Modeling of the polarization behavior of elliptical surface-relief VCSELs

We undertake a theoretical study of the polarization behavior and mode structure of Vertical-Cavity Surface-Emitting Lasers (VCSELS) with an elliptical surface relief. The aim of the relief is twofold, first to enhance the single mode operation by introducing spatially distributed losses, and second, to enhance polarization stability by making these losses anisotropic. First, we use an analytical variational approach, for the two fundamental VCSEL modes within a Gaussian and weak guidance approximation. As a second approach we use a more refined numerical technique based on vectorial plane wave decomposition with periodic boundary conditions, which we formulate to include material anisotropy. Our studies show that whereas the polarization direction is governed by the orientation of the index ellipsoid, the selection of the lasing LP mode is mainly determined by the anisotropy in the mirror losses introduced by the elliptical surface relief.