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 me 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 scaler formulations in order to check their performances, point out weaknesses, and suggest future developments. The results obtained highlight once more the inadequacy of scaler approaches in dealing with actual photonics devices and suggest vector formulations worthy of further development and future research. (C) 2000 Optical Society of America [S0740-3232(00)01206-0].