599 (1981).
[CrossRef]

S. T. Kirsch, “Determining the Refractive Index and Thickness of Thin Films from Prism Coupler Measurements,” Appl. Opt. 20, 2085 (1981).
[CrossRef] [PubMed]

1980 (1)

W. M. Prest, D. J. Luca, “The Alignment of Polymers During the Solvent-Coating Process,” J. Appl. Phys. 51, 5170 (1980).
[CrossRef]

1979 (2)

W. M. Prest, D. J. Luca, “The Origin of the Optical Anisotropy of Solvent Cast Polymeric Films,” J. Appl. Phys. 50, 6077 (1979).
[CrossRef]

W. D. Westwood, J. S. Wei, “Guided Optics Techniques for Investigation of Films,” Can. J. Phys. 57, 1247 (1979).
[CrossRef]

1978 (1)

J. S. Wei, W. D. Westwood, “A New Method for Determining Thin-Film Refractive Index and Thickness Using Guided Optical Waves,” Appl. Phys. Lett. 32, 819 (1978).
[CrossRef]

1975 (2)

R. Th. Kersten, “A New Method for Measuring Refractive Index Thickness of Liquid and Deposited Solid Thin Films,” Opt. Commun. 13, 327 (1975).
[CrossRef]

R. Th. Kersten, “The Prism-Film Coupler as a Precision Instrument Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
[CrossRef]

1969 (1)

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Light Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Cohen, Y.

Y. Cohen, S. Reich, “Ordering Phenomena in Thin Polystyrene Films,” J. Polym. Sci. Phys. Ed. 19, 599 (1981).
[CrossRef]

Ding, T.-N.

Garmire, E.

Kersten, R. Th.

R. Th. Kersten, “The Prism-Film Coupler as a Precision Instrument Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
[CrossRef]

R. Th. Kersten, “A New Method for Measuring Refractive Index Thickness of Liquid and Deposited Solid Thin Films,” Opt. Commun. 13, 327 (1975).
[CrossRef]

Kirsch, S. T.

Leclerc, G.

G. Leclerc, A. Yelon, “Temperature Dependence of Birefringence of Atactic Polystyrene: The Liquid–Liquid Transition,” J. Macromol. Sci. Phys. 22 (5 and 6), 861 (1983).
[CrossRef]

Luca, D. J.

W. M. Prest, D. J. Luca, “The Alignment of Polymers During the Solvent-Coating Process,” J. Appl. Phys. 51, 5170 (1980).
[CrossRef]

W. M. Prest, D. J. Luca, “The Origin of the Optical Anisotropy of Solvent Cast Polymeric Films,” J. Appl. Phys. 50, 6077 (1979).
[CrossRef]

Martin, R. J.

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Light Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Prest, W. M.

W. M. Prest, D. J. Luca, “The Alignment of Polymers During the Solvent-Coating Process,” J. Appl. Phys. 51, 5170 (1980).
[CrossRef]

W. M. Prest, D. J. Luca, “The Origin of the Optical Anisotropy of Solvent Cast Polymeric Films,” J. Appl. Phys. 50, 6077 (1979).
[CrossRef]

Reich, S.

Y. Cohen, S. Reich, “Ordering Phenomena in Thin Polystyrene Films,” J. Polym. Sci. Phys. Ed. 19, 599 (1981).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Light Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Ulrich, R.

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Light Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Wei, J. S.

W. D. Westwood, J. S. Wei, “Guided Optics Techniques for Investigation of Films,” Can. J. Phys. 57, 1247 (1979).
[CrossRef]

J. S. Wei, W. D. Westwood, “A New Method for Determining Thin-Film Refractive Index and Thickness Using Guided Optical Waves,” Appl. Phys. Lett. 32, 819 (1978).
[CrossRef]

Westwood, W. D.

W. D. Westwood, J. S. Wei, “Guided Optics Techniques for Investigation of Films,” Can. J. Phys. 57, 1247 (1979).
[CrossRef]

J. S. Wei, W. D. Westwood, “A New Method for Determining Thin-Film Refractive Index and Thickness Using Guided Optical Waves,” Appl. Phys. Lett. 32, 819 (1978).
[CrossRef]

Yelon, A.

G. Leclerc, A. Yelon, “Temperature Dependence of Birefringence of Atactic Polystyrene: The Liquid–Liquid Transition,” J. Macromol. Sci. Phys. 22 (5 and 6), 861 (1983).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Light Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

J. S. Wei, W. D. Westwood, “A New Method for Determining Thin-Film Refractive Index and Thickness Using Guided Optical Waves,” Appl. Phys. Lett. 32, 819 (1978).
[CrossRef]

Can. J. Phys. (1)

W. D. Westwood, J. S. Wei, “Guided Optics Techniques for Investigation of Films,” Can. J. Phys. 57, 1247 (1979).
[CrossRef]

J. Appl. Phys. (2)

W. M. Prest, D. J. Luca, “The Origin of the Optical Anisotropy of Solvent Cast Polymeric Films,” J. Appl. Phys. 50, 6077 (1979).
[CrossRef]

W. M. Prest, D. J. Luca, “The Alignment of Polymers During the Solvent-Coating Process,” J. Appl. Phys. 51, 5170 (1980).
[CrossRef]

J. Macromol. Sci. Phys. (1)

G. Leclerc, A. Yelon, “Temperature Dependence of Birefringence of Atactic Polystyrene: The Liquid–Liquid Transition,” J. Macromol. Sci. Phys. 22 (5 and 6), 861 (1983).
[CrossRef]

J. Polym. Sci. Phys. Ed. (1)

Y. Cohen, S. Reich, “Ordering Phenomena in Thin Polystyrene Films,” J. Polym. Sci. Phys. Ed. 19, 599 (1981).
[CrossRef]

Opt. Acta (1)

R. Th. Kersten, “The Prism-Film Coupler as a Precision Instrument Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
[CrossRef]

Opt. Commun. (1)

R. Th. Kersten, “A New Method for Measuring Refractive Index Thickness of Liquid and Deposited Solid Thin Films,” Opt. Commun. 13, 327 (1975).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Experimental arrangement for the measurements.

Fig. 2
Fig. 2

Calculated refractive indices as a function of the absolute error in (a) the prism index; (b) the position of xo. The birefringence is the vertical distance between the two curves.

Tables (1)

Tables Icon

Table I Tolerances for a Parameter y Whose Value δy Produces an Error of 10−3 In A the Refractive Index, B the Birefringence

Equations (8)

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n sin θ m = n - π 2 ( m + 1 ) 2 2 n [ 2 π h λ + Q 0 / Q 1 ( n 2 - 1 ) 1 / 2 ] 2 ,
x m - x o = R tan γ m + d tan [ arcsin ( sin γ m n p ) ] ,
n sin θ m = n p sin [ α - arcsin ( sin γ m n p ) ] .
Δ n = n TM - n TE .
n TM = 1.587 ± 0.002 ; n TE = 1.582 ± 0.002 ; Δ n = 0.005 ± 0.001 ,
Δ n = n TM - n TE ,             δ Δ n < δ n TM + δ n TE
n TE = 1.582 , n TM = 1.588 , h = 5.0 μ m ,
n p = 1.75 ,             R = 200 mm , α = 65 ° ,             d = 10 mm .

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