Small-Signal Analysis of High-Performance VCSELs

Abstract

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 singlemode 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.

Equivalent Circuit Model of High-Performance VCSELs

“…The parameter n In order to de-embed the pure intrinsic modulation response H int (ω) from the total modulation response, either the direct rate equations solution or the proposed equivalent circuit model derived in this work can be used. As shown in Reference [4], even though it is very accurate, the calculated H int (ω) is very complex to implement and an advanced fitting procedure is required to determine its physical parameters. Alternatively, the equivalent circuit model presented in this work has fewer fitting parameters compared to the rate equation model on one side, and secondly, it can be easily integrated in the overall system cascaded network.…”

“…Small-signal advanced MM rate equations for high-speed MM VCSELs, which are based on mode competition for carrier density in the active region, were recently developed [3,4]. In order to map these rate equations to the proposed equivalent circuit model, we quickly review the different derivation steps leading to the system's intrinsic modulation response and interaction matrices.…”

“…In this circuit, we can consider, just like in the SM model, that Iso1 = ηIdI/Vo1 and Iso2 = ηIdI/Vo2 and that s21I12 and s12I21 are dependent current sources, which represent the interaction of the two carrier reservoirs with each other. This is an important aspect to consider, as it has been recently shown in MM VCSELs that the split carrier reservoirs of the lasing mode ensembles overlap and impact each other [3,4]. Equivalent electrical circuit model of a two-mode multi-mode VCSEL intrinsic dynamic operation.…”

“…Furthermore, analyzing and modeling these lasers enable the enhancement and optimization of their design and performance. Recently, an advanced and accurate MM small-signal model, which is based on the carrier reservoir splitting approach, was developed [3,4]. This rate equation-based model enables the extraction of reliable information from the intrinsic dynamics of high-speed MM VCSELs, as it takes into account the effect of spatial hole-burning (SHB), gain compression, and inhomogeneity in the carrier distribution between the modes.…”

“…For SM VCSELs, the solution of the rate equations is straight forward and the fitting procedure for parameter extraction is simple. For MM VCSELS, however, and as shown in Reference [4], even for two-mode ensembles, the analysis becomes very complex and the parameter extraction and development of an analytical intrinsic modulation expression becomes rigorous.…”