Azimuthal dispersion and energy mode condensation of grating-coupled surface plasmon polaritons

The excitation conditions for surface plasmon polaritons (SPPs) on a silver-gold bilayer coated sinusoidal grating can be varied over a wide range by tuning the azimuthal grating orientation (alpha). Grating coupling induces rotation of the SPP wave vector which, for specific conditions, can be directed perpendicular to the exciting light direction. Certain alpha orientations allow the excitation of two SPPs with the same frequency but different propagation directions. Other azimuthal orientations allow excitation of many SPP modes characterized by propagation over a large angular range. The kinematics of SPP propagation can be described by a model based on the wave-vector conservation law. Using this model, SPP dispersion relation, propagation direction, and mode density have been computed and shown to be in agreement with experimental measurements. The wave-vector dispersion is characterized by an energy threshold for the SPP excitation that increases as alpha increases. The angular spread is accompanied by an energy condensation of the SPP modes in correspondence to the energy threshold.