We derive an integral equation describing surface-plasmon polaritons in graphene deposited on a substrate with a planar surface and a dielectric protrusion in the opposite surface of the dielectric slab. We show that the problem is mathematically equivalent to the solution of a Fredholm equation, which we solve exactly. In addition, we show that the dispersion relation of the channel surface plasmons is determined by the geometric parameters of the protrusion alone. We also show that such a system supports both even and odd modes. We give the electrostatic potential and the intensity plot of the electrostatic field, which clearly show the transverse localized nature of the surface plasmons in a continuous and flat graphene sheet.
Bibliographical noteFunding Information:
A.J.C. acknowledges a scholarship from the Brazilian agency CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico). N.M.R.P. acknowledges the European Commission through the project Graphene-Driven Revolutions in ICT and Beyond (Ref. No. 696656) and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2013. D.R.C. and G.A.F. acknowledge CNPq under the PRONEX/FUNCAP grants and the CAPES Foundation.
© 2018 American Physical Society.