422 Million Q Planar Integrated All-Waveguide Resonator with a 3.4 Billion Absorption Limited Q, Sub-MHz Linewidth and 3005 Finesse

High Q optical resonators that are a key component for ultra-narrow linewidth lasers, frequency stabilization, precision spectroscopy and quantum applications. Integration of these resonators in a photonic waveguide wafer-scale platform is key to reducing their cost, size and power as well as sensitivity to environmental disturbances. However, to date, the intrinsic Q of integrated all-waveguide resonators has been relegated to below 150 Million for a non-etched waveguide resonator and 230 Million for a waveguide-coupled etched silica microresonator. Here, we report an all-waveguide Si 3 N 4 resonator with an intrinsic Q of 422 Million and a 3.4 Billion absorption loss limited Q. The resonator linewidth measures at 453 kHz intrinsic linewidth, 906 kHz loaded linewidth with finesse of 3005. The corresponding linear loss of 0.060 dB/m is the lowest reported to date for an all-waveguide design with deposited upper cladding oxide. These are the highest intrinsic and absorption loss limited Q factors and lowest linewidth reported to date for a photonic integrated all-waveguide resonator. This level of performance is achieved through a careful reduction of scattering and absorption loss components and redeposition of a thin nitride layer. We quantify, simulate and measure the various loss contributions including scattering and absorption and describe a surface-state dangling bond absorption that we believe is passivated by the redeposited layer. In addition to the ultra-high Q and narrow linewidth, the resonator has a large optical mode area and volume, both critical for ultra-low laser linewidths and ultra-stable, ultra-low frequency noise reference cavities. These results demonstrate the performance of bulk optic and etched resonators can be realized in a photonic integrated solution, paving the way towards photonic integration compatible Billion Q cavities for precision scientific systems and applications such as nonlinear optics, atomic clocks, quantum photonics and high-capacity fiber communications systems on-chip.


