Abstract

The prism coupler, known from experiments on integrated optics, can be used to determine the refractive index and the thickness of a light-guiding thin film. Both parameters are obtained simultaneously and with good accuracy by measuring the coupling angles at the prism and fitting them by a theoretical dispersion curve. The fundamentals and limitations of this method are discussed, its practical use, and mathematical procedures for the evaluation.

© 1973 Optical Society of America

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References

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  1. P. K. Tien, Appl. Opt. 10, 2395 (1971).
    [CrossRef] [PubMed]
  2. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  3. J. H. Harris, R. Shubert, J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
    [CrossRef]
  4. P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
    [CrossRef]
  5. R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
    [CrossRef]
  6. P. K. Tien, G. Smolinsky, R. J. Martin, Appl. Opt. 11, 1313 (1972).
    [CrossRef]
  7. R. Ulrich, H. P. Weber, Appl. Opt. 11, 428 (1972).
    [CrossRef] [PubMed]
  8. R. Ulrich, J. Opt. Soc. Am. 61, 1467 (1971).
    [CrossRef]
  9. F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).
  10. M. Tacke, R. Ulrich, Opt. Commun. 6, 234 (1973).
    [CrossRef]

1973

M. Tacke, R. Ulrich, Opt. Commun. 6, 234 (1973).
[CrossRef]

1972

1971

1970

1969

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

Harris, J. H.

Knecht, W. L.

F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).

Martin, R. J.

P. K. Tien, G. Smolinsky, R. J. Martin, Appl. Opt. 11, 1313 (1972).
[CrossRef]

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

McGraw, R. B.

F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).

Polky, J. N.

Shubert, R.

Sloan, E. L.

F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).

Smolinsky, G.

Tacke, M.

M. Tacke, R. Ulrich, Opt. Commun. 6, 234 (1973).
[CrossRef]

Tien, P. K.

Ulrich, R.

Weber, H. P.

Webster, J. C.

F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).

Zernike, F.

F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).

Appl. Opt.

Appl. Phys. Lett.

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

J. Opt. Soc. Am.

Opt. Commun.

M. Tacke, R. Ulrich, Opt. Commun. 6, 234 (1973).
[CrossRef]

Other

F. Zernike, E. L. Sloan, J. C. Webster, R. B. McGraw, W. L. Knecht, Topical Meeting on Integrated Optics, Guided Waves, Materials, and Devices, Paper TuA9, Las Vegas, Nevada (February1972).

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Figures (5)

Fig. 1
Fig. 1

Schematic cross section through a prism-film coupler.

Fig. 2
Fig. 2

Schematic arrangement of prism, input optics, and observation screen. The double arrows indicate adjustments.

Fig. 3
Fig. 3

Two possible prism shapes: (a) symmetric prism, useful with samples that are slightly flexible (e.g., glass substrates ≤ 1 mm) and yield elastically under the clamping pressure; (b) half prism, may also be used with thick samples because the coupling spot is close to the edge.

Fig. 4
Fig. 4

Arrangement to keep the coupling spot stationary at C when the prism is rotated. The line CD is normal to AB and has length lp. The axis of the rotary table coincides with the center M of the dashed circles. The radius of these circles is r = lp/np, where np is the refractive index of the prism. The adjustment is optimum when the lines AB and CD and the incident beam are all tangential to the circles. This requires the beam to be offset by r from the axis of the table, and this offset must be toward B if α > 0 as indicated in (a), but toward A if α < 0 [see (b)].

Fig. 5
Fig. 5

Range of relative propagation constants N that can be measured with a prism of prism angle . Parameter at the curves is the prism index np. For each value of np there are two curves, giving the lower and upper limits of the possible N range.

Tables (1)

Tables Icon

Table I Examples for the Determination of Index n and Thickness W of Two Light-Guiding Filmsa

Equations (28)

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N ˜ m = c / v m = n p sin θ m .
N m = N ( m , n , W , k , n 0 , n 2 , ρ ) .
α m = ± ( Γ m - Γ ) ,
N ˜ = sin α cos + ( n p 2 - sin 2 α ) 1 / 2 sin .
N m ( p ) · - N m = - K m cot 2 ϕ 32 .
K m 1 2 δ N Ω .
cot 2 ϕ 32 < ( n p / n 2 ) 2 ρ / 2 cos θ .
M tot π - 1 k W ( n 2 - n 0 2 ) 1 / 2 ,
δ W / W 2 δ n / ( n - n 0 ) .
k W ( n 2 - N m 2 ) 1 / 2 = Ψ m ( n , N m ) ,
Ψ m ( n , N m ) m π + ϕ 0 ( n , N m ) + ϕ 2 ( n , N m )
ϕ j ( n , N m ) a r c tan [ ( n n f ) 2 ρ ( N m 2 - n j 2 n 2 - N m 2 ) ] 1 / 2 ,
n 2 = F ( n 2 ) ,
F ( n 2 ) ( N ˜ μ 2 Ψ ν 2 - N ˜ ν 2 Ψ μ 2 ) / ( Ψ ν 2 - Ψ μ 2 ) .
n [ q ] 2 = F ( n [ q - 1 ] 2 ) .
n 2 = lim q n [ q ] 2 ,
n [ 0 ] 2 > N ˜ μ 2             and             n [ 0 ] 2 > N ˜ ν 2 .
σ ( n , w ) = m [ N ˜ m - N m ( n , w ) ] 2 .
σ n ( n ¯ , w ¯ ) = 0 and σ w ( n ¯ , w ¯ ) = 0 ,
n [ q + 1 ] = n [ q ] + ( σ w σ n w - σ n σ w w ) / d e t ,
w [ q + 1 ] = w [ q ] + ( σ n σ n w - σ w σ n n ) / d e t ,
d e t ( σ n n σ w w - σ n w σ w n ) .
σ n = [ σ ( 1 , 0 ) - σ ( - 1 , 0 ) ] / 2 h n , σ w = [ σ ( 0 , 1 ) - σ ( 0 , - 1 ) ] / 2 h w , σ n n = [ σ ( 1 , 0 ) - 2 σ ( 0 , 0 ) + σ ( - 1 , 0 ) ] / h n 2 , σ w w = [ σ ( 0 , 1 ) - 2 σ ( 0 , 0 ) + σ ( 0 , - 1 ) ] / h w 2 , σ n w = σ w n = [ σ ( 1 , 1 ) - σ ( - 1 , 1 ) - σ ( 1 , - 1 ) + σ ( - 1 , - 1 ) / 4 h n h w .
σ ( r , s ) = σ ( n [ q ] + r h n , w [ q ] + s h w ) .
n ( m ) = n ¯ + 2 h n [ N ˜ m - N m ( n ¯ , w ¯ ) ] / [ N m ( n ¯ + h n , w ¯ ) ] .
δ n ¯ = { n [ n ( m ) - n ¯ ] 2 / ( M - 1 ) ( M - 2 ) } 1 / 2 ,
δ w ¯ = { n [ w ( m ) - w ¯ ] 2 / ( M - 1 ) ( M - 2 ) } 1 / 2 .
w m ( N ) = ( n 2 - N 2 ) - 1 / 2 Ψ m ( N )

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