Optical coatings are rarely used in an ideal environment. They are subjected to various environmental disturbances ranging from abrasion to high temperature and humidity. These disturbances cause performance degradation, which is often manifested as irreversible and usually visible destruction of the layers.
However, performance can also degrade less dramatically through the simple acquisition of contaminants. Such contaminants may not have any aggressive effect on the layers other than reducing the level of performance of the coating as a whole.
The action of water vapor, which is adsorbed through capillary condensation and causes a spectral shift in the coating, is well known. This section focuses on much smaller amounts of absorbing material, such as carbon, in the form of sub-molecular thicknesses that may occur at some point during the construction of the coating or, more usually, over the surface after deposition.
Although there are many tests to assess a coating’s resistance to environmental disturbances, there is no standard test for measuring susceptibility to contamination. Yet it can be shown that the response of coatings can vary enormously depending on many factors, including design, wavelength, and even errors made during deposition.
A coating’s performance can often be restored through careful cleaning, but this does not prevent the degradation between cleanings. Coatings more susceptible to contamination may require more frequent cleanings.
Fortunately, it is possible to predict coating response to low levels of contamination and assess comparative sensitivity. Electric field distribution and potential absorption are key to understanding the phenomenon. If the contamination layer is on the front surface, it receives the full irradiance entering the multilayer. The admittance at the contamination layer determines both the reflectance and the potential absorptance.
The key expressions involving absorptance \( A \) and potential absorptance \( A’ \) are derived as:
\[
A = \left( \frac{2 \pi}{\lambda} \right)^2 nkd \, \text{Re}(Y) \tag{12.2}
\]
\[
A’ = (1 – R) A \tag{12.3}
\]
Thus, we can express absorptance sensitivity as:
\[
A / H = \frac{4 \left( \text{Re}(y_0) + x^2 + z^2 \right)}{\pi \lambda nkd} \tag{12.4}
\]
Here, \( H \) is a measure of the absorption capacity of the film, while \( A \) is the actual absorptance. \( A/H \) represents the sensitivity to absorptance of an optical coating. Sensitivity is purely a function of the optical admittance of the complete coating. Furthermore, from Equation (12.4), contours of constant sensitivity are circles in the admittance plane centered on the point \( -y_0 \), exhibiting decreasing sensitivity with increasing radius.
To simplify matters, the value of \( y_0 \) is set to 1.00. The contour lines for this case are shown in Figure 12.11. For instance, consider amorphous carbon with optical constants \( 2.26 – i1.025 \) at 1000 nm and a thickness of 0.1 nm. A plot of \( H \) is shown in Figure 12.12, with values ranging between 0.003 and 0.006 across the visible spectrum.
Antireflection coatings aim to terminate their loci at the point \( (y_0, 0) \). This implies \( A/H = 1/(y_0) \), giving absorptance across the visible spectrum from approximately 0.3% to 0.6% for a perfect antireflection coating with a carbon film 0.1 nm thick. Typical results for a four-layer antireflection coating are shown in Figure 12.13. The design of the coating has little influence on these results for coatings with precisely zero reflectance.
Dielectric reflectors, particularly extended-zone high-reflectance coatings, show greater sensitivity. In such coatings, the admittance of the outer layers often circles near the imaginary axis, leading to absorptance values of 1%–2% for a 0.1 nm carbon layer over parts of the visible spectrum. This behavior is illustrated in Figures 12.14 and 12.15 for a 39-layer extended-zone reflector.
Aluminum Reflectors and Quarter-Wave Stacks
Aluminum reflectors are typically protected by a thin low-index layer, often a half-wave or quarter-wave in thickness. Figure 12.16 shows the sensitivity to contamination for these configurations. Quarter-wave stacks are among the most common high-performance reflectors. At the center wavelength, where all layers are quarter-waves, the admittance of a quarter-wave stack is real. Absorptance for the stack is given by:
\[
A = \frac{0.0116}{1 + Y^2} \tag{12.7}
\]
The absorptance as a function of the (odd) number of layers is shown in Figure 12.17. Agreement between simplified calculations and full matrix theory is excellent for up to 15 layers, beyond which absorptance levels off due to limitations of the thin-layer approximation.
Effects of Monitoring Errors and Moisture
Thermally evaporated coatings are susceptible to moisture penetration, which alters the electric field distribution and the absorptance associated with a contamination layer. Figure 12.18 illustrates how moisture enters localized spots, spreads out in circular patches, and affects field distribution. Monitoring errors that have negligible effects on reflectance can significantly impact contamination sensitivity.
