Lacunarity of multi-gap fractal superlattices using wavelet analysis

Multi-gap superlattices having the same fractal (similarity) dimension may differ in their distribution of gap sizes. This distribution is characterized by a fractal descriptor denoted the lacunarity. From the wavelet analysis of the superlattice's impulse response, we extract the lacunarity. We show that the skeleton of wavelet-transform modulus maxima overlaps two hierarchical structures in the time-scale domain: one allows the direct remote extraction of the similarity dimension, while the other gives an accurate estimation of the lacunarity of the interrogated superlattice.