An exact perturbative formulation of the dielectric integral equations for lossy interfaces

In modeling scattering from lossy surfaces, the surface is often approximated as a perfect electric conductor (PEC). However, when loss and wave penetration become important, the IBC model is typically employed and is adequate for many numerical simulations. However, the IBC's range of validity is considered unclear and an accurate quantification of its error is difficult. Consequently, other more exact implementations are necessary, such as integral equation methods. In this paper, a novel numerical implementation of the exact dielectric integral equations has been developed for scattering from a two-dimensional (2D), lossy dielectric interface. The formulation presented herein combines the coupled integral equations to form a single equation. This equation is easily interpreted as the magnetic field integral equation (MFIE) for a 2D, PEC surface with a perturbative term related to the finite conductivity of the surface. The advantage of this perturbation approach is that for ocean and other high loss surfaces, the solution is expected to be rapidly convergent with respect to other approaches and will reproduce the correct result even for surfaces with small curvature radii. Test cases demonstrate increased convergence with increased loss and increased contrast for perpendicular polarization. However with parallel polarization, convergence problems are uncovered and are associated with the Brewster angle effect.