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

Abstract

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 $(\ensuremath{\alpha})$. Grating coupling induces rotation of the SPP wave vector which, for specific conditions, can be directed perpendicular to the exciting light direction. Certain $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ increases. The angular spread is accompanied by an energy condensation of the SPP modes in correspondence to the energy threshold.