Image Theory for Dipole Excitation of Fields above and below a Wire Grid with Square Cells

The exact imnage theory, recently introduced by two of the present authors 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 small compared to the wavelength and the wire diameter small compared to the mesh size, whence the Kontorovich averaged boundary condition concept is applicable. The image current consists of two exponential-line-current waves located in complex space. The theory is seen to produce simple asymptotic expressions for the field close to the grid surface. Also, an integral expression for the calculation of the change in the vertical-electric-dipole impedance due to the grid is constructed.