# Widely-Tunable Ring-Resonator Semiconductor Lasers
## 3 Comparison of Classical Widely-Tunable Architectures  
We compare four ring-based laser topologies, as shown in Figure 4, all of which have rings with two different circumferences to form the Vernier effect for tuning. The first is a ring-bus-ring (RBR) laser, which utilizes two ring filters in series in add-drop configuration, and two Sagnac loop mirrors. The second is a single-sided coupled-ring resonator (CRR 1\(\times\)) laser which utilizes a CRR mirror on one side as both reflector and filter, and a Sagnac loop mirror on the other side. The third is a Vernier racetrack laser, which utilizes two bus waveguides, one of which has a gain region and phase tuner, and two ring resonators that are coupled to the bus waveguides. The fourth design is a double-sided coupled-ring resonator (CRR 2\(\times\)) laser, which utilizes a CRR mirror on both sides as both reflector and filter. All lasers have resistive heaters overlaying the rings to provide active tuning of the wavelength. Ring circumferences of the RBR laser are 256 \(\upmu\)m and 271 \(\upmu\)m, giving an expected tuning range of 42.1 nm, with the power coupling coefficient same for all couplers, and equal to 20%. For the CRR 1\(\times\) laser, the selected circumference values for Ring 1 and Ring 2 were 337 \(\upmu\)m and 368 \(\upmu\)m, respectively, and the selected power coupling coefficient values for \(K_{1}\), \(K_{2}\) and \(K_{3}\) are 2.25%, 2.25% and 36%, respectively. This results in an expected tuning range of 20.4 nm. A more detailed description of CRR mirror properties is found in [23]. Vernier racetrack laser has two rings, with circumferences equal to 400 \(\upmu\)m and 420 \(\upmu\)m, with the power coupling coefficient same for  
Figure 4: Four considered widely-tunable ring-based laser designs. Thermal heaters are drawn in yellow: (**a**) Ring-bus-ring laser (RBR); (**b**) Single Coupled-Ring-Resonator laser (CRR 1\(\times\)); (**c**) Vernier racetrack resonator and (**d**) Double Coupled-Ring-Resonator laser (CRR 2\(\times\)). Figure 3: (**a**) Effective cavity length calculated for a 3 mm long cavity with SWF from Figure 1b; (**b**) Longitudinal mode spacing for the same cavity; (**c**) Phase of the complex amplitude reflectivity \(r_{\textit{eff}}\) for the same cavity; (**d**) Coefficients \(A\), \(B\) and \(F\) calculated from Equations (8) and (9) for the same cavity. In all cases, the horizontal axis corresponds to the detuning from the resonance. all couplers, and equal to 20%. The design tuning range is equal to 31.6 nm. Finally, the CRR 2\(\times\) laser has two pairs of rings, each pair having nominally the same radius of 368 \(\upmu\)m and 402 \(\upmu\)m. The coupling coefficient values for both pairs are equal and the same to those on CRR 1\(\times\) laser. The design tuning range is 18.6 nm. The calculated function of the passive ring filters is shown in Figure 5.  
We have fabricated the lasers using heterogeneous III/V silicon process. Optical photographs of lasers are shown in Figure 6. Wavelength tuning for lasers was mapped out vs. ring heater voltage squared (proportional to power), as shown in Figure 7. The RBR laser had a measured tuning range of 42 nm, the CRR 1\(\times\) laser had a measured tuning range of 21 nm, while the Vernier racetrack laser had a measured tuning range of 47 nm, and the theoretical tuning range of CRR 2\(\times\) laser is 18.6 nm. We do not show the 2D tuning map for CRR 2\(\times\) laser due to unpredictable tuning performance, that we addressed in Section 3.1. The tooth-shaped tuning map of the Vernier racetrack laser is due to the wavelength hopping between two wavelengths separated by the design tuning range of ~31 nm, when the laser work at the states where net gain between these two modes are similar in magnitude. The maximum measured double-sided output power was 7.7 mW for the RBR laser, 10.5 mW for the CRR 1\(\times\) laser laser, 12.7 mW for the Vernier racetrack laser, and 14.2 mW for the CRR 2\(\times\) laser. The output powers were measured using an integrating sphere.