Investigation of Purcell Factor for an Activator Ion due to Surface Plasmon Modes

We considered earlier the role of the surface plasmon states in the spontaneous decay of an optically active ion in proximity to a flat, metallic surface.1 In this work we have extended our earlier results to obtain an expression for the density of plasmon states accessible to the ion. We express the spontaneous decay rate of the ion into the surface plasmon field in terms of the density of final states and the appropriate "Einstein" B-coefficient, which depends on the matrix elements of the ion-surface plasmon interaction. Next we derive an expression for the contribution of the surface plasmons to the total radiative decay rate, and determine the Purcell factor of this system. Finally, calculations are presented showing how the Purcell factor for an optically active ion near a silver surface depends on the wavelength of the transition and distance of the ion from the surface.