Electric and magnetic field dyadic Green´s functions and depolarizing dyad for a magnetic current immersed in a uniaxial dielectric-filled parallel plate waveguide

The dyadic Green´s functions and depolarizing dyad for the electric and magnetic fields due to a magnetic current immersed in a uniaxial dielectric-filled parallel plate waveguide with perfect electric conducting (PEC) boundaries are developed here. The Green´s functions are derived directly from Maxwell´s equations using the superposition of a particular (i.e., principal) and complementary (i.e., reflected) solution based upon a spectral domain analysis. It is shown that the magnetic current maintains both ordinary and extraordinary waves which are TE^z and TM^z, respectively, and that these field sets do not couple at the parallel-plate PEC boundaries. The physical meaning of the various terms in the Green´s functions is provided as well as a simple formulation for computing the magnetic field Green´s function from the electric field Green´s function. A simple approach for computing the depolarizing dyad term due to the source point singularity in the principal magnetic field representation is presented and consequently leads to a Green´s function expression that is valid both externally and internally to the source region. Applications which motivate the need for these Green´s functions, such as the measurement of hexagonal honeycomb core composites and uniaxial crystals, are also discussed.