Small-Signal Analysis of High-Performance VCSELs

In this paper, a comprehensive model to describe the small-signal modulation response of ultra-high performance single- and multi-mode vertical-cavity surface-emitting lasers (VCSELs), with modulation bandwidths exceeding 30 GHz, is presented. Traditionally, utmost simplified dynamic models are used to extract dynamic figures of merit from single-mode edge-emitting lasers. These methods are later on also applied to evaluate the dynamic performance of VCSELs, even though these devices have a very different geometrical layout and modal confinement. However, to understand the dynamic performance of high-speed VCSELs, a model supporting the transverse and longitudinal mode profile, and the driving current inhomogeneity in the active region, is needed. Therefore, multi-mode VCSEL rate equations are established here. Moreover, to access the dynamic figures of merit of these devices, a comprehensive analytical fitting function based on our carrier reservoir splitting approach is derived. Thus, because of the high carrier and photon densities inside these optimized VCSELs, the common carrier reservoir splits up as a result of numerous effects such as mode competition, carrier diffusion and spatial hole burning. These and other effects have a tremendous impact on the small signal modulation response shape and bandwidth, and also on the current distribution profile in the carrier reservoirs. Compared with our recently reported work, this novel model presented includes the effects of gain compression and inhomogeneous current injection between the different lasing modes. Consequently, it is found that the further tuning of our multi-mode VCSEL dynamic model, to include these effects, yields a more physical and consistent figures of merit of high-performance VCSELs.