OPTICS OF FRACTAL CLUSTERS IN THE ANOMALOUS DIFFRACTION APPROXIMATION

The principles of anomalous diffraction approximation of van de Hulst have been used to calculate the absorption sigma(a) and scattering sigma(s) cross-sections for fractal clusters of a large mass M. The formulas obtained describe the transition from the single scattering regime (sigma(s) is similar to M2-2/D; sigma(a) is similar to M; fractal dimension D > 2) to the geometrical optics regime (sigma(a), sigma(s) is similar to M2/D; D > 2). For clusters with fractal dimension D less-than-or-equal-to 2, our results reduce to the mean field theory of Berry and Percival in the limit M >> 1: sigma(a), sigma(s) is similar to M if D < 2, and sigma(s) is similar to M log M if D = 2. It is shown that for models with the exponential cut-off function of density correlations, h(x = r/R) = exp (-bx(v)), there is a logarithmic correction in the asymptotic behaviour of cross-sections (sigma(s), sigma(a) is similar to (log M1-2/D)2/v M2/D; D > 2; M >> 1), whereas the porous sphere model, h(x > 1) = 0, gives the exact geometrical optics limit. Smoke clusters are considered as an example, and their scattering and absorption cross-sections are compared with those calculated using the mean field theory.