Strong fluctuation theory for a mean EM field in a statistically inhomogeneous medium: case of cylindrically-layered medium

A lossy electrically isotropic random medium is considered whose mean permittivity distribution, as well as the multipoint statistical moments are invariant under arbitrary rotations about and translations along a fixed symmetry axis, and are inhomogeous in the radial direction. This model is practically related to plasma diagnostics, design of artifical dielectrics, fiber optics etc. In the report, a modified renormalization method is proposed to calculate the effective permittivity operator (EPO) of such medium in the strong fluctuation case. The crux of said modification lies in taking into proper account a delta function singularity of the spectral Green´s function (SGF) rather than that of the spatial Green´s function as is done in the previous approaches, On this basis, a rigorous expression for the permittivity of a background medium is found, a bilocal approximation for the EPO is derived, its applicability to a strong fluctuation case is verified, and some examples are analyzed.