Scattering from fractal superlattices with variable lacunarity

Abstract

Reflection and transmission properties of polyadic fractal superlattices are formulated, solved analytically, and characterized for variations in fractal dimension, lacunarity, number of gaps, stage of growth, and angle of incidence. We systematically study the effect of the lacunarity or homogeneity of gaps on the scattering characteristics of these superlattices. The salient features of this scattering are captured by families of reflection data that denote twist plots. We find evidence that fractal dimension, lacunarity and stage of growth, can be distinguished in these plots. The analytic solution described here is a doubly recursive technique that efficiently provides the reflection and transmission coefficients of a large class of Cantor superlattices. This may provide a significant computational advantage over traditional methods as the number of interfaces becomes large.