Analysis of single-mode efficiency of electrically pumped VECSELs

We present a model and results of simulations and experiments investigating the L-I characteristics of electrically pumped (EP-) VECSELs in the single- and multi-mode regime. In our model we use a mode expansion ansatz to treat the electromagnetic field inside the VECSEL cavity. The eigenmodes of the passive cavity are computed using the bidirectional beam propagation method (BDBPM) to solve the Helmholtz equation. The BDBPM allows us to account for the complex refractive index distribution within the semiconductor heterostucture, composed of approximately thousand interfaces along the optical axis in addition to lateral refractive index variations in oxide-confined devices as well as the macroscopic external cavity. We simulate the time evolution of the modal powers of several transverse modes and the spatial distribution of the inversion carriers in the quantum well plane. Therefore we solve an differential equation system composed of multimode rate equations and the carrier diffusion equation. With this ansatz we are able to identify cavity geometries suitable for single-mode operation assuming typical current profiles that are taken from photoluminescence measurements of the devices under investigation. Furthermore, we identify effects limiting the single-mode efficiency, such as poor gain and mode matching, reabsorption in unpumped regions of the quantum wells or enhanced carrier losses due to strong spatial hole burning. Critical parameters of the equations, such as optical losses, injection effciency, carrier recombination constants and gain parameters are obtained from experiments, microscopic models and literature. The simulation results are compared to experimental results from EP-VECSELs from Philips Technologie GmbH U-L-M Photonics