## 3 Experimental Results  
The co-integrated, widely tunable laser-SOA booster was mounted on a temperature-controlled holder set at T = 20 \({}^{\circ}\)C. Figure 3a shows the measured propagation losses as a function of the optical wavelength for strip and rib Si waveguides. Narrow lines represent the average value from 10 measured dies, and the colored area around them corresponds to the experimental deviation. Strip (rib) Si waveguides present an average propagation loss of 2 dB/cm (1 dB/cm) all over the measured wavelength range (\(\lambda\) = 1510 nm-1590 nm). Figure 3b represents the measured V-I response of thermal heaters, showing a similar series resistance of R \(\approx\) 35 \(\Omega\) and a reasonably low voltage. Indeed, ramping up the driving current of an individual heater to 30 mA (V \(<\) 1.2 V) is enough to induce a sweep in the  
Figure 2: **(a)** Simulated Vernier filter transmission for a wavelength range from \(\lambda\) = 1500–1600 nm. The upper inset shows a zoom-in view around one of the Vernier’s maximum transmission lobes (orange trace) overlaid with the simulated longitudinal mode spectrum of the laser cavity (blue trace). The inset below shows a cross-section optical mode simulation of the Si waveguide Vernier filter. **(b)** Simulated reflectivity spectrum of the Bragg mirror with 39 periods (blue trace) and with four periods (pale red trace). The inset shows a cross-section optical mode simulation of the Si waveguide Bragg mirror. laser's emission wavelength up to half of the [PERSON]'s FSR (i.e., 25 nm). The remaining lasing wavelength is covered by the other thermal heater, which sweeps the emission wavelength in the opposite direction in the spectrum (one racetrack resonator induces a red shift and the other one a blue shift). Figure 3c shows the V-I curve of the laser's gain section (see the 3D schematic at the inset). We measure a differential resistance of 6 \(\Omega\), in agreement with the values reported elsewhere in similar devices [18; 36]. To evaluate the output optical power of the widely tunable laser uniquely, P-I measurements were performed on equivalent tunable lasers decoupled from the SOA booster. In this case, however, reflectionless vertical grating couplers were designed at the laser output to allow for on-chip characterization [38]. A cleaved fiber with an angle of 11.5\({}^{\circ}\) is used. The P-I characteristic for a laser emission wavelength around of \(\lambda\) = 1549 nm is shown in Figure 2d. A laser threshold of 10 mA (<1 KA/cm\({}^{2}\)) and a maximum fiber-coupled output power of 1 mW for an injected current of I = 100 mA were obtained. For higher injected currents, thermal roll-off quickly degrades the fiber-coupled optical power. Thus, assuming that the optical mode mismatch between the vertical grating coupler and the optical fiber induces 3 dB of coupling losses, we can consider a maximum on-chip coupled optical power around of 2 mW (3 dBm) in this standalone configuration. The kinks observed on the P-I curve correspond to longitudinal mode hopping in the cavity caused by localized Joule heating in the gain section as the current injection is increased. Such misalignment between the spectral transmission of the passive Vernier filter and the optical phase of the gain's section can be suppressed by adding a phase shifter in the laser cavity to automatically readjust the optical cavity length [39]. Similar to the widely tunable laser, the SOA booster has been first characterized independently. For that, we used the co-integrated system from Figure 1, characterizing the SOA-booster from its output facet while being the tunable laser in open circuit. The output power is measured in a butt-coupling configuration with a lensed fiber with a waist diameter of 3 \(\upmu\)m, accounting 3 dB coupling losses. Figure 4a shows the V-I characteristic of the SOA-booster device.