Fractal superlattices and their wavelet analyses
H. Aubert, D.L. Jaggard · Optics Communications · 1998
Abstract We theoretically investigate Cantor superlattices which are interrogated by a normally incident pulse. Here a continuous wavelet transform is applied to the impulse response for the remote extraction of fractal characteristics of these superlattices. When a hierarchical structure of wavelet-transform modulus maxima is revealed in scale-time domain, we show that such structure displays the construction rule of the Cantor set which governs its fractal geometry for the cases considered here. It follows that specified singularities in the impulse response present a spatial arrangement analogous to the distribution of discontinuities in the refractive index profile of the interrogated medium. The similarity dimension is extracted from the scaling properties of this wavelet analysis.