Polyadic Cantor superlattices with variable lacunarity

Reflection and transmission properties of polyadic fractal superlattices are formulated, solved analytically, and characterized for variations in stage of growth, fractal dimension, and lacunarity. This is the first time to our knowledge that the effect of lacunarity on wave interactions with such structures has been considered. The results are summarized by families of reflection data that we denote twist plots. A new doubly recursive computational technique efficiently provides the reflection and transmission coefficients for a large class of Cantor superlattices with numerous interfaces.