Wavelet analysis of transients in fractal superlattices

Fractal superlattices are designed by alternating dielectric layers according to an iterative fractal process. The discrete self-similarity of such stratified structures can be remotely detected from interrogation by an incident pulse. In this paper, the impulse response of one-dimensional Cantor superlattices is computed and the wavelet transform is applied to the reflected signal in order to explore its temporal distribution of singularities. For a sufficiently narrow pulse, the skeleton of the wavelet-transform modulus-maxima exhibits a hierarchical structure that makes apparent the iterative process governing the construction rule of the interrogated fractal superlattice and its geometry. In the reflected signal, such hierarchy reveals the existence of singularities that are distributed on the governing Cantor set. Finally, the similarity dimension is extracted from reflection data and a strategy for estimating the stage of growth is developed.