Main

At shorter wavelengths (400–1,100 nm), waveguide losses surge because of two fundamental limitations9,10. First, scattering losses increase as the optical wavelength approaches the scale of surface roughness (surface Rayleigh scattering). Second, absorption losses increase as photon energy enters the Urbach tail of amorphous or crystalline dielectrics. However, many important photonic applications operate in these wavelengths14,15, such as optical clocks, quantum computing and networks, bioimaging, astronomical observation, underwater and data centre communications, compact lidar, and atomic physics studies in general (Fig. 1a). Silica (SiO2) and germanium-doped silica (germano-silicate or Ge-silica) have been widely adopted in optical fibres for short-wavelength operation because of their exceptionally low material absorption16. Nevertheless, because of the need for suspended geometries in the case of silica17,18, or the lack of well-developed fabrication processes for germano-silicate19, the promise of fibre-like loss in a photonic integrated circuit (PIC) platform remains untapped.

Fig. 1: Ultrahigh-Q germano-silicate device from violet to near IR.

a, Spectrum coverage of photonics application in the visible and short-NIR regions14. QD, quantum dot; YDFA, Yb-doped fibre amplifier. b, Waveguide propagation loss across broadband spectrum of state-of-the-art integrated platforms compared with the present work. Annealed Ge-silica waveguide losses are 0.49 dB m−1 at 458 nm, 0.32 dB m−1 at 532 nm, 0.32 dB m−1 at 685 nm, 0.19 dB m−1 at 780 nm, 0.14 dB m−1 at 965 nm and 0.08 dB m−1 at 1,064 nm, 0.09 dB m−1at 1,550 nm. Unannealed Ge-silica waveguide losses are 1.76 dB m−1 at 458 nm, 1.02 dB m−1 at 532 nm, 0.56 dB m−1 at 685 nm, 0.29 dB m−1 at 780 nm, 0.21 dB m−1 at 965 nm, and 0.19 dB m−1 at 1,064 nm, 0.15 dB m−1 at 1,550 nm. Data from refs. 9,36,37,38 for ULL Si3N4; refs. 10,15,39,40 for Si3N4; refs. 41,42,43 for LiNbO3; ref. 16 for the material limit of Ge-silica (standard modern fibre with a GeO2 content around 3.5 mol%). c, Schematic of high-performance visible PICs with multi-material integration for on-chip atom/ion control, consisting of blocks of III–V lasers, Ge-silica microresonators, LiNbO3 electro-optic modulators and vertical grating couplers. d, Microscopy image of a Ge-silica microring device. e, SEM image of annealed waveguide. f, Transmission spectra and corresponding intrinsic Q factors (Q0) of Ge-silica microring resonators at seven wavelengths spanning from violet to NIR. The observed double-dip features at 780 nm and 1,064 nm arise from mode splitting induced by backscattering in the microcavity, whereas the Fano lineshape at 458 nm originates from multimode interference (see detailed analysis in the Supplementary Information). Scale bars, 500 μm (d); 2 μm (e).

In this work, we present the first step towards using the materials of fibre optics in achieving planar integrated photonic circuits with fibre-like loss. As in fibre optics, GeO2 doping elevates the refractive index of the Ge-silica core, enabling optical confinement within a silica cladding. A deep-ultraviolet (DUV) stepper lithography-based manufacturing process is developed to fabricate planar integrated waveguide circuits on silicon wafers. Leveraging the famously low material loss of Ge-silica16 and the unique low-viscosity reflow properties20 at standard furnace temperatures, we achieve sub-dB m−1 waveguide losses spanning the violet to telecom bands (Fig. 1b). Notably, the waveguide loss in the violet band is 13 dB lower than any current integrated platforms, whereas the lowest loss of 0.08 dB m−1 at 1,064 nm reaches a loss level close to the first low-loss optical fibre produced by Corning in 1970 (0.02 dB m−1) (ref. 21). Crucially, ultralow losses without post-processing thermal annealing can be achieved, which is an important enabler for monolithic/heterogeneous integration with temperature-sensitive materials11.

Beyond its record-low loss performance, several material and practical advantages of this platform are demonstrated. First, the DUV-stepper-defined waveguides are readily dispersion-engineered as required for soliton microcomb generation (demonstrated by soliton microcomb). Second, GeO2 doping reduces the acoustic velocity relative to silica, enabling simultaneous confinement of an optical and acoustic mode within the waveguide core (demonstrated by Brillouin lasing). Finally, it can support thicknesses over 4 μm, enabling low thermorefractive noise (TRN) by the generation of a large mode area (LMA) circuit (demonstrated by low-frequency-noise self-injection locking (SIL)). Overall, this platform incorporates essential ingredients of high-performance multi-functionalized visible PICs, including ultralow loss, multi-material integration ability and high noise suppression, thereby paving the way for high-complexity system-level applications such as on-chip atom and ion control22 (Fig. 1c).

