  The construction of the unconditionally stable planar rank 2 scattering
matrix for stratified systems is detailed from Fresnel equations. Several
matrix decompositions and numerical calculations performed on the planar S
matrix allow for the expedient characterization of purely absorbing, brewster,
surface plasmon, and wave-guide modes. A figure of merit is presented from the
decompositions of the scattering matrix constructed from the Chandezon method
for corrugated surfaces. This figure of merit represents the hyper-area of the
scattering matrix transform and allows for rapid distinguishability between
lossy absorption phenomena, and surface plasmons. Some extension of this
technique is possible for surface plasmon polaritons in the infrared region.
