Diffraction by a circular aperture in a unidirectionally conducting screen

The diffraction of a normally incident plane electromagnetic wave with wave number
k
by a circular aperture of radius
a
in a unidirectionally conducting plane screen of zero thickness and infinite extent is considered. In the limit of large
ka
, the ratio of the transmission cross section to the geometrical optics value
\pi a^{2}
, is found up to the order
(ka)^{-3/2}
.