Image theory for a vertical electric dipole above a wire grid with square cells

An exact image theory for the Sommerfeld problem is applied to the problem of a vertical electric dipole above a plane metallic grid with rectangular cells. The mesh size is assumed to be small compared to the wavelength and the wire diameter small compared to the mesh size, so that the Kontorovich averaged boundary condition concept is applicable. The image current consists of two exponential current waves located in complex space. The theory is seen to produce a simple expression for the TM surface wave excited by a vertical electric dipole.