Modified WKB methods for the propogation and scattering of electromagnetic waves

A new formulation of scattering and propagation problems has been developed using Green´s functions with essentially correct local behavior. This formulation, which is exact, yields the familiar WKB result as its zeroth approximation. Higher order corrections depend on the spatial variation of the local index of refraction. The convergence is rapid if these variations are gradual. By way of illustration, the method has been applied to the propagation of electromagnetic waves in an isotropic stratified medium and to the scattering of waves by an inhomogeneity. In the former case, the problem of total reflection, as by the ionosphere, has been studied and corrections to the usual WKB phase shift have been obtained. These corrections arise as a consequence of deviations of the effective dielectric constant from linearity in the neighborhood of the turning point, and also because of the slow approach of the height-gain function to its asymptotic value far from the turning point. In the latter example, approximate expressions are obtained for both the scattering amplitude and the close-in electric field which are valid when the index of refraction of the scattering center is close to unity. Polarization effects are examined explicitly.