Scattering of Surface Plasmon Polaritons at Abrupt Surface Discontinuities: Implications for Nano-Scale Cavities

We have developed a rigorous mode matching approach for the exact semi-analytical analysis of surface plasmon propagation across non-uniform semi-infinite dielectric-metal interfaces. We address two key deficiencies of related approaches in the literature: firstly, we resolve issues of accuracy and convergence and secondly, while we focus on the analysis of two-dimensional problems, we present a framework for three-dimensional problems for the first time. Analytical derivations of coupling coefficients between guided and radiation modes allow an efficient scattering matrix formulation to describe general structures with multiple discontinuities. Studies of the reflection, transmission and radiation of surface plasmons incident on both dielectric and metallic surface discontinuities show a correspondence with an effective Fresnel description. We also model a surface plasmon Distributed Bragg Reflector (DBR) capable of reflecting between 80% and 90% of incident surface plasmon power. Radiation mode scattering ultimately limits the DBR’s reflection performance rather than the intrinsic absorption of the metal. Thus alternative plasmonic geometries that suppress radiation modes, such as gap and channel structures, could be superior for the design of strongly reflective DBRs for integration in high Q-factor nano-scale cavities. We anticipate that this method will be an invaluable tool for the efficient and intuitive design of plasmonic devices based on structural non-uniformities