The PE solution of natural waveguides in atmosphere: ducts and elevated ducts

The propagation phenomena through 2D surface duct-to-elevated duct transition is described in terms of parabolic equation (PE) method. The split step marching solution of the PE method is first compared with the reference solutions obtained from Helmholtz wave equation in longitudinally invariant surface duct problem and the excellent agreement between the results is presented. Then the PE method is applied to propagation through surface duct-to-elevated duct transition problem which is non-separable in any of the known orthogonal coordinate system. The transformation of the surface trapped modes into propagating elevated beams is shown with the PE method.