Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures

It has been difficult to compute the band structures for photonic crystals with metallic components included in the periodic units. The existence of modes of surface plasmon polariton presents the major difficulty not only because of the localized nature of the modes but also of the apparent necessity of handling a nonlinear eigenvalue problem. Here we show that by introducing an interfacial operator within the finite-difference framework, we are able to formulate the problem for computing modes of surface plasmon polariton in the format of standard eigenvalue problems. Results are uncovered by applying the method to periodic structures with corrugated interfaces between metals and dielectric materials, as well as other classes of interfaces.