Modal Analysis of 2-D Material-based Plasmonic Waveguides by Mixed Spectral Element Method with Equivalent Boundary Condition

Recently, atomically thin two-dimensional (2-D) materials have attracted significant attention due to their promising applications in optoelectronic devices. Among them, surface plasmon-polaritons (SPPs) stimulated by 2-D material-based waveguide provide a new mechanism to propagate and enhance lightwaves in the deep subwavelength. However, the modeling and simulation of the 2-D material-based structures are still a challenge due to the mismatch between their electrically small in thickness and electrically large in transversal cross-section. In order to obtain a high-efficiency modal analysis of 2-D material-based plasmonic waveguides, the mixed spectral element method (mixed-SEM) with surface current boundary condition (SCBC) is proposed in this paper. The new method introduces a variational formulation that combines the transversal vectorial Helmholtz equation with the Gauss’ law, and a SCBC that is implemented as the equivalent boundary condition to eliminate 2-D nanoscale thin sheets from the computational domain. It thus avoids an enormous number of unknowns and significantly reduces the computational costs. To verify the proposed method, some typical 2-D material-based plasmonic waveguides including those composed of anisotropic black phosphorus are analyzed and numerical results are compared in various ways. Excellent agreements are obtained for all the cases which clearly suggest that the proposed method can efficiently and accurately simulate 2-D materials-based plasmonic waveguides.