Scaling condition for multiple scattering in fractal aggregates

Abstract

It is well known that under the first Born approximation, the differential cross-section dsigma/dOmega for light scattered by a fractal of dimension d(f) scales with wave vector Q as Q(-df). The use of this formula to interpret experiments performed at frequencies close to the resonances of the system for which multiple scattering is not negligible is questionable. We study the scaling properties of the light scattered by colloidal aggregates employing a novel multi-resolution hierarchical algorithm which allows the study of large systems taking fully into account the long range of the interactions in multiple scattering calculations. We obtain the conditions under which scaling may be present and find that even under resonant conditions, the scattering cross-section may scale with the fractal dimension d(f), but only if the aggregate is larger than a dissipation and frequency-dependent length-scale L-h, confirming within a full vectorial calculation a result previously found for scalar interactions. For smaller aggregates, dsigma/dOmega might scale with a different exponent or it might not scale at all, depending on the frequency of light employed. This could explain the discrepancies between experiments performed on similar systems within the strong scattering regime. (C) 2003 Elsevier B.V. All rights reserved.