Static Surface Mode Expansion for the Electromagnetic Scattering From Penetrable Objects

We introduce longitudinal and transverse static surface modes and use them to solve the scattering problem from penetrable objects with arbitrary shapes. The longitudinal static modes are the eigenmodes, with zero surface-curl, of the electrostatic integral operator that determines the tangential component of the electric field, as a function of the surface charge density. The transverse static modes are the eigenmodes, with zero surface-divergence, of the magnetostatic integral operator that determines the tangential component of the vector potential, as a function of the surface current density. These static modes are solely determined by the object's shape, thus, the same static basis can be used regardless of the operating frequency or material properties. We expand the unknown surface currents of the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation in terms of the static modes and solve it using Galerkin-projections. The static modes expansion allows for the regularization of the integral operators and also leads to a significant reduction in the number of unknowns compared to a discretization based on sub-domain basis functions. As a consequence, the CPU-time required for the numerical solution of the scattering problem from arrays of identical particles is significantly reduced by employing an expansion in terms of static modes of the isolated particle.