Path integral analysis of paraxial radiowave propagation over a nonlevel plateau

The attenuation function, normalised with respect to the free space field, for waves propagating over a perfectly conducting, nonlevel plateau situated on a perfectly conducting ground plane, is derived. The general case of having a raised transmitter and receiver is considered. A high frequency path integral formulation is employed to obtain an approximate propagator for a sloping ground plane geometry. The plateau propagator is derived by using the above result as an elementary building block and is given by a sum of general surface Fresnel integrals. The paper also includes the solution to the problems of propagation over two perfectly absorbing half planes, and propagation over a sloping roof plateau situated on a perfectly absorbing ground plane as special cases. Numerical results show that the result contains the solution obtained by the compensation theorem for a flat-roof plateau, when both the source and the observation points are set at ground level. The validity of the solution is also confirmed by laboratory experiments