## 1. Introduction

[2] Complex electromagnetic (EM) environments are characterized by the fact that EM fields behave as random or quasi-random quantities. They can be studied in an efficient manner with the aid of statistical electromagnetics methods. With regard to the interaction of random fields with their environment, a fundamental problem of interest is the evolution of statistical properties of the field upon propagation through stratified media, including reflection and refraction at their interfaces. For incidence onto a perfectly electrically conducting (PEC) surface, previous studies of the average value [*Dunn*, 1990], standard deviation and first-order probability density function (pdf) [*Arnaut and West*, 2006] of the electric and magnetic energy densities have demonstrated a direction-dependent damped oscillatory behavior of their average value and standard deviation as a function of the distance of the point of evaluation to the interface. This behavior is a consequence of the interference between incident and reflected fields. As a result, unlike for deterministic waves, a boundary zone exists for random fields adjacent to the PEC surface, in which the statistical field properties are inhomogeneous and fundamentally different from those at larger (theoretically infinite) distance. Further insights that were gained from these studies pertain to the statistical anisotropy and polarization state of the field within the boundary zone and, for vector fields, the transitions of the pdf of the energy density from one- or two-dimensionally confined random fields at the interface to fully developed three-dimensional random fields at distances that are large relative to the wavelength. In addition, spatial correlation functions have been obtained previously for unbounded [*Bourret*, 1960; *Sarfatt*, 1963; *Mehta and Wolf*, 1964; *Eckhardt et al.*, 1999; *Hill and Ladbury*, 2002] and single-interface [*Arnaut*, 2006a, 2006b] vector EM fields that elucidate the spatial structure of random fields via their two-point coherence properties.

[3] In the present paper, the methods and results for statistical properties of random fields near a PEC surface are extended to a magneto-dielectric isotropic semi-infinite medium. Having previously analyzed the second-order spatial coherence and correlation properties for an impedance boundary [*Arnaut*, 2006b], here we are again concerned with local first-order statistical, i.e., distributional properties only. On the basis of previous results for nonlocal spatial coherencies of the electric field 〈*E*_{α}(**r**_{1}) *E**_{β}(**r**_{2})〉 (*α*,*β* = *x*, *y*, *z*), the polarization coefficient and pdf for the local energy density are determined. Because of the single interface and isotropy of the medium, the polarization coefficient is degenerate, whence the pdfs are one-parameter compound exponential (CE-1) distributions [*Arnaut*, 2002; *Arnaut and West*, 2006]. However, unlike for a PEC medium, the angular spectra of reflected and refracted random fields exhibit directivity because reflection and transmission coefficients of plane waves for a magneto-dielectric semi-infinite medium depend on the wave polarization and angle of incidence. We shall confine the analysis and results to the electric field **E**; corresponding results for the magnetic field follow without difficulty. Since we express results in terms of Fresnel reflection and transmission coefficients for an isotropic half-space, analogous results for multilayer strata are easily obtained from the listed integral expressions, on substituting with the appropriate coefficients. In particular, probability distributions of reflected and transmitted fields on either side of a single layer of finite thickness are easily computed.