The Ultimate Reflectance of Multilayer Dielectric Mirrors

The theory of multilayer dielectric mirrors with residual absorptance is re-examined to determine whether lower absorptances and therefore higher reflectances can be achieved than with the usual type of alternating quarter-wave system. It is shown that considerable improvements are indeed possible if the layers of the material with high refractive index and residual absorption are made with optical thickness less than a quarter-wave, and the other layers with correspondingly greater optical thickness. Simple formulae are derived for the factor of improvement and the required optical thickness of the films of low refractive index. Moreover, by applications of the concept of potential transmittance and the principle of equivalent layers, a relationship is established between the desired limiting reflectance of the system and the necessary number of layers.