Scattering of plane waves by locally homogeneous dielectric noise

Abstract

The scattering of acoustic and electromagnetic radiation by random refractive index fluctuations of the scattering medium (e.g. the troposphere, the ocean) is a problem of considerable contemporary interest. For brevity, we shall refer to these refractive index fluctuations as dielectric noise. The purpose of this paper is to compare two approaches to the problem of the scattering of incident plane waves by a confined region of dielectric noise. In the first approach, which is the conventional one, the scattering dielectric noise is represented as a ‘section’ of a homogeneous (i.e. spatially stationary) random process. In the second approach, which is based on a recent generalization of the notion of stationarity (1), the scattering dielectric noise is represented as a locally homogeneous random process. The advantage of representing the dielectric noise as a locally homogeneous process, rather than as a homogeneous process, is that one can thereby take into account in a natural way the spatial variation of the average noise power, without departing from the physically reasonable requirement that the process be approximately homogeneous in suitably restricted domains.