Abstract
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.
Highlights
Plasmons in two-dimensional electron systems (2DESs) hold promise for a number of terahertz devices, notably emitters [1,2,3,4,5] and detectors [6,7,8,9]
The resulting integral equation is solved numerically. Another approach, used to study plasmon reflection and transmission at waveguide junctions, is modal analysis, in which the electromagnetic fields at both sides of a junction are expanded into the waveguide eigenmodes [5,16,22,31,32,33,34]
Modal analysis originated in the theory of closed metallic waveguides, and was adopted to open waveguides [40], including three-dimensional plasmonic ones [41]
Summary
Plasmons in two-dimensional electron systems (2DESs) hold promise for a number of terahertz devices, notably emitters [1,2,3,4,5] and detectors [6,7,8,9]. Conditions at the junctions of gated and ungated 2DESs include the ballistic current condition [23] and continuity of the potential [24] These single-point boundary conditions may be combined with the conditions for the whole junction; an example is the continuity of the plasmon power flow [24]. The resulting integral equation is solved numerically Another approach, used to study plasmon reflection and transmission at waveguide junctions, is modal analysis, in which the electromagnetic fields at both sides of a junction are expanded into the waveguide eigenmodes [5,16,22,31,32,33,34].
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