Identifying contributions of individual layers constituting multilayer dielectric mirrors

First-order approximations have been used to study the recursion expressions of the reflection and transmission coefficients of a weakly absorptive multilayer mirror. It has been proved that in the proximity of the central frequency ω0 of a quarter-wave mirror, contributions of an individual layer to the reflection delay time and absorption-induced reflectivity reduction can be quantitatively specified with a single weighting factor pertinent to that layer. Derivations have indicated that the absorption-induced reductions of mirror reflectivity and reflection delay can be reduced by selecting an odd layer number and a large index ratio between alternating high and low refractive index coating materials. Calculations have also suggested that the absorbed incident light is not distributed, among the reflected and transmitting parts, according to the ratio between the reflectivity and potential transmission.