  The non-resonant electromagnetic transmission of a normal-incident plane wave
through a single hole in a perfect conductor metal slab of finite width is
studied. The cases of rectangular and circular holes are treated in detail. For
holes in the extreme subwavelength regime, in a film of finite thickness, the
transmittance is shown to have the Rayleigh dependency upon the wavelength and,
in addition, is mainly suppressed due to attenuation of the fundamental
waveguide mode. In the limit of an infinitesimally thin screen Bethe's result
is recovered for the circular hole. The numerical computations are fitted,
providing expressions for the transmission in a wide region of parameters. We
reformulate our results in terms of multipole expansion, interpreting the
waveguide modes inside the hole as induced multipole moments. This result
provides the link between the modal expansion method and the one based on a
multipole expansion.
