A direct spatial-domain representation for the fields excited by an arbitrary incident field at a planar dielectric interface

A new expression is constructed for scattering from a planar dielectric interface. This expression provides the exact boundary fields excited by all arbitrary incident field on a flat surface without requiring operator inversion or spectral decomposition of the incident field. While analytically exact, the simulation results can be affected by numerical and discretization errors when the operators are not handled properly. Particular attention must be paid to operator products and discretization. Extension of this result to smooth closed bodies is addressed in a separate presentation.