Propagation of surface plasmon modes through discontinuities

Based on the electromagnetic equations, we have reinvestigated the propagation of a surface plasmon mode on a metal-dielectric interface with a discontinuity. Our rigorous study of the boundary conditions illustrates a mismatch between the normal components of the wavevectors of the fundamental plasmon modes, which results in the excitation of higher order modes. Furthermore, analytical relations based on the plane wave expansion method reveal the existence of radiation modes above the surface and at the vicinity of discontinuity. If these modes are not included, the boundary conditions are not satisfied. This phenomenon, which has not been considered in previous works, is also demonstrated by numerical simulations.