Self-consistent modelling of VCSELs with non-cylindrical geometry

Summary form only given. VCSELs have a circular beam cross-section and a very short cavity length (a single longitudinal mode is supported). Unlike the edge emitting lasers there is no definite gain or loss (waveguiding) preference for a certain polarization direction. Some amount of polarization stabilization in VCSELs was experimentally achieved by breaking the transverse symmetry of the VCSEL. Rectangular air-post structures, asymmetric oxide apertures and an elliptic hole in the bottom entitling lasers have been suggested. To the best of our knowledge no suitable model has been developed to predict and assess the polarization stabilisation in such VCSELs. The reason is that a 3D problem has to be solved. We present a self-consistent model for the carrier-diffusion and the optical field distribution in non-circular cross-section VCSELs. We apply the FDTD method, already successfully used for VCSELs with circular geometry. In order to allow the integration in Cartesian coordinates we apply the alternating directions implicit method to both the carrier diffusion equation and wave equation. The optical problem is treated using the semi-vectorial approach developed for optical waveguides, after reducing the 3D VCSEL cavity to a 2D layer with the effective index method.