An Efficient Numerical Method For Model Analysis Of 2-D Nanomaterial-based Plasmonic Waveguides

The development of micro-nano technology and integrated circuit technology has continued to reduce the physical size of components,circuits,and devices,which have reached their limits.In this context,photonic communication is considered as a new method of information transmission and surface plasmon-polaritons(SPPs)in 2-D nanomaterial provides a new mechanism to propagate and enhance light-waves in the deep subwavelength,which promotes the research and development of new optical materials.However,the modeling and simulation of the 2-D nanomaterial-based structures are still a challenge due to the mismatch between their electrically small in thickness and electrically large in transversal cross-section.To obtain a high-efficiency modal analysis of 2-D nanomaterial-based plasmonic waveguides,the mixed spectral element method(mixed-SEM)with surface current boundary condition(SCBC)is proposed in this paper.The mixed-SEM introduces a new variational formulation that combines the transversal vectorial Helmholtz equation with the Gauss' law.GaussLobatto-Legendre(GLL)polynomials establish the vector curl-conforming basis functions to approximate the tangential vector of the electric field.GLL completely continuous nodal basis functions approximate the longitudinal electric field.The mixed spectral element method used to maintain the unique spectral accuracy of the spectral method thus results in spectral convergence of numerical consequence and can eliminate the pseudo-physical modes in the generalized eigenvalue problem.The surface current boundary 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 computational costs.To verify the proposed method,we analyzed some typical 2-D nanomaterials(graphene and black phosphorus)plasmonic waveguides and optical devices and compared them with the traditional method and analytical solutions.Excellent agreements are obtained for all the cases which suggest that the proposed method can efficiently and accurately simulate 2-D materials-based plasmonic waveguides.