Alternative Finite Element Eigenvalue Formulations for the Simulation of Arbitrarily Bianisotropic Media

We derive two alternative formulations for the implementation of arbitrarily bianisotropic materials for the finite element analysis of eigenmode problems. The e-formulation solves for the Bloch–Floquet periodic envelope of the electric field, and the e–b formulation computes the periodic envelopes of the electric field and magnetic induction. Implementation is carried out in in-house codes and in the Weak Form Module of COMSOL Multiphysics, exhibiting identical results. Extracted dispersion diagrams are compared to the existing solutions in the literature showing perfect agreement. Convergence rates between the proposed formulations are illustrated, with the scaled version of e–b formulation exhibiting faster convergence, due to its linear matrix system and its well-conditioned matrices.