Study of surface plasmon polariton interaction with 2D discontinuities: Reflection and transmission

Surface plasmon polaritons (SPPs) have been studied extensively in the past decades by virtue of their implications in nanotechnology, communications, and life sciences. Their ability to localize light beyond the limit of diffraction has given rise to different types of nano-optical devices, such as plasmonic waveguides and nano-antennas. In the analysis and design of discontinuities that may inevitably persist on such structures, complex computational tools such as full-scale electromagnetic solvers are mostly used. In order to provide a simpler design route, approximate yet efficient models, akin to the ones developed for microwave circuits in the 20th century, are needed. In this work, SPP behavior at canonical 2D discontinuities have been characterized by approximate and semi-analytical models, from which the reflection and transmission coefficients were derived. The first part of this thesis focuses on two possible simplified terminations of a 2D metallic half-space: i) dielectric and ii) metallic half-plane discontinuities. Following a review of electromagnetic theory behind plasmonics, SPP reflection coefficients from these terminations were derived through effective medium and mode-matching techniques. The validity and limits of these models were comparatively assessed through results obtained from finite-difference time-domain (FDTD) simulations in conjunction with the mode expansion method. The characteristic behavior of these terminations was associated with those of their counterparts in microwave transmission lines. The second part of this thesis involves the analysis of more complex geometries, including step and gap discontinuities, via approximate models and numerical results. The reflection and transmission coefficients of these discontinuities were contextualized within a microwave network formalism, which yielded intuitive results on the resonant behavior of SPPs at discontinuities with small dimensions.