Leaky and bound modes of surface plasmon waveguides

While theoretical studies of finite width plasmonic waveguides have focused on the bound modal solutions of metallic structures in homogeneous or near-homogeneous dielectric matrices, experimental studies have mainly probed the leaky surface plasmon modes along the air-exposed surfaces of metallic stripes on glass substrates. Combining a full-vectorial, magnetic field finite-difference method with complex coordinate stretching perfectly matched layer boundary conditions, we have solved for both the leaky and bound modes of metallic slab and stripe waveguides. Solutions for the leaky modes excited via attenuated total reflection in the Kretschmann configuration provide added insight into the results of recent near and far-field experimental studies. For these cases, an analytical approximation for the number of allowed modes as a function of waveguide width is derived based upon the guidance condition of dielectric waveguide theory. Then, consistent with a ray optics interpretation for surface plasmon-polariton propagation, a direct comparison is made between our simulations and published results with regard to field profiles and propagation lengths.