High-frequency propagation in elevated tropospheric ducts

An analytical method combining a mixture of ray-optical fields and normal mode fields guided along the concave side of the duct boundary or between the duct boundary and the Earth's surface is described. The duct is modeled by two circular cylindrical boundaries representing, respectively, the Earth's surface and the interface separating the duct region (high refractive index) from the exterior. Excitation is from an electric current line source with time harmonic variation. After deriving the Green's function for the duct environment in an integral form, three different representations are obtained for the field; one involving only normal modes, one involving only geometric-optical rays and the hybrid ray-mode representation that includes rays, modes, and some remainder integrals that are shown to be negligible in most cases. Field values are then computed. The number of rays and modes included in the hybrid solution is determined.