A comparison of mode-matching formulations for the analysis of high-contrast gratings

The recent renewed interest in diffraction gratings as mirrors for vertical-cavity surface-emitting lasers (VCSELs) stimulated the development of fast and accurate full-wave simulators. In fact, their modeling requires large sets of scattering analyses, which can be effectively carried out by means of mode-matching techniques. In this framework, a crucial point is the numerical synthesis of the grating modes, which should be performed trading-off the accuracy required by the scattering problem and the computational time necessary to compute the projection matrices. Two approaches applied to different problems, discussing which is the most convenient in each situation.