  We have investigated the spontaneous decay rate of an excited molecule placed
near a circular aperture in a metal film of finite thickness and finite
conductivity. We have considered the metal film both suspended freely in vacuum
and lying on a substrate. A significant effect of molecule the position and the
presence of the substrate on the rate of spontaneous emission of the molecule
is shown. The asymptotes which can be used to describe this process are found.
Total, radiative, and non-radiative spontaneous decay rates of the excited
molecule are extracted and compared. The results may be useful in the
development and interpretation of experiments investigating a single molecule
with a scanning optical microscope and in the design of optical nanodevices
based on the control of elementary quantum systems emission with a nanohole.
