Exact Image Theory for the Sommerfeld Half-Space Problem with a Vertical Magnetic Dipole

摘要

Applying the Laplace transform, the exact distributed image current function is obtained for the Sommerfeld half-space problem with vertical magnetic current source. The resulting field integral is well behaved when the image current is situated in complex space. The theory is valid for any distance, source height frequency and half-space parameters. It is demonstrated that the theory reduces to the dipole image at complex depth for large dielectric parameters of the half space. The reflection-coefficient method is obtained as a far field approximation. Calculation of fields through exact image integration is seen to reduce computer time compared to the original Sommerfeld integration. The multivalued Green's function arising from a dipole source in complex space is also studied.