Spontaneous decay rate of an excited molecule placed near a circular aperture in a metal film

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.