Extension of On-Surface Radiation Condition Theory to Scattering by Two-Dimensional Homogeneous Dielectric Objects

The recent new analytical formulation of electromagnetic wave scattering by perfectly conducting two-dimensional objects using the on-surface radiation boundary condition approach is conveniently extended to the case of twodimensional homogeneous convex dielectric objects. The existing classical solution for the scattering and penetration analysis of dielectric objects is based upon coupled field formulation with the external and internal fields directly coupled together through the electromagnetic surface boundary conditions. It is shown here that a substantial simplification in the analysis can be obtained by applying the out-going radiation boundary condition on the surface of the convex homogeneous dielectric object. This analysis procedure decouples the fields in the two regions to yield explicitly a differential equation relationship between the external incident field excitation and the corresponding field distribution in the interior of dielectric object. The interior fields can be obtained by solving the differential equation using either an analytical approach or a suitable numerical method. Two dimensional scattering examples along with validations are reported showing the near surface field distributions for a homogeneous circular dielectric cylinder and an elliptic dielectric cylinder each with transverse magnetic plane wave excitation. The resulting surface currents are compared with good agreement to those obtained from the integral equation solution.