Abstract

This paper describes a study of the absorptance of thin films with the aim of elucidating the region of validity for a direct relationship between the absorptance and the absorption coefficient. The calculations are performed for an unsupported film, a film on a transparent or metallic substrate, and for the absorptance as a function of polarization.

© 1977 Optical Society of America

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References

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  1. D. Beaglehole, Appl. Opt. 7, 2218 (1968).
  2. T. M. Donovan, in M. H. Brodsky, S. Kirkpatrick, D. Weaire, Eds. Tetrahedially Bonded Amorphous Semiconductors (American Institute of Physics, New York, 1974); T. M. Donovan, M. L. Kotek, J. E. Fischer, in Amorphous and Liquid Semiconductors, J. Stuke, W. Breming, Eds. (Taylor and Francis, London, 1974).
  3. F. Abelès, in Advanced Optical Techniques, A.C.S. Van Heel, Ed. (North-Holland, Amsterdam, 1967).
  4. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).
  5. For an unsupported film the electric wave amplitudes as a function of depth relative to the incident electric wave are given by E(x)=(1-r) exp(-iγx){1-r exp[-iγ2(d-x)]1-r2exp(-iγ2d)}. The wave intensity of Fig. 3 is given by E(x)E*(x), while in Fig. 4 this intensity has been averaged over the thickness d.
  6. A. Vasicek, in Optics of Thin Films, G. Hass, Ed. (North-Holland, Amsterdam, 1960).
  7. The irradiance is the power per unit solid angle per unit area perpendicular to the direction of propagation.

1968 (1)

Abelès, F.

F. Abelès, in Advanced Optical Techniques, A.C.S. Van Heel, Ed. (North-Holland, Amsterdam, 1967).

Beaglehole, D.

Donovan, T. M.

T. M. Donovan, in M. H. Brodsky, S. Kirkpatrick, D. Weaire, Eds. Tetrahedially Bonded Amorphous Semiconductors (American Institute of Physics, New York, 1974); T. M. Donovan, M. L. Kotek, J. E. Fischer, in Amorphous and Liquid Semiconductors, J. Stuke, W. Breming, Eds. (Taylor and Francis, London, 1974).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

Vasicek, A.

A. Vasicek, in Optics of Thin Films, G. Hass, Ed. (North-Holland, Amsterdam, 1960).

Appl. Opt. (1)

Other (6)

T. M. Donovan, in M. H. Brodsky, S. Kirkpatrick, D. Weaire, Eds. Tetrahedially Bonded Amorphous Semiconductors (American Institute of Physics, New York, 1974); T. M. Donovan, M. L. Kotek, J. E. Fischer, in Amorphous and Liquid Semiconductors, J. Stuke, W. Breming, Eds. (Taylor and Francis, London, 1974).

F. Abelès, in Advanced Optical Techniques, A.C.S. Van Heel, Ed. (North-Holland, Amsterdam, 1967).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

For an unsupported film the electric wave amplitudes as a function of depth relative to the incident electric wave are given by E(x)=(1-r) exp(-iγx){1-r exp[-iγ2(d-x)]1-r2exp(-iγ2d)}. The wave intensity of Fig. 3 is given by E(x)E*(x), while in Fig. 4 this intensity has been averaged over the thickness d.

A. Vasicek, in Optics of Thin Films, G. Hass, Ed. (North-Holland, Amsterdam, 1960).

The irradiance is the power per unit solid angle per unit area perpendicular to the direction of propagation.

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Figures (10)

Fig. 1
Fig. 1

R, T, and A vs d/λ according to Eqs. (1) and (2) for films with optical constants n = 4.4, k = 0.1.

Fig. 2
Fig. 2

Film absorptance A vs d/λ for various values of the extinction coefficient k and with constant n = 4.4.

Fig. 3
Fig. 3

The variation of the electric wave intensity (relative to the incidence intensity) as a function of depth in a film of fixed thickness (=0.5 μm) for various values of the extinction coefficient.

Fig. 4
Fig. 4

Shown in comparison with A is the thickness—averaged electric wave intensity as a function of d/λ for n = 4.4 and k = 0.1.

Fig. 5
Fig. 5

As as a function of angle of incidence for various values of d/λ. The optical constants used in the calculations are n = 4.4 and k = 0.1.

Fig. 6
Fig. 6

Ap as a function of angle of incidence for various values of d/λ. The optical constants used in the calculations are n= 4.4 and k = 0.1.

Fig. 7
Fig. 7

The angular averaged absorptance vs d/λ with n = 4.4 and k = 0.01 compared with normal incidence absorptance.

Fig. 8
Fig. 8

The variation of α (the first term in the expansion of A/nηd in terms of nηd) with d/λ and Δϕ (the phase shift for one pass through the film). Results displayed are for an unsupported film, for a film on transparent substrate with ns = 1.5 and ns = 3.3, and for a film on a metallic substrate (insert).

Fig. 9
Fig. 9

A plot of A/nηd vs nηd having k the variable for various values of d/λ for an unsupported film. n equals 4.4.

Fig. 10
Fig. 10

The variation of β (the second term in the expansion) with d/λ and Δϕ for an unsupported film.

Equations (8)

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R = | r 1 + r 2 exp ( - 2 i γ d ) 1 + r 1 r 2 exp ( - 2 i γ d ) | 2 ,
T = | t 1 t 2 exp ( - i γ d ) 1 + r 1 r 2 exp ( - 2 i γ d ) | 2 ,
A ( θ ) β = 0 π / 2 A β ( θ ) cos θ sin θ d θ 0 π / 2 cos θ sin θ d θ .
R = R + T 2 R 0 1 - R 0 R ,
T = T ( 1 - R 0 ) 1 - R 0 R ,
R = | r 2 + r 1 exp ( - 2 i γ d ) 1 + r 1 r 2 exp ( - 2 i γ d ) | 2 .
A n η d [ 4 R 0 1 - n s 2 + 2 T 0 2 ( 1 + n s ) ( 1 - R 0 ) ] ,
E ( x ) = ( 1 - r ) exp ( - i γ x ) { 1 - r exp [ - i γ 2 ( d - x ) ] 1 - r 2 exp ( - i γ 2 d ) } .

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