Spatial correlation functions of random electromagnetic fields in the presence of a semi-infinite isotropic medium

We extend a previous analysis of spatial correlation functions for classical electromagnetic vector fields near a perfectly conducting boundary [Arnaut, Phys. Rev. E, 73, 036604 (2006)] to the case of an isotropic semi-infinite medium with planar interface and characterized by a first-order impedance boundary condition. The analytical results are illustrated with calculations for the case of point separations in the direction perpendicular to the interface. For the incident plus reflected field, the dependence of the complex-valued and inhomogeneous spatial correlation function on the permittivity, permeability, and conductivity of the medium is determined. For the refracted field, the spatial correlation is again complex valued but homogeneous and highly sensitive to the value of the refractive index. Based on the derived dependencies, nonlocal measurement methods for precision characterization of electromagnetic material properties are suggested. The influence of the directionality of incidence for electromagnetic beams is investigated. Narrowing the beam width results in a slower decrease of the amplitude of the correlation function as a function of point separation. Previously obtained asymptotic results for statistically homogeneous random free fields are retrieved as special cases.