Small-Signal Analysis of Ultra-High-Speed 30 GHz VCSELs Using an Advanced Multi-Mode Approach

Vertical-cavity surface-emitting lasers (VCSELs) have emerged as a pioneering solution for many high-speed data communication challenges. Therefore, higher bandwidth optical interconnects with data rates in the range of 100 Gbit/s require directly modulated VCSELs with ultimate speed ratings. The small-signal modulation response of a VCSEL can be isolated from the entire system, thus providing accurate information on the intrinsic laser dynamics. Until now, it is assumed that the dynamic behavior of oxide-confined multi-mode VCSELs can be fully modeled using the single-mode rate equations developed for edge-emitters, even though the deviation between the single-mode based model and the measured data is substantially large. Using an advanced theoretical approach, rate equations for multi-mode VCSELs were developed and the small-signal modulation response of ultra-high speed devices with split carrier reservoirs corresponding with the resonating modes were analyzed. Based on this theoretical work, and including gain compression in the model, the analyzed VCSELs showed modulation bandwidth around and exceeding 30 GHz. The common set of figures of merit is extended consistently to explain dynamic properties caused by the coupling of the different reservoirs. Furthermore, beside damping and relaxation oscillation frequency, the advanced model, with gain compression included, can reveal information on the photon lifetime and highlights high-speed effects such as reduced damping in VCSELs due to a negative gain compression factor.