Terahertz Plasmon Resonances in Two-Dimensional Electron Systems: Modeling Approaches

Known approaches to modeling terahertz plasmons in two-dimensional electron systems may differ significantly in their assumptions. There has, however, been little effort to analyze the differences between and application of different models to the same sets of structures. This paper discusses, develops, and compares several different theoretical approaches—namely, an effective-medium approximation, a transmission-line model, modal analysis, and full-wave simulations. In particular, we present a transmission-line model that takes into account the dielectric-air surrounding a two-dimensional system. Using modal analysis, we also solve analytically the problem of plasmon reflection and transmission when plasmons are incident on a junction between gated and ungated two-dimensional waveguides. Comparing the predictions made by the models for several structures, we find good agreement between full-wave simulations and both analytical and numerical modal analysis. The results of the effective-medium approximation and the transmission-line model also agree with each other, but differ quantitatively from those of the full-wave simulations and modal analysis. We attribute the differences to the phases of the plasmon reflection and transmission coefficients obtained with the different approaches. Our analytical expressions for the plasmon transmission and reflection coefficients represent a simple, yet accurate way to model plasmons in two-dimensional systems comprising both gated and ungated sections.