High-frequency diffraction of plane waves by an infinite slit for grazing incidence

The scattering of plane electromagnetic waves of wave number
k
by an infinite slit of width
2a
formed by two perfectly conducting coplanar screens of zero thickness is considered. In the limit of large
ka
and at grazing incidence, the asymptotic series for the transmission cross section per unit length of the slit is evaluated up to the order
(ka)^{-11 i 2}
.