Decomposition of electromagnetic boundary conditions at planar interfaces with applications to TE and TM field solutions

Electromagnetic fields in homogeneous source-free regions can be decomposed into fields that are TE and TM with respect to a particular reference direction (e.g., the z direction). If transverse sources exist, both TE and TM fields may be excited simultaneously. This paper considers the case of two infinite regions having a common planar interface and prescribed sources (surface currents) on the interface. The source currents are decomposed in a manner consistent with the decomposition of the fields. Accordingly, a procedure is established for describing the boundary conditions at the interface in terms of the longitudinal field components E_z, H_z and the surface currents J¯_s. The development is unique in that the continuity of the transverse field components at the boundary are not explicitly considered but interpreted in terms of z-directed fields. This boundary condition approach is shown to give results consistent with those obtained by matching the tangential fields at the interface using vector transforms. A simple example illustrating the procedure using a ring of current in free-space is presented