Test of a Mean Field Theory for the Optics of Fractal Clusters

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Abstract
Fractal aggregates such as soot particles are modelled as connected clusters of N spherules of radius a and complex refractive index µ, whose density correlation function p(x) varies like x D − 3 as x → 0, where D is the fractal dimension. They scatter scalar or vector waves of wavelength 2π/k where ka ≪ 1. Multiple scattering effects are included using a mean field theory. Optical cross-sections are derived in terms of N D ka and µ using an analytic form for p(x). The theory predicts that for clusters with D < 2 the specific scattering cross-section saturates at some large value as N → ∞ and absorption saturates at a level near 1; whilst for D > 2 both scattering and absorption decay as N → ∞ after reaching a maximum.