Analysis of Graphene Plasmonic Waveguides via the Mixed Finite Element Method with Equivalent Boundary Condition

This paper presents the mixed finite element method with the surface current boundary condition (SCBC) for mode analysis of the graphene plasmonic waveguides. By considering the atom-like thickness of graphene layer as an infinitely thin conductive sheet with finite surface conductivity, the surface current boundary condition is obtained for efficient modeling and simulation. Besides, in order to suppress the zero spurious modes, the new weak formulation combines the Gauss' law with the Helmholtz equation and the second order curl-conforming vector LT/QN basis functions are employed to expand the transverse components of the electric field, and the nodal-based scalar basis functions are applied to discretize its longitudinal component. To verify the applicability and accuracy of the proposed algorithm, a graphene-on-gold plasmonic waveguide is thoroughly investigated.