Pseudodecoupling ansatz for electromagnetic aperture coupling in three dimensions

Hertzian potentials are commonly used to describe the scattering of electromagnetic waves in three dimensions. However, when apertures are present in the scattering object, mixed boundary conditions arise and the TE and TM modes of the scattered field become coupled. Numerous attempts to decouple these TE and TM modes have led to solutions of Maxwell's equations which fail to satisfy Meixner's edge conditions. It has been found that by introducing additional gauge potentials which are homogeneous solutions of the boundary condition equations, a pseudodecoupling of the TE and TM modes can be achieved while still satisfying Meixner's edge conditions.