A hybrid (parabolic equation)-(Gaussian beam) algorithm for wave propagation through large inhomogeneous regions

The wide-angle split-step parabolic equation (PE) algorithm is used to model electromagnetic wave propagation over general inhomogeneous terrain up to a height h. The PE-computed fields at h are then projected onto a complete Gabor basis from which we effect Gaussian beam propagation at altitudes greater than h. The Gaussian beams can be propagated through general inhomogeneous media, devoid of failures at caustics and shadow boundaries (as befalls ray tracing). The accuracy of the Gaussian beam algorithm is demonstrated via two realistic examples: (1) low-frequency (HF) ionospheric propagation with application to over-the-horizon radar and (2) near-grazing high-frequency propagation for communication or surveillance applications. In the context of these examples, we discuss relevant numerical issues associated with the hybrid algorithm from which general advantages and disadvantages are addressed