Numerical calculations on optical localization in multilayer structures with random-thickness layers

A study of localization effects in random, one-dimensional optical systems is presented, based on calculations in superlattices with random-thickness layers. A numerical treatment of the problem of electromagnetic wave propagation in these systems is employed with a transfer-matrix formalism. A localization length l is determined numerically in each case. In order to ensure that the computation results have more general validity in as wide a range of wavelengths as possible, there was no restriction imposed on the number of layers necessary to obtain the value of l with a given accuracy. Appropriate dimensionless variables have been used that greatly simplify the presentation of results. The numerical calculation gives interesting hints about the dependence of the localization length on the gap structure of the corresponding regular superlattice, i.e., the one formed by reducing to zero the standard deviation of layer thickness. This dependence is more intricate than a simple broadening of the regular's gaps, a creation of band tails, induced by disorder.