Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing

conductivity profile r(x) by finding the electrostatic charge distribution q(x) on the graphene sheet from Laplace’s equation, leading to the chemical potential lcðxÞ and the conductivity via the Kubo formula. It was shown that the ridged structure does indeed allow for the formation of a channel in the vicinity of the ridge for SPP propagation using a single bias, but that the resulting boundary has, as expected, a softened profile (i.e., a soft boundary (SB)) wherein the conductivity is not constant. The work 27 was concerned with the properties of the soft boundary and resulting channel, and the current distribution of the fundamental SPP mode. In this work we consider the various other modes that can propagate along the SB channel, including higher-order modes and edge modes. In particular, we show that unlike the HB case, for a soft boundary the higher-order modes have no apparent low-frequency/long-wavelength cutoff, although as frequency is lowered modal energy tends to spread out laterally along the effectively wider channel. We also show that lowloss edge modes can propagate for which the location where energy is concentrated can be controlled electronically. We then consider two applications of the structure, as a plasmonic voltage-controlled switch and a frequency demultiplexer. Fig. 2 shows the conductivity profile r(x) of the graphene sheet for a representative set of geometrical and FIG. 1. Graphene sheet gated with a ridged, perfect electrically-conducting (PEC) ground plane for the electrostatic bias, forming a soft-boundary graphene nanoribbon. The red area depicts the SPP channel having Im rðxÞ 0 and SPP propagation is prohibited.