Circuit theory of metal-enhanced fluorescence

Metal-enhanced fluorescence (MEF) comprises several linear phenomena which can be successfully described either by a classical theory or by a quantum one. Usually different phenomena are described by different classical models. Recently, an analytical model for a metal nanoantenna coupled to a quantum emitter was suggested that grants an approximate solution covering all basic linear phenomena observed in MEF from the Purcell effect to the fluorescent quenching. In this paper, the further development of this model is presented in terms of the equivalent circuits. The circuit model allows us to express the non-radiative Purcell factor of a nanoantenna through the previously evaluated radiative Purcell factor, to find the threshold of the fluorescence quenching and to determine the conditions when a fluorescent nanostructure transforms into a surface-plasmon laser (spaser).