SPECTRUM OF WAVES IN STOCHASTICALLY MODULATED SUPERLATTICES

A theory of the spectrum of waves in partially randomized multilayers is developed. A model of the superlattice in the form of a harmonic fu nction with stochastically modulated period is considered. Correlation functions of the superlattice are deduced for different shapes of the modulation: plane one-dimensional defects, prolate along the superlat tice axis, two-dimensional defects, and isotropic three-dimensional in homogeneities. The law of the correlation decay depends essentially on the dimension of short-wave inhomogeneities and is Gaussian for long- wave inhomogeneities irrespective of their dimension. Dispersion laws and damping of waves are calculated at the boundary of the Brillouin z one of the superlattice in the weak-binding approximation. Both the da mping and modification of the dispersion law depend on the dimension o f the inhomogeneities and their correlation radii. In the absence of r andomization a gap in the spectrum is determined by the change of some physical parameter at the interfaces. Randomization leads to the mono tonic decrease of the gap for the case of short-wave inhomogeneities. For the case of long-wave inhomogeneities randomization leads at first to the increase of the gap and only then to its decrease and closing.