Abstract
An asymptotic theory is developed for the electromagnetic field near a smooth convex, impedance or perfectly-conducting, surface in the shadow region of an incident ray-optical wave. The theory is based on Fock's postulates and represents an extension of his method of parabolic equations from penumbra to shadow. The new results include the cross-polarization effect for a torsional surface ray on an impedance surface and an adiabatic creeping mode solution for a ray with varying curvature on such a surface.
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