Field of a short dipole above a dielectric half-space with rough interface

The accurate prediction of radiowave coverage at high frequency-ultra high frequency over irregular terrain features is of importance in the design and development of low-cost and low-power communication systems. This study studies the problem of electromagnetic wave propagation, excited by a short dipole, above a dielectric ground plane with an arbitrary dielectric profile and an irregular interface. This investigation is a natural extension of the classical Sommerfeld problem with the exception of the random surface irregularities at the interface between the two dielectric media. It is assumed that the interface profile height variations are small compared with the wavelength. First, the bistatic scattering of a plane wave illuminating the rough surface is solved using a perturbation solution of an integral equation for the induced polarisation current. Analytical expressions for the coherent field and incoherent scattered power at an arbitrary observation point are obtained. Then, the solutions for the coherent and incoherent scattered power generated by a small dipole of arbitrary orientation and position are derived by expanding the field of the dipole in terms of a continuous spectrum of plane waves and using superposition. The effects of the rough interface on the surface waves and on depolarisation are studied.