Reflection by absorbing periodically stratified media

Existing theory gives the optical properties of a periodically stratified medium in terms of a two by two matrix. This theory is valid also for absorbing media, because the matrix remains unimodular. The main effect of absorption is that the reflection (of either polarization) becomes independent of the number of periods N, and of the substrate properties, provided N exceeds a certain value which depends on the absorption. The s and p reflections are then given by simple formulae. The stop-band structure, which gives total reflection in bands of frequency and angle of incidence in the non-absorbing case, remains influential in weakly absorbing media, causing strong variations in reflectivity. The theory is applied to the frequency dependence of the normal-incidence reflectivity of a quarter-wave stack in which the high-index and low-index layers both absorb weakly. Analytical expressions are obtained for the frequency at which the reflectivity is maximum, the maximum reflectivity, and also for the reflectivity at the band edges of the stop band of the non-absorbing stack. (paper)