On the asymptotic frequency behavior of uniform GTD in the shadow region of a smooth convex surface

A number of canonical plane-wave and line-source solutions involving circular cylinders have led to a widely accepted uniform geometrical theory of diffraction (GTD) formulation for the scattered electromagnetic field in the shadow region of a smooth convex surface. The current solution does not constitute a properly formulated asymptotic high-frequency theory in the sense that it becomes increasingly inaccurate with increasing frequency. This inaccuracy results from transition-function dominance in the deep shadow region over the Pekeris caret function that is used. An improved formulation that circumvents this difficulty by avoiding use of a transition function is derived via a straightforward extension of the canonical line-source solution given by Jones (1963). This new solution takes the form of Keller-type modes with modified diffraction coefficients that result in convergence at the shadow boundary provided that the source and observation point are not both located at asymptotic distances from the scatterer.<
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