Convergence Properties of the Perturbative Expansion in Scalar Wave Scattering on Random Media

Abstract

Scalar wave propagation in an isotropic randomly fluctuating medium is analyzed in terms of the multiple-scattering expansion, i.e., expansion of the scattering coefficient in powers of the fluctuation strength. It is shown that, in the limit of small absorption and sufficiently weak fluctuations, the leading terms in the multiple-scattering series can be summed exactly, and represented in terms of the radiative transfer equation (or its modification, taking into account back-scattering enhancement). On the other hand, the full series, including non-leading terms, is only asymptotic (non-convergent). For a weakly absorbing medium, and a typical shape of the correlation function, the first, the next-to-leading, correction to the cross-section is of the order π δ (2,πα/λ0)3 , δ being the variance of two-point correlations, α the correlation length, and λ0 the wavelength. The main effect of this correction is to modify the interaction kernel of the radiative-transfer equation in the way that favors individual back-scattering events in the multiple-scattering process.