If we assume that a surface can be approximated by an infinite plane separating two media that have different conductivity and permittivity parameters, then equations relating a reflected EM wave to its incident EM wave and the dielectric properties of the two media can be obtained. Initially we will assume that the media are infinitely wide so that the surface is the only discontinuity in the environment. Both media are also assumed to be homogeneous, and the surface between them perfectly smooth.
The polarization of a wave reflected off a surface has an effect on the reflection coefficient associated with the reflected wave. The effects of polarization are quantified as follows [86]:
We can define the intrinsic impedance, , of a
medium by (3.10). The relative permeability,
, can
be taken as unity for non-magnetic materials, thus
. Assuming this to be the case, we can define
as
a function of the two media as
where the incident and reflected fields exist within medium I, and the
refracted component within medium II. The reflected field
can then be defined in terms of the incident field
for
both vertical and horizontal polarizations. In the case of horizontal
polarization, with grazing angle of incidence,
, as
and for the vertical polarization case,
where and
are reflection coefficients with phase angles
and
.
Derivations for these, and selected subsequent equations are presented in Appendix A.