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An infinite sheet of graphene lying above a perturbed ground plane isstudied. The perturbation is a two dimensional ridge, and a bias voltage isapplied between the graphene and the ground plane, resulting in a graphenenanoribbonlike structure with a soft-boundary (SB) The spatial distribution ofthe graphene conductivity forming the soft-boundary is studied as a function ofthe ridge parameters and the bias voltage. The current distribution of thefundamental TM surface plasmon polariton (SPP) is considered. The effect of theridge parameters and shape of the soft boundary on the current distributionsare investigated, and the conditions are studied under which the mode remainsconfined to the vicinity of the ridge region.

Soft-boundary graphene nanoribbon formed by a graphene sheet above a perturbed ground plane: conductivity profile and SPP modal current distribution