Purcell factor for point-like dipolar emitter coupling to 2D-plasmonic waveguides

We theoretically investigate the spontaneous emission of a point--like dipolar emitter located near a two--dimensional (2D) plasmonic waveguide of arbitrary form. We invoke an explicite 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 non-radiative contributions to the spontaneous emission are also discussed in details.