Abstract

The validity of effective thickness expressions for sample films used in internal reflection spectroscopy is obtained by comparing them to exact computer calculations for various refractive indices, angles of incidence, extinction coefficients, and film thicknesses.

© 1971 Optical Society of America

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References

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  1. N. J. Harrick, F. K. du Pré, Appl. Opt. 5, 1739 (1966).
    [CrossRef] [PubMed]
  2. N. J. Harrick, Internal Reflection Spectroscopy (Interscience-Wiley, New York, 1967).
  3. Fluornoy and Huntsburger have shown previously that reflectivity decrease vs film thickness follows curve similar to those in Figs. 2–5. They placed nitrocellulose films of various thickness on a Ge reflection plate and measured the strength of an absorption band at a wavelength of 6.03 μ vs film thickness. (See Fig. 7, p 24 of Ref. 2.)
  4. See, e.g., J. A. Stratton, Electromagnetic Theory (McGraw-Hill1941, New York, p. 515.

1966 (1)

du Pré, F. K.

Harrick, N. J.

N. J. Harrick, F. K. du Pré, Appl. Opt. 5, 1739 (1966).
[CrossRef] [PubMed]

N. J. Harrick, Internal Reflection Spectroscopy (Interscience-Wiley, New York, 1967).

Stratton, J. A.

See, e.g., J. A. Stratton, Electromagnetic Theory (McGraw-Hill1941, New York, p. 515.

Appl. Opt. (1)

Other (3)

N. J. Harrick, Internal Reflection Spectroscopy (Interscience-Wiley, New York, 1967).

Fluornoy and Huntsburger have shown previously that reflectivity decrease vs film thickness follows curve similar to those in Figs. 2–5. They placed nitrocellulose films of various thickness on a Ge reflection plate and measured the strength of an absorption band at a wavelength of 6.03 μ vs film thickness. (See Fig. 7, p 24 of Ref. 2.)

See, e.g., J. A. Stratton, Electromagnetic Theory (McGraw-Hill1941, New York, p. 515.

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Figures (9)

Fig. 1
Fig. 1

Experimental arrangement for measurements on thin films via internal reflection spectroscopy. Medium 1 is the optically transparent internal reflection element, medium 2 is the sample material, the surrounding medium 3 is usually air.

Fig. 2
Fig. 2

Relative effective thickness for a weak absorber placed on KRS-5 (n1 = 2.4) vs actual film thickness for ‖-polarization and a number of angles of incidence. The solid lines represent exact computer calculations, and the dashed lines represent values obtained from the low absorption approximations.

Fig. 3
Fig. 3

Same as Fig. 2 except for ⊥-polarization.

Fig. 4
Fig. 4

Same as Fig. 2 except that medium 1 is Ge (n1 = 4) rather than KRS-5 (n1 = 2.4).

Fig. 5
Fig. 5

Same as Fig. 4 except for ⊥-polarization.

Fig. 6
Fig. 6

Relative effective thickness vs increasing extinction coefficient of medium 2 for thick and thin films. The internal reflection element is KRS-5 (n1 = 2.4). In regions where the curves have a horizontal slope, the approximate equations for effective thickness are valid.

Fig. 7
Fig. 7

Same as Fig. 6 except that the internal reflection elements are Ge (n1 = 4) rather than KRS-5 (n1 = 2.4).

Fig. 8
Fig. 8

Relative effective thickness vs extinction coefficient of medium 2 for θ just above the critical angle. The solid lines are exact calculations and the dashed lines are approximate values.

Fig. 9
Fig. 9

Relative effective thickness vs film thickness for highly absorbing medium 2 placed on KRS-5 at a number of angles of incidence. Note the maxima in effective thickness which result from a resonance phenomenon in the thin film.

Equations (7)

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I / I 0 = e - α d .
I / I 0 1 - α d .
R = 1 - α d e ,
d e λ 1 = n 21 cos θ π ( 1 - n 21 2 ) ( sin 2 θ - n 21 2 ) 1 2 ,
d e λ 1 = n 21 cos θ ( 2 sin 2 θ - n 21 2 ) π ( 1 - n 21 2 ) [ ( 1 + n 21 2 ) sin 2 θ - n 21 2 ] ( sin 2 θ - n 21 2 ) 1 2 ,
d e = [ 4 n 21 d cos θ / ( 1 - n 31 2 ) ] ,
d e = 4 n 21 d cos θ [ ( 1 + n 32 4 ) sin 2 θ - n 31 2 ] ( 1 - n 31 2 ) [ ( 1 + n 31 2 ) sin 2 θ - n 31 2 ] .

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