Spatio-Temporal Modeling of the Optical Properties of VCSELs in Presence of Polarization Effects

In this paper, we develop an optical dynamical model for vertical-cavity surface-emitting lasers (VCSELs) which describes, in an unified way, polarization and spatial effects. The model is based on equations for the lateral dependence of the slowly-varying amplitudes of the optical field in both circular polarizations, and equations for the carrier density in both spin orientations. This provides a natural generalization of the Spin Flip Model for the description of polarization properties of VCSELs extensively used in the literature. In its present form, the model assumes given functional dependence of the guiding mechanisms (built-in refractive index and thermal lensing) as well as the spatial dependence of the current density.

We investigate the transverse mode behavior of gain-guided, bottom and top-emitter VCSELs by implementing the model with an analytical approximation to the susceptibility of quantum-well semiconductors. We demonstrate that the stronger the thermal lens, the stronger the tendency towards multimode operation, which indicates that high lateral uniformity of the temperature is required in order to maintain single mode operation in gain-guided VCSELs. We perform analytical calculations of the threshold curves in both types of VCSELs. Also, close-to-threshold numerical simulations show that, depending on the current shape, thermal lensing strength and relative detuning, different transverse modes can be selected.