A closed form, high-frequency solution is presented for the field radiated by an electric dipole located upon a rectangular, ground- ed dielectric slab. This solution, which is based on a physical optics formulation, is given in terms of the geometrical optics field plus ray-diffracted field contributions from the four edges. These ray-diffracted fields are decomposed into space waves, surface waves and leaky waves contributions. By superimposing the effects of elementary dipoles, the radiation of a current distribution is obtained, that simulates the effects of a patch radiating on a finite grounded substrate. Also, a closed-form solution is derived in the case when the current distribution exhibits an analytical expression of its Fourier transform. Comparisons with measurements are presented to validate the asymptotic solution.