Abstract

Vertical-Cavity Surface-Emitting Lasers (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 stabilisation 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 emitting 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 three dimensional (3D) problem has to be solved. In this paper we present a self-consistent model for the carrier diffusion and the optical field distribution in non-circular cross-section VCSELs. To this aim we apply the Finite Difference Time Domain (FDTD) method, already successfully used for VCSELs with circular geometry [1]. In order to allow the integration in Cartesian co-ordinates we apply the Alternating Directions Implicit (ADI) method to both the carrier diffusion equation and wave equation. The optical problem is treated using the semivcctorial approach developed for optical waveguides [2], after reducing the three dimensional (3D) VCSEL cavity to a 2D layer with the effective index method [1].

© 2000 IEEE