Symmetrical Properties of Dyadic Green´s Functions for Mixed Boundary Conditions and Integral Representations of the Electric Fields for Problems Involving a PEMC

Perfect electromagnetic conductor (PEMC) is a recently introduced fundamental medium in which certain linear combinations of electromagnetic fields are required to vanish. Since electric and magnetic dyadic Green´s functions are required to satisfy dyadic mixed boundary conditions on PEMC surface, it is necessary to develop a new classification of electric and magnetic dyadic Green´s functions based on a parameter M of a PEMC boundary. This classification, while including dyadic Dirichlet and Neumann boundary conditions, should be general as well. In this paper, a new classification of dyadic Green´s functions is introduced and symmetrical properties of these functions are presented. Furthermore, integral representations of electric fields in problems of two isotropic media involving a PEMC are derived. Finally, using symmetrical properties of the dyadic Green´s functions, the expressions for electric fields are proposed in an appropriate integral form in terms of volume currents and electric and magnetic fields on apertures.