Abstract

The optical performance of an ideal thin film can be represented by a single point on a triangular coordinate graph, because the sum of the reflectance, transmittance, and absorption is unity. Several examples are presented to show how the triangular coordinate graph provides a useful perspective to the interplay between the performance and the optical properties of a semitransparent metal film.

© 1990 Optical Society of America

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References

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  1. H. O. McMahon, “Thermal Radiation from Partially Transparent Reflecting Bodies,” J. Opt. Soc. Am. 40, 376–380 (1950).
    [CrossRef]
  2. J. H. Apfel, “Optical Coatings for Collection and Conservation of Solar Energy,” J. Vac. Sci. Technol. 12, 1016–1022 (1975).
    [CrossRef]
  3. P. H. Berning, A. F. Turner, “Induced Transmission in Absorbing Films Applied to Band Pass Filter Design,” J. Opt. Soc. Am. 47, 230–239 (1957).
    [CrossRef]

1975 (1)

J. H. Apfel, “Optical Coatings for Collection and Conservation of Solar Energy,” J. Vac. Sci. Technol. 12, 1016–1022 (1975).
[CrossRef]

1957 (1)

1950 (1)

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Figures (9)

Fig. 1
Fig. 1

Calculated reflectance, transmittance, and absorption of an unsupported nickel film as a function of thickness.

Fig. 2
Fig. 2

Calculated reflectance, transmittance, and absorption of an unsupported nickel film as a function of thickness. Reflectance, represented by the lower curve, is plotted in the conventional manner. Transmittance is represented by the distance between the two curves. Absorption is represented by the distance between the upper curve and the top of the graph.

Fig. 3
Fig. 3

Triangular coordinate graph for plotting reflectance (R), transmittance (T), and absorption (A) of a specular optical element such as a coated surface. The intensity of each variable is measured linearly from the opposite side toward the labeled apex. The dashed line grid represents increments of 0.1 in each variable. The boundaries are labeled with the special cases in which one of the variables is zero.

Fig. 4
Fig. 4

Triangular coordinate graph of the calculated optical performance of a nickel film as a function of thickness. The tick marks indicate 10 nm thickness increments. The solid lines radiating from the R = 1 apex are lines of constant potential transmittance.

Fig. 5
Fig. 5

Triangular coordinate graph of the calculated optical performance of twelve metals whose properties are given in Table I. The tick marks represent 10 nm thickness increments.

Fig. 6
Fig. 6

Calculated reflectance, transmittance, and absorption of a metal film at a radio frequency.

Fig. 7
Fig. 7

Triangular coordinate graphical representation of the calculated performance of a thin metal film at a radio frequency. The tick marks starting near the R = 1 apex indicate increasing sheet resistance in ohms per square. The shortest tick marks are for steps of 10 Ω per square, the next size ticks are 100, and the largest ticks are 1,000-Ω per square values. The peak absorption is near 190 Ω per square.

Fig. 8
Fig. 8

Calculated reflectance, transmittance, and absorption of a transparent conducting coating represented by the free electron model. The coating has a thickness of 1 μm, a sheet resistance of 2 Ω/square and is composed of material with resistivity of 2 × 10−4 Ω-cm mobilty of 54 cm2/V-s and a carrier density of 5.83 × 1020 cm−3.

Fig. 9
Fig. 9

Triangular coordinate graphical representation of the performance of the transparent conducting coating shown in the previous figure. The wavelength is indicated by tick marks. The small ticks near the T apex are for 0.1 μm increments. The larger ticks are for one micron increments.

Tables (2)

Tables Icon

Table I Optical Constants of Metals at the Wavelength of 632.8 nm

Tables Icon

Table II Properties of the transparent conducting film for which the optical performance is shown In Figs. 8 and 9

Equations (2)

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R = { g 2 + g } 2 ,
T = { 2 2 + g } 2 .

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