Broadband ultrahigh-Q microresonators

To evaluate performance across the broadband spectrum, microring resonators are fabricated. For this work, air-cladded microring resonators with a 3-mm diameter (corresponding to a 21.2 GHz free spectral range) are used mostly for convenience in coupling and measurement, while also completely eliminating substrate leakage and bending losses (for details, see Supplementary Figs. 1 and 2). The microscopy image of a typical microring resonator is shown in Fig. 1d. The ring and pulley coupler are colorized in green, with ridge waveguides fabricated by etching trenches around the ridges to increase etch efficiency. Unlike Si3N4 photonic circuits, these PICs do not require stress release patterns even at 4 μm of thickness. The inherent low viscosity of Ge-silica can be accessed at standard furnace annealing temperatures, thereby allowing for surface-tension-induced smoothing. By choosing the appropriate temperature, the resonators can achieve atomic-scale smoothness without deformation of the waveguide shape (Fig. 1e). This smoothness overcomes the typical scattering limitations at short wavelengths in integrated microresonators.

U-shape tapered-fibre couplers23 are used to measure Q factors from 458 nm to 1,550 nm. Intrinsic Q factors were determined from transmission spectra scans in the undercoupled regime (for some stronger coupled modes in the visible band, see Supplementary Fig. 5), in which resonant transmitted power and linewidth were used to infer loaded, coupled and intrinsic optical Q factors. A series of tunable external cavity lasers, each calibrated by a separate interferometer, were used to measure Q at each wavelength. Seven resonator transmission spectra at different wavelengths are shown in Fig. 1f, demonstrating intrinsic Q factors exceeding 180 million across a broad wavelength range from 458 nm to 1,550 nm, with the highest Q of 463 million at 1,064 nm, corresponding to a waveguide loss of 0.08 dB m−1. The waveguide loss α is calculated from resonators Q0 by (\alpha ({\rm{dB}},{{\rm{m}}}^{-1})=10\times {\log }_{10}({\rm{e}})\times \frac{2{\rm{\pi }}{n}_{{\rm{eff}}}}{{Q}_{0},\lambda }). Here, neff is the effective index of optical modes and λ is the wavelength. The atomic-scale smoothness, along with the broad ultralow-material-loss window of Ge-silica, enables it to break the short-wavelength limitation and achieve the lowest waveguide propagation losses among all integrated platforms within the visible and short-NIR ranges (Fig. 1b). Notably, the loss at 458 nm is 0.49 dB m−1, which is a 13-dB improvement over previous records.

CMOS-compatible fabrication

The fabrication process for this work is shown in Fig. 2a. In the devices studied, a 4-μm-thickness germano-silica layer (25 mol% GeO2, corresponding to an approximately 2% refractive index difference) is deposited around 270 °C (setting the anneal-free thermal budget for the fabrication flow) by plasma-enhanced chemical vapour deposition (PECVD) on a thick (15 μm) layer of thermal oxide on silicon wafer. The Ge-silica layer is then processed into ridge waveguides through ruthenium (Ru) and silica hard masking24, deep-ultraviolet (DUV) lithography and inductively coupled plasma etching. The Ru mask provides high selectivity in fluorine-based etches enabling high-fidelity deep etching of Ge:silica. To reduce the roughness-induced scattering loss limitation and achieve ultrahigh Q across the broadband spectrum, the entire wafer is subjected to furnace annealing at 1,000 °C for 12–18 h. As shown in Fig. 2b (bottom left), the sidewalls of the Ge-silica waveguides undergo reflow, removing the etch-induced roughness, whereas the thermally grown oxide (THOX) substrate remains unaffected.

Fig. 2: CMOS compatibility and process flow of Ge-silica ultralow-loss PICs.

a, Schematic of fabrication workflow for ultrahigh-Q Ge-silica resonators. ALD, atomic layer deposition. b, Photograph of Ge-silica PICs on silicon at wafer scale, SEM image showing the sidewall of an annealed waveguide (intentionally overetched to show the contrast in reflow compared with non-reflowed material) and cross-section of cladded waveguides. c, Anneal-free waveguide loss (C band) compared with temperature for state-of-the-art low-loss PICs11,44,45,46,47,48,49,50 compared with the present work. CVD, chemical vapour deposition; PVD, physical vapour deposition. d, Examples of monolithic/heterogeneous integration applications of ultralow-loss anneal-free Ge-silica PICs, including co-integration with III–V materials, organic electronics/photonics, thin-film lithium niobate, thermal-engineered quartz substrates and Ge-on-silicon photodetectors. Scale bars, 500 nm (b, bottom left); 5 μm (b, bottom right).

