Full-wave analysis of mixed-mode propagation in forest environment

The electromagnetic radiation of an electric dipole in a medium with four layers is examined using dyadic Green's functions in their vector wave eigenfunction expansion forms. In this four-layered model, two lossy dielectric layers are used to represent the canopy and trunks of vegetation that covers the ground plane. The dyadic Green's functions for four-layered media are first applied to derive the integral expression of the electric fields. Asymptotic evaluations of the integrals are then made using the steepest descent method, and the branch-cut integrations in complex planes; and correspondingly the direct wave, multi-reflected waves, and lateral waves along various interfaces have been obtained. Numerical calculations of the transmission losses in the presence of vegetation have been carried out for typical forest.