Plasmons in two-dimensional waveguides are traditionally analysed within the electrostatic approximation, which assumes that the plasmon phase velocity is much smaller than the velocity of light. However, novel effects have recently been demonstrated for plasmons whose velocity is comparable to the velocity of light. In this retardation regime, electrostatic models are inaccurate. For a junction between two plasmonic waveguides, we present an analytical and a numerical model both valid in the retardation regime and compare them to an electrostatic model. We quantify the reflected and transmitted powers and the radiation loss in several scenarios. We found that power is radiated from a junction at the expense of the power of the reflected plasmon, but retardation has little effect on the phases of the reflected and transmitted plasmons. The radiation loss is typically below several percent when the plasmon velocities are five or more times below the light velocity. However, radiation still persists for slower plasmon velocities for a junction between a twodimensional waveguide and a perfectly conducting sheet. As a result, retardation is expected to degrade the quality factors of plasmonic resonators without affecting their eigenfrequencies.
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 transmissionline 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.
Using two rigorous electromagnetic approaches, we study plasmon scattering in twodimensional systems and show that plasmon amplification is possible in the presence of dc currents. Two scenarios are considered: plasmon scattering from an interface between different two-dimensional channels and plasmon reflection from electric contacts of arbitrary thickness. In each case, the effect of a dc current of the plasmon reflection and transmission coefficients, and the plasmon power are both quantified. A resonant system is studied where plasmon roundtrip gain may exceed unity, showing the possibility of plasmon generation.
Abstract-Plasmons in two-dimensional systems find applications in terahertz oscillators, detectors, filters, plasmonic crystals, etc. Numerous approaches to modeling plasmonic spectra exists, but little work has been done to compare results from theoretical calculations with each other, and so to understand their limitations. Using three different techniques (full-wave simulations, mode matching, and trasmission-line model), we analyse here a realistic structure comprising three coupled plasmonic resonators. While the results of all three models offer qualitatively similar results, revealing a rich spectrum of coupled modes, the values of the predicted resonant frequencies differ between the models. The best agreement is found between fullwave simulations and mode matching, both of which are based on rigorous solution of Maxwell's equations.
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