INTRODUCTION
Ultra-high Q resonators play a critical role across a wide range of applications including ultranarrow linewidth lasers 1-3 , optical frequency combs [4][5][6] , optical gyroscopes 7 , optical atomic clocks 8 and quantum communications and computation [9][10][11][12][13] . These resonators, typically used for laser linewidth narrowing and frequency stabilization, have been relegated to benchtop and bulk-optic implementations. Record low 40 mHz laser linewidths and frequency stabilization of 1×10 -16 over 1 second have been achieved with a single crystal silicon cavity cryogenically cooled and environmentally isolated Fabry-Perot resonator 1 while table-top ultra-low expansion glass cavities can realize sub-Hz linewidth semiconductor lasers and frequency stabilization on the order of 2.7×10 -15 over 1 second 14 . Progress has been made with miniaturization of tapered-fiber and freespace coupled ultra-high Q bulk optical resonators [15][16][17][18][19][20] to achieve Qs of 63 Billion 18 . For example, state-of-the-art centimeter-scale microrod cavities with 1 Billion Q are capable of delivering a 25 Hz integral linewidth semiconductor laser with fractional frequency stability of 7×10 -13 at 20 ms in a compact centimeter structure 3 .
Translating the performance of ultra-high Q resonators to integrated waveguide designs will lead to a dramatic reduction in size, power, cost and reduced sensitivity to environmental disturbances as well as enabling higher level of on-chip integration [21][22][23] . Designs that support high power linear operation through a large mode area and that mitigate thermo-optic frequency noise through a large resonator mode volume are desirable 24,25 . All-waveguide silicon nitride ring-bus resonators have demonstrated intrinsic Q as high as 81 million 26 , and a large mode-volume and 120 cm long spiral silica waveguide resonator with facet mirrors demonstrated 140 million Q 25 . By employing a hybrid design consisting of a silicon nitride waveguide bus coupled to a dual polarization mode on-chip etched silica ring resonator, an intrinsic 206 Million Q was achieved 27 . The latter is not fully compatible with wafer-scale fabrication, is susceptible to environmental conditions, and needs hermetic covering, and requires careful mode engineering. The challenges to increasing the Q and reducing loss are dependent on reducing waveguide scattering losses with high-aspect ratio designs 28,29 and low surface roughness etching 30 . The ultimate limit is determined by material losses and eventually Rayleigh scattering [31][32][33][34] . A measure of the waveguide absorption-limited loss Q is a good metric for what is achievable for a given waveguide and resonator technology if waveguide scattering mechanisms can be mitigated 30 . Intrinsic loss sets the lower bound for the resonator full width half maximum (FWHM) linewidth. New solutions are needed for allwaveguide resonator designs with Qs approaching 500 Million, capable of exceeding several Billion, with sub-MHz FWHM resonances, large mode area and volume, and compatible with photonic integration and wafer-scale processing.
In this paper we report a significant advancement in integrated waveguide resonator performance. A Si3N4 bus-coupled ring-resonator with a measured intrinsic Q of 422 Million is demonstrated. The intrinsic linewidth is 453 kHz and the corresponding linear loss of 0.060 dB m -1 represents the lowest waveguide loss on-chip achieved with a deposited SiO2 upper cladding 29 . The loaded resonator has a 906 kHz full-width half maximum (FWHM) linewidth and a corresponding fineness of 3005, realizing a below MHz linewidth for the first time in a photonic integrated planar circuit with a record high finesse. Moreover, we report a 3.4 Billion absorption loss limited Q measure using a photothermal measurement technique 34,35 . These are the highest intrinsic and absorption loss limited Q factors and lowest linewidth reported to date for a photonic integrated resonator, especially one of a deposited upper-cladding fabrication process. This performance is achieved through a careful reduction of scattering and absorption loss components and redeposition of a thin nitride layer. By modeling scattering loss and measuring total intrinsic loss and absorption loss, we nail down each loss origin. In addition to these commonly known loss origins, we perform the secondary ion mass spectroscopy (SIMS) measurements to investigate the potential dangling bond resonances at the etched SiN/Oxide interface as another potential loss origin. The large resonator mode area and mode volume enables ultra-low laser linewidths and ultra-stable, ultra-low frequency noise reference cavities. These results demonstrate promise to bring the performance of bulk optic and etched resonators to planar all-waveguide solutions and pave the path towards integrated all-waveguide Billion Q cavities for atomic clocks, quantum computing and communications, precision spectroscopy and energy efficient coherent communications systems.
The low loss waveguide ring resonator is depicted in Fig. 1a and an SEM micrograph cross section is shown in Fig. 1b. The waveguide surface roughness couples the guided energy into radiation continuum causing scattering loss and the bulk material absorption converts the guided optical energy into heat leading to bulk absorption loss, as illustrated in Fig. 1c. Point defects on the waveguide surface created during the material deposition or waveguide etching processes can introduce coupling between different longitudinal modes or between the forward and backward propagating modes, causing random resonance splitting, as illustrated in Fig. 1d. Material deposition or waveguide etching processes can create reconstructed Si-Si bonds and dangling Siand N-bonds , which can also become secondary bonds with hydrogen impurities such as Si-H, N-H, and Si-O-H. These defect bonds are a potential major origin of surface absorption loss 34,36 . Excess loss at bus-to-resonator coupling can be another major origin of resonator loss at ultra high Q regime. It has been shown that careful design of bus-to-resonator coupling such as pulley coupling and weakly tapered coupling as opposed to straight coupling is less susceptible to introducing excess loss 26 .

