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

An approximate calculation method for light propagation in random multilayer films is presented. It is applied to a particular structure consisting of alternating lower- and higher-refractive-index materials with one type of layer having random thickness. An analytical expression for the localization length is derived. It is found to be in excellent agreement over a broad wavelength range, with numerical calculations performed by use of the transfer matrix formalism without any simplifying assumptions. Furthermore, this approximation accounts very well for anomalous reflectance effects that have been reported in experimental studies of amorphous silicon-silicon nitride multilayer films with random-thickness layers. Within the approximation presented, one can identify separate terms that are responsible for localization and for anomalous reflectance. This separation is helpful in clarifying the origins of both effects.