Finite-element waveguide solvers revisited

A general analysis of potential- or field-based finite element solvers for axially uniform electromagnetic waveguides is presented. Explicit equations for the set of permissible gauge transformations are derived, which are later utilized to identify side effects that may affect the reliability of present approaches. We show that such limitations can be eliminated by an enhanced formulation employing a decomposition of the transverse components of the vector potential together with a particular choice of gauge. Numerical results support our findings.