Junctions between two-dimensional plasmonic waveguides in the presence of retardation

Abstract

Plasmons in two-dimensional (2D) 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 2D waveguide and a perfectly conducting sheet. As a result, retardation is expected to degrade the quality factors of plasmonic resonators without affecting their eigenfrequencies.