## 2 Device Design and Structure  
A 3D schematic view of the co-integrated, widely tunable laser-SOA booster is shown in Figure 1. The co-integration of III-V/Si lasers and optical amplifiers presents several challenging points that need to be carefully evaluated. First, we have designed both devices using the same III-V epitaxial material to make them compatible with the heterogeneous wafer bonding technique, which is the most mature technology for the III-V/SOI platform up to now [32]. Nevertheless, this choice imposes a trade-off on the number of MQWs in the active region since the optimum III-V stack may differ for the laser and the SOA. From the laser's perspective, a relatively large number of MQWs leading to a high differential gain (a) and a comfortable gain margin may be desirable to target applications where directly modulated lasers are needed, or for high temperature operation [33]. On the other hand, the saturation power (P\({}_{\text{sat}}\)) decreases with the number of MQWs, which is detrimental for the SOA [34]. Moreover, for a given total loss \(\alpha_{\text{total}}\), there is an optimum number of MQWs that minimizes the laser's current threshold [35]. In our particular case, we have designed our devices with four MQWs, which seems to be a reasonable trade-off between these two parameters [36]. Concerning the material's choice, AlGaInAs quantum wells grown by metal organic vapour phase epitaxy (MOVPE) have been used as an optical gain medium. The use of Al-based quaternary alloys provides better performance and a robust operation over temperature compared to P-based alloys (InGaAsP) due to a larger conduction band offset that minimizes thermionic emission of confined electrons. The optical confinement in the MQWs (\(\Gamma\)) is another parameter that plays a key role on the device performance. As for the number of MQWs, different \(\Gamma\) values are often adopted to optimize the design of the laser and the SOA. A high \(\Gamma\) is desirable to lower the laser's current threshold, although it also lowers the P\({}_{\text{sat}}\) of the SOA. Fortunately, the  
Figure 1: 3D schematic view of the co-integrated, tunable laser-SOA booster. From left to right: the highly reflective Bragg mirror; the Vernier filter; the III-V gain section of the laser; the low reflective Bragg mirror; the III-V gain section of the SOA booster; and the output facet for fiber coupling. The upper insets show the fundamental TE-like mode cross-section for the ring-based Vernier filter (left), the tunable laser (middle), and the SOA booster (right). The insets below show the fundamental TE-like mode propagation in the laser (left) and in the SOA booster (right). heterogeneous III-V/SOI platform allows for a tight control of the \(\Gamma\) value by varying the width of the Si ridge placed underneath the gain section. To illustrate that, optical mode simulations using FIMMwave commercial software are presented in Figure 1, showing the fundamental TE-like mode cross-section in the Si ring-based Vernier filter (the upper inset at the left hand-side); in the active region of the tunable laser (inset at the middle); and in the SOA booster (inset at the right hand-side). The insets below show the fundamental TE-like mode propagation in the laser (left) and in the SOA booster (right). As can be observed, a higher \(\Gamma\) value can be set for the widely tunable laser with respect to the SOA booster by a proper engineering of the device cross-section geometry, attaining \(\Gamma\) = 1.5%/well for the widely tunable laser and \(\Gamma\) = 0.9%/well for the SOA booster. The vertically stacked III-V and Si waveguides are also marked by yellow and pale red traces. A narrow ridge III-V mesa with a width of 2.4 \(\upmu\)m has been used. It is worth remarking that, for the Si rib waveguides placed under the III-V gain sections, we have used a higher core height of 500 nm compared to the one used for the rest of Si photonic circuit (300 nm) to ease the mode transfer from the III-V to the Si rib waveguide.