Simple Expressions for Calculating the Effect of Volume or Interface Absorption in Thin Films on the Performance of High Reflectance or Antireflectance Multilayer Coatings

Approximate closed-form expressions are developed for predicting the effect of volume and interface absorption in thin films on the performance of quarterwave multilayer coatings. For highly reflecting coatings on dielectric substrates the volume absorption expressions are equivalent to those obtained by Sparks using a perturbation approach. The results are extended to metal substrates by introducing the concept of a generalized substrate index. An approximate expression for scattering losses for high reflectance coatings is included. Multiple quarter-wave antireflectance coatings are also analyzed using admittance theory. A technique for experimentally separating and determining interface and volume absorption in single-layer films has recently been reported. The expressions developed in this paper make it possible to predict the performance of high reflectance and antireflectance multilayer stacks from these single-film measurements without recourse to a computer.