Three-dimensional finite-element beam propagation method: Assessments and developments

In recent years the finite-element method (FEM) has been widely applied to three-dimensional beam propagation analysis, and several FEM propagators have been presented. Up to now, as far as we know, an exhaustive, deep, and comparative analysis of these formulations and of the related algorithms has never been presented. We critically analyze and numerically compare, to our knowledge for the first time, different vectorial, semivectorial, and scalar formulations in order to check their performances, point out weaknesses, and suggest future developments. The results obtained highlight once more the inadequacy of scalar approaches in dealing with actual photonics devices and suggest vector formulations worthy of further development and future research.