The efficient mixed FEM with ITBC for computing graphene plasmonic waveguide modes

Abstract

The optical waveguide structures, such as, photonic crystal fibers, plasmonic, and hybrid plasmonic waveguides, gain their extensive applications in communication, signal processing, integrated optics, and biophotonics. Advanced numerical methods with high efficiency and accuracy are required to determine propagation modes and to optimize geometrical and material parameters. An efficient mixed finite element method (FEM) with mass-lumping technique and impedance transmission boundary condition (ITBC) is proposed for computing the optical waveguide modes. By incorporating the Gauss' law into the vectorial wave equation, the new weak form is completely free of spurious modes. It utilizes the curl-conforming linear tangential and quadratic normal (LT/QN) edge elements to expand the tangential component of the electric field, and the modified nodal-based scalar basis functions which can get the diagonal mass matrix are used to expand the longitudinal component. Furthermore, to avoid the very fine spatial discretization of thin lossy sheet, ITBC have been employed for the new mixed FEM formulations. Numerical examples can verify that the mixed FEM with mass-lumping and ITBC techniques is free of any spurious eigenmodes and has high efficiency. The new contributions of this work include: (a) the mixed FEM with mass lumping is proposed for the first time to remove all spurious modes, and the diagonal mass matrix and the smaller eigenvalue equation speed up the computation. (b) The ITBC is first implemented in the new FEM formulation. Finally, numerical results on the graphene plasmonic waveguide and hybrid plasmonic waveguide clearly demonstrate that the proposed mixed FEM with mass lumping and ITBC technique is an efficient alternative method to determine the optical waveguide modes.