The Mixed Finite-Element Method With Mass Lumping for Computing Optical Waveguide Modes

A new mixed finite-element method is proposed for computing the anisotropic, lossy, and open waveguide modes. By incorporating Gauss' law into the vectorial wave equation, the variational formulation 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 to expand the longitudinal component. A smaller scale generalized eigenvalue problem is obtained by employing the mass lumping technique. Numerical examples verify that the mixed finite-element method with mass lumping is free of any spurious eigenmode and has high efficiency.