On a new condition for physical realizability of planar antennas

The behavior that all physically realizable aperture distributions (tangential electric field in an aperture consisting of holes in a perfectly conducting planar sheet) must have at their edges is shown to be as follows. The components perpendicular and parallel to the aperture edge must each vanish with distance
d
from the edge as
d^{\alpha}
, with
\alpha = 1
for the perpendicular component and
\alpha = 2
for the parallel component. An interesting consequence of this realizability condition is that the pedestal form of edge behavior usually assumed in aperture theory is physically impossible.