A representation theorem based analysis of two-dimensional electromagnetic scattering from materials and resistive cards

Representation-theorem-based surface integral operators are presented and used to predict electromagnetic scattering from a material body with an embedded resistive card. The integral operators are obtained from a representation theorem for the 2-D Helmholtz equation in a region with constant electrical properties characterized by complex permittivity and permeability. A resistive card embedded in the region is introduced by enforcing a resistive boundary condition on the representation theorem integrals as the thickness of a geometrically thin region surrounding an embedded card approaches zero. Surface integral operators are obtained by letting the field point in the representation theorem equations approach material boundaries and resistive cards. Multiple regions with constant electrical properties (including perfect conductors) are allowed by enforcing boundary conditions between regions. Two polarizations of normally incident plane wave radiation are considered. Prediction and experiment are in good agreement for a resistive card embedded in a bulk material