Electric and magnetic dyadic Green's functions of bounded regions

The eigenvector-expansion method is applied to obtain the electromagnetic fields in a closed region of space in terms of volume integrals over the sources and surface integral of the tangential electric field over the boundary. The field expressions are written in a convenient dyadic form, and thus the appropriate electric and magnetic dyadic Green's functions in an infinite triple-series form are extracted. Finally, the general formulas for the Green's dyadics are specialized for the case of a circular cylindrical cavity for which the series is reduced to a double summation. This reduction reveals the discontinuous nature of the fields in the source region.