Resonator design and fabrication:
The geometry of our Si3N4 waveguide resonator is designed to be 11 μm wide and 40 nm thick, and such a high-aspect-ratio geometry mitigates sidewall scattering 26,28 . The bus waveguide is designed to be 7 μm by 40 nm to ensure the single mode operation 28 . Our waveguide mode simulation suggests both the bus and resonator waveguides only support the fundamental TE mode and other higher order modes have large bending losses thus are not supported because of the asymmetric refractive indices in the upper and lower claddings, as demonstrated in the Supplementary Information. The resonator radius is 11.787 mm which is larger than the critical bending radius of the fundamental TE mode. The directional coupler is designed to be a weakly tapered coupler to avoid excess coupler loss 26 . Based on our previous measurement and coupling simulation, the gap between the bus and resonator waveguides is 6.898 μm such that the resonator is under-coupled, as discussed in the Supplementary Information. Since the high-aspect-ratio waveguide can suffer from the top and bottom surface roughness scattering, we include an additional nitride deposition step in our waveguide fabrication process through which the waveguide top surface can be potentially smoothed and the top surface scattering reduced.
The fabrication process flow includes standard wafer patterning, etching, upper cladding deposition, and annealing. The bottom cladding is 15 μm thick thermally grown oxide on the silicon substrate. The upper cladding is 6 μm TEOS-LPCVD deposited silicon dioxide. The final step is annealing at 1100 ℃ for 9 hours. The additional nitride deposition comes after etching and before upper cladding deposition: we deposit a few tens of nm of silicon nitride by LPCVD and subsequent heat treatment, creating a boundary between etched waveguide core and silicon dioxide which contributes to a smoother interface. The detailed fabrication process flow is illustrated in the Supplementary Information. The addition of the second SiN layer reveals the boundary between the upper and lower cladding in the scanning electron microscope (SEM) image of the cross section of the waveguide shown in Fig. 1b, which also allows us to observe that there is overetching into the lower cladding by about 100 nm. Q-factor, linewidth and loss: Spectral scans for the ultra-high-Q (UHQ) ring resonator with a tunable external cavity laser are performed for the Q factor characterization. Figure 3a shows the multi-FSR scan of our UHQ resonator fabricated with the boundary layer at 1550 nm. To demonstrate the loss reduction benefit of this technique, we fabricated another wafer's UHQ resonator devices (device under test, DUT) without the extra redeposition-and-annealing step for comparison ("control"). We employ a fibre Mach-Zehnder interferometer (MZI) with a calibrated FSR of 5.871 MHz for the optical frequency calibration. A Lorentzian fit of the resonance extracts the total linewidth ! , the loaded Q factor " = 0 / ! , the coupling rate #$ , the intrinsic linewidth %& , and the intrinsic Q factor, %& = 0 / %& . The calibrated MZI linewidth measurement is performed on non-splitting resonances from 1550 nm to 1600 nm with intrinsic linewidth, intrinsic Q, and propagation loss for both the DUT and control shown in Fig. 2c, 2d, 2e, where we find the highest intrinsic Q of 422 Million at 1570 nm for the DUT. The spectral plots of the total linewidth, intrinsic linewidth, and coupling rate are shown in the Supplementary Information, which confirms the designed under-coupling operation at 1550 nm for the DUT. The linewidth measurement at 1570 nm shown in Fig. 2a reveals that the DUT reaches a total linewidth of 906 kHz and an intrinsic linewidth of 453 kHz. With the FSR at 1570 nm measured to be 2.720 GHz as shown in the supplementary, the corresponding finesse is 3005. To further confirm this highest Q, a ring-down experiment is performed at this resonance which gives an intrinsic Q of 434 Million. The comparison between the DUT and control shows that the additional nitride layer step significantly reduces the propagation loss.  Resonance splitting: Resonance splitting is often created intentionally and in a well-controlled manner by introducing coupling between the clockwise (CW) and counter-clockwise (CCW) modes of a ring resonator. This can be achieved, for example, by adding Bragg gratings to the waveguide 37,38 , or by putting well-positioned scatterers near the resonator waveguide 39,40 . On the other hand, the mode coupling can be induced by waveguide roughness or surface defects resulting in resonance splitting, which can be purely random across different resonances. As illustrated in Fig. 3b, the coupling between the CW and CCW modes creates a stopband resulting in resonance splitting. Resonance splitting has been reported in high Q WGM resonators. Yet, resonance splitting has not been resolved and observed in planar waveguide resonators until the Q reaches 10 Million 30,40 . The coupled mode equation (CME) method models resonance splitting by incorporating the mode coupling 33,34,41,42 , as demonstrated in the Supplementary Information. Resonance splitting also emerges in our UHQ waveguide resonator whereas it is not seen or not resolved in the control device. The insets in Fig. 3a reveal the zoom-in view of each individual resonance and different resonance splitting rates. The splitting appears random across different resonances. Moreover, the resonances that have less obvious splitting tend to have larger extinction ratios at resonance, which implies a narrower linewidth given that the resonator is under-coupled. Figure 3c shows the plot of the intrinsic linewidth versus the splitting rate of 96 resonances near 1550 nm for three devices fabricated on one wafer, which shows a positive correlation between linewidth and splitting rate.

Fig. 2. Linewidth and ring-down measurement of the DUT and control resonators, as well as the photo-thermal absorption loss measurement of the resonators. a,
Resonance splitting has been utilized for suppression of higher order cascaded stimulated Brillioun scattering lasing 37 and nano-particle detection 38 . Yet, the random resonance splitting in the UHQ resonators could cast shadow on a lot of applications of UHQ waveguide resonators that prefer non-splitting resonances such as stimulated Brillioun lasers and Kerr frequency comb, especially when the linewidth is even narrower than the splitting.

