Approximate closed-form expressions are developed for predicting the effect of volume and interface absorption in thin films on the performance of quarter-wave multilayer coatings at normal incidence. For highly reflecting coatings the resulting expressions are an extension of Koppelmann’s equation. The contribution of both dielectric and metal substrates is included explicitly in these equations as is the contribution of interface absorption and scattering losses. Closed-form expressions are also developed for the transmittance of absorbing and scattering antireflection coatings. Techniques for experimentally separating and determining interface and volume absorption in single-layer films and for estimating interfacial and volume scattering have recently been reported in the literature. The expressions developed in this paper make it possible using this experimental data to predict the performance of quarter-wave high-reflectance and antireflectance multilayer stacks at the design wavelength without recourse to a computer.
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