# Ultra-Low-Loss Silicon Waveguides for Heterogeneously Integrated Silicon/III-V Photonics
## 3 Passive Device Demonstrations
### High Quality Factor Ring Resonators  
One key component made possible by low-loss waveguides is the high-\(Q\) ring resonator. The ring resonator is an essential building block to realize compact optical filters and delays on chip. Higher \(Q\)-factors enable sharper, narrowband filters and longer delays, which are requirements for the aforementioned ultra-long laser cavity. There has been a plethora of recent work to demonstrate high-\(Q\) integrated resonators using different materials and cavity geometries. These results include fully integrated resonators with an intrinsic \(Q\) of 22 million in silicon [26], 81 million in a silicon nitride resonator [35] and over 200 million in a silica resonator [36]. However, the results of the latter two are multimoded, which can lead to multiple sets of resonances or excess loss at the coupling regions unless special care is taken to optimize the coupler [37]. These three results all have bend radii >2 mm, which limits the compactness of the device, and complicates the design of a Vernier-effect filter due to the small free spectral range of each ring. Finally, it is unlikely that these resonators were designed with laser integration in mind, and cannot be integrated with the heterogeneous silicon/III-V laser without significant extra processing [25; 38].  
In this work, we demonstrate ring resonators readily integratable with the heterogenous silicon/III-V platform with a loaded \(Q\) of 2.1 million, and an intrinsic \(Q\) of 4.1 million. The ring is in an all-pass configuration, and is 1.8 microns in width, which is single-mode for the TE polarization. The ring is connected to a bus waveguide of the same dimensions using a straight-to-curved coupler with a 1.2 micron coupling gap. The transmission spectra of the ring is measured by sweeping a high-resolution tunable laser (0.1 pm steps) across the resonance, and measuring the output power. The resulting spectra is depicted in Figure 5a, and fitted with a Lorentzian function. The measured full width half max (FWHM) is 91.3 MHz.  
The ring in Figure 5a has a 750 \(\upmu\)m bend radius, for which we did not observe any bend-loss induced radiation in the resonator. To confirm this, we investigated rings with varying radii, and plot their intrinsic \(Q\) factor alongside the theoretical bend-loss limit for \(Q\) in Figure 5b. The experimental results are extracted from the measured FWHM, while the dashed lines are simulated using Lumerical MODE solutions. The simulations are shown for three different etch depths, as that is the most sensitive parameter to the bend-loss. We find that our ring in this experiment is actually overetched compared to the target 56 nm, judging by the \(Q\) of the smaller rings. We do not observe significant bend loss in the rings until the radius is less than 550 \(\upmu\)m. For practical reasons, the ring radius should be larger than 700 \(\upmu\)m to avoid bend-loss possibly caused by an underetch of the waveguide.  
Figure 5: **(a)** Measured spectral responses of the 750 \(\upmu\)m radius Si ring resonator (all-pass configuration) plotted with a Lorentzian fit. The extracted intrinsic quality factor \(Q_{int}\) = 4.1 million. **(b)** Simulated bend-loss limited intrinsic \(Q\) of the rings versus ring radius at three etch depths. The experimental data of the targeted 56 nm etch depth are depicted as blue circular markers.