Dynamical Hysteresis and Thermal Effects in Vertical-Cavity Surface-Emitting Lasers

We study numerically the polarization-resolved light-output characteristic of vertical-cavity surface-emitting lasers (VCSELs) using the spin-flip model for VCSELs extended to take into account thermal effects via a dynamical equation for the active region temperature, including heat dissipation, heating due to nonradiative carrier recombination, and Joule effect. The temperature dynamics is coupled to the carrier and optical field dynamics via a frequency and temperature-dependent gain coefficient. We show that the interplay of thermal effects and injection current variation can result in turn-on and turn-off hysteresis cycles that can be, depending on various model parameters, positive or negative. In the first case, the turn-on occurs at a higher value of the bias current than the turn-off; in a negative hysteresis cycle, the laser turns-on at a lower value of the bias current than the turn-off. These results are interpreted in terms of the interplay of the two time-scales determined by the injection current swept rate and the thermal relaxation rate.