Cl. Rino et Hd. Ngo, FORWARD PROPAGATION IN A HALF-SPACE WITH AN IRREGULAR BOUNDARY, IEEE transactions on antennas and propagation, 45(9), 1997, pp. 1340-1347
The parabolic wave equation (PWE) has been used extensively for modeli
ng the propagation of narrow beams in weakly inhomogeneous random medi
a. Corrections have been developed to accommodate wider scattering ang
les and boundaries have been introduced. Nonetheless, the formalism re
mains approximate and irregular surfaces with general boundary conditi
ons present difficulties that have yet to be overcome. This paper pres
ents an alternative approach to the entire class of propagation proble
ms that strictly involve forward propagation, Forward-backward iterati
on has recently been shown to be a powerful procedure for computing th
e source functions that support propagation over irregular boundaries
at low grazing angles, In this paper, we show that the source function
s for any unidirectional sweep can be computed by using a marching sol
ution. This is not only more efficient than the single-sweep computati
on, but it facilitates accommodation of inhomogeneities in the propaga
tion media, An exact equation for forward propagation in unbounded inh
omogeneous media is used to derive a correction term that is applied a
t each forward-marching step. Results that combine ducting atmospheres
and rough-surface scattering effects are presented for both the Diric
hlet and Neumann boundary conditions.