LIGHT-PROPAGATION AND LOCALIZATION IN DISORDERED BINARY MULTILAYER FILMS - AN APPROXIMATE ANALYTICAL SOLUTION

An approximate calculation method for light propagation in random mult ilayer films is presented. It is applied to a particular structure con sisting of alternating lower- and higher-refractive-index materials wi th one type of layer having random thickness. An analytical expression for the localization length is derived. It is found to be in excellen t agreement over a broad wavelength range, with numerical calculations performed by use of the transfer matrix formalism without any simplif ying assumptions. Furthermore, this approximation accounts very well f or anomalous reflectance effects that have been reported in experiment al studies of amorphous silicon-silicon nitride multilayer films with random-thickness layers. Within the approximation presented, one can i dentify separate terms that are responsible for localization and for a nomalous reflectance. This separation is helpful in clarifying the ori gins of both effects.