Novel symmetric hierarchical mixed finite element analysis for nanophotonic devices

A Novel symmetric mixed finite element is introduced for the accurate modal analysis of optical waveguides and photonic devices. In addition to the advantages of conventional curl conforming mixed finite elements, the proposed element is symmetric and hierarchical. Symmetry ensures that the solution accuracy is not dependent on the shape functions chosen. On the other hand, hierarchy property allows p-adaptation that enables the use of elements with different orders in the same mesh which makes it very efficient. The numerical results show the effectiveness of the proposed element in modelling optical waveguides and other important photonic structures such as silicon nanowires and hybrid dielectric plasmonic waveguides.