Absorption loss:
The Q-factor spectral characterization for the DUT shows a significant loss reduction of the smoothing step compared to the control. To fully understand its loss reduction benefit, we also perform photothermal absorption loss measurements. It has been demonstrated that the photothermal effect and consequent thermal bistability of a resonator can be characterized to measure absorption loss 34,35,43,44 . The photothermal effect emerges in the spectral scan across resonance when the on-chip power is large enough to induce a photothermal redshift of resonance that is comparable to or larger than the resonance linewidth and this provides information which can be used to extract the absorption loss as illustrated in the Supplementary Information. Hydrogen-impurity-related absorption has been identified as a significant loss origin in the ultralow loss regime, which has an absorption peak near 1520 nm 29,35,43,44 . The recent broadband absorption loss measurement on ultra low loss waveguides by Liu et al. showed that hydrogenimpurity-related absorption loss can in fact dominate the absorption loss near 1520 nm. In that work, the absorption-limited linewidth was reduced from 20 MHz for a partial anneal to around 0.3 MHz for a more complete anneal 43 .
The measured absorption loss spectrum is shown along with intrinsic loss in Fig. 2e, where we find that the narrowest absorption-limited linewidth at 1600 nm from the device is 51 kHz corresponding to an absorption-limited Q of 3.4 Billion. It is worth noting that the scattering loss is still dominant in both the DUT and control. Now it is clear that the additional processing reduces both absorption loss and scattering loss. The absorption loss reduction could be from the high temperature anneal that helps drive out hydrogen and the scattering loss reduction could be from a smoother boundary between core and upper cladding created by the nitride layer. Based on the measured total intrinsic loss and absorption loss, we fit the non-absorption loss spectrum with our scattering loss model, as shown in the Supplementary Information. Since our scattering loss model suggests that the sidewall scattering loss for our high-aspect-ratio waveguide with a typical RMS sidewall roughness of 1 nm and a correlation length of 50 nm is on the order of 0.001 dB m -1 and the top or bottom scattering loss with a typical RMS roughness of 0.2 nm and a correlation length of 10 nm is on the order of 0.1 dB m -1 , we take the sidewall scattering as negligible. The nonabsorption loss is fitted with an effective top surface roughness of 0.24 nm and 0.35 nm for the UHQ and control devices, respectively (the correlation length is assumed to be a typical value of 10 nm 29,30,35 ).

Surface loss effects:
The increasing trend of the absorption loss at shorter wavelengths shown in Fig. 3e suggests a likely hydrogen-impurity-related absorption peak near 1520 nm. Yet, it is not clear whether the hydrogen impurity is distributed in the bulk material or at the waveguide surface. To profile the densities of hydrogen and oxygen impurities, secondary ion mass spectroscopy (SIMS) is performed on a wafer sample after the etching process, and another wafer sample after the etching and nitride deposition and subsequent heat treatment, and the results are shown in Fig.  4. In the Si3N4 core, after the heat treatment, the hydrogen concentration drops to 1.3×10 20 (0.14 %) from 1.6×10 21 (1.7 %); at the boundary between the oxide and remaining redeposited Si3N4, there is a hydrogen concentration peak of 1.0×10 21 (1.1 %). Therefore, the heat treatment step also acts as an annealing process to drive out hydrogen which can contribute to the absorption loss reduction as we see in Fig. 2e. Surface absorption due to surface reconstruction could impose a Q-factor limit 34,36 . Here we notice that at the interfaces between different materials there is an increase of hydrogen which may be attached to reconstructed defect bonds such as Si-H, N-H, and Si-O-H, illustrated in Fig. 1e, which could impose a Q-factor limit on the order of Billion in the UHQ resonator performance.

DISCUSSION
It is desirable to have single-mode waveguides; yet dual-polarization waveguides show that TM is less susceptible to waveguide roughness and has lower propagation loss 27 . Therefore, we anticipate that by a dual-polarization design of our waveguide in the future work could achieve even high loaded and intrinsic Q with TM mode. As we have noted that the annealing process drives out hydrogen, it could be beneficial to add an additional annealing process right after etching to drive out hydrogen in the first place. With these potential improvements, we could eventually reach Billion Q photonic integrated resonators.