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 characteriz ed by a fractal descriptor denoted the lacunarity. From the wavelet analysi s of the superlattice's impulse response, we extract the lacunarity, We sho w that the skeleton of wavelet-transform modulus maxima overlaps two hierar chical structures in the time-scale domain: one allows the direct remote ex traction of the similarity dimension, while the other gives an accurate est imation of the lacunarity of the interrogated superlattice. (C) 2001 Elsevi er Science B.V. All rights reserved.