Asymptotic theory for dipole radiation in the presence of a lossy slab lying on a conducting half-space

The basic theory for dipole radiation in the presence of a two-layer half-space is outlined with special reference to its use as a model for studying radio propagation through and over heavily vegetated terrain. The source dipole may be located above or below the top surface of the slab. The dipole orientation is either vertical or horizontal. The asymptotic derivations for the field expressions are carried out without making the usual assumption that the refractive index of the uppermost layer is large compared with unity. The final results exhibit the expected inverse square dependence of the field on horizontal range.