Purcell factor for a point-like dipolar emitter coupled to a two-dimensional plasmonic waveguide

We theoretically investigate the spontaneous emission of a point-like dipolar emitter located near a two-dimensional plasmonic waveguide of arbitrary form. We invoke an explicit link with the density of modes of the waveguide describing the electromagnetic channels into which the emitter can couple. We obtain a closed form expression for the coupling to propagative plasmon, extending thus the Purcell factor to plasmonic configurations. Radiative and nonradiative contributions to the spontaneous emission are also discussed in detail.