Overview on finite-element time-domain approaches for optical propagation analysis

Several finite-element based time-domain approaches for the analysis of photonic devices are discussed in details. Narrowband and different kinds of wideband formulations are derived highlighting strengths and weaknesses related to the initial analytical equation and to the numerical implementation through the finite element method. A formulation which directly implements the unknown field without separating the envelope and the fast varying carrier is also presented. Performances and limits of the various algorithms are discussed by analyzing the simple and clear case of time and space evolution of gaussian beams propagating in a homogeneous medium. Comparison of the modules and arguments of the spectral response is also provided