Wave propagation in isotropic random media with nondiscrete spherical perturbations

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Abstract
In our studies on the optical properties of artificial anisotropic material, synthesized with methods of nuclear trace and etching technology, we have to investigate wave scattering by nondiscrete cylindrical perturbations. Unfortunately, most previous Twersky-type multiple-scattering theories as well as Keller-type random-medium theories exclusively deal with discrete scattering problems. In this preliminary work we use the theory of stochastic differential equations in order to study the low-frequency limit of scalar and electromagnetic wave scattering from an unbounded isotropic medium into which isotropic nondiscrete (partially overlapping) spherical perturbations are embedded. By taking into proper account the strong singularity of the Green’s tensor in the application of the first-order smoothing method it is shown that the effective dielectric tensor is a multiple of the unit dyad and can be calculated approximately via isotropic two-point autocorrelation functions which allow overlap of the spherical scatterers. These random-medium results are compared with those from discrete scattering theory. It is shown that there exists a joint scope of both theories in the limit of small volume fraction and of small size of the perturbations. In the electromagnetic case the degree of agreement between both methods is not as significant as in the scalar case. Finally, we present isotropic correlation functions for overlapping circular cylinders of finite as well as of infinite length.