Diffraction of an electromagnetic plane wave by a funnel-shaped screen

The field on the axis behind a funnel-shaped screen with a circular aperture, on which a plane electromagnetic wave is incident along the axis, is computed by means of an approximate method proposed previously by the author for the case of short wavelengths. The deviation from plane-screen diffraction and the dependence on the angle
\phi_{0}
defining the shape of the funnel is given for both concave-side and convex-side incidence. Simple closed form results are obtained.