From here, an optional upper silica cladding layer can be deposited. Two cladding deposition methods are investigated in this work and applied to different devices. First, a 14-μm thick slightly P-doped (1.5 mol% P2O5) silica cladding is used for full acoustic confinement (Fig. 2b, bottom right). Second, a higher-quality inductively coupled plasma PECVD (ICP-PECVD) is used to protect the devices from contamination and degradation due to long-term atmospheric exposure. With the addition of this ICP-PECVD >6 μm cladding (Extended Data Fig. 2a), the Ge-silica PICs have been confirmed to maintain ultralow loss (optical Q factors >108, as shown in Extended Data Fig. 2b), when exposed to the atmosphere for over several months.

Owing to the high quality of the PECVD Ge-silica layer, high precision of DUV lithography and the well-developed etching process24, the Ge-silica microresonators can achieve ultrahigh Q even before annealing. Air-clad resonators without the reflow smoothing anneal are measured and attain ultrahigh Q of nearly 200 million and maintain ultrahigh Q across a similarly broad spectrum (Extended Data Fig. 1). This corresponds to a lowest waveguide loss of 0.15 dB m−1 at 1,550 nm. Figure 2c compares anneal-free waveguide loss (C band) of state-of-the-art integrated platforms with the present work, which exhibits a more than 10-fold reduction over the previous record. This anneal-free improvement in waveguide loss will enhance the performance of applications requiring co-integration with temperature-sensitive material such as III–V devices, organic electronics/photonics, thin-film lithium niobate, thermal-engineered quartz and Ge-on-silicon photodetectors (Fig. 2d).

Advantages and demonstrations

Beyond the ultralow loss across a broadband spectrum, the Ge-silica PICs have three more key advantages in dispersion engineering, acoustic confinement and thermal noise mitigation. To demonstrate them, soliton microcombs, stimulated Brillouin lasing (SBL) and SIL laser experiments are performed using the new platform. As these applications do not require monolithic or heterogeneous integration with other materials, annealed Ge:silica devices are used.

Single-ring soliton generation

Soliton microcombs represent the main new application area of microcavities and enable transfer of large-scale frequency comb technology to an integrated photonic chip. The Q factor of the microcavity determines the microcomb pumping power required as well as its coherence. However, at this time, the only ultrahigh-Q integrated platform—thin Si3N4—has a limited dispersion-engineering ability because of its thin waveguide thickness. This platform exhibits only normal dispersion and requires coupled-ring structures to generate soliton microcombs25. Here, an integrated Ge-silica resonator is used to demonstrate a new ability for an integrated design: soliton generation in a single ultrahigh-Q microring with anomalous dispersion. The microring resonator was designed to have anomalous dispersion and single-mode transmission as required for soliton generation (Supplementary Figs. 3 and 4). And the soliton mode family dispersion is characterized by measuring the frequency of all modes between 1,520 nm and 1,630 nm using an external cavity laser calibrated by a Mach–Zehnder interferometer (Fig. 3a). There is no observable mode-crossing-induced distortion of the mode family, therefore making the mode family well suited for soliton formation.

Fig. 3: Demonstration applications using the germano-silicate platform.

a, Dispersion of a Ge-silica single-ring resonator, Dint = ω**μ − ω0 − D1μ, where μ = 0 is assigned to the mode at 1,550 nm, D1/2π is the mean free spectral range and D2 is the group velocity dispersion (GVD) (positive for anomalous GVD). A fitting gives D1/2π = 21.2 GHz and D2/2π = 8.9 kHz. Inset, soliton step in transmission. b, Optical spectrum of generated soliton microcomb (left) and radiofrequency spectrum of microcomb beatnote (right). RBW, resolution bandwidth. c, Measured SBS gain spectrum of a fully cladded Ge-silica waveguide. The simulation result is overlaid on the measurement response. Insets, electric-field mode profile of the fundamental TE mode (left) and Brillouin-scattering induced displacement response (right). d, Optical spectrum of stimulated Brillouin laser (left) and radiofrequency spectrum of SBL beatnote (right). a.u., arbitrary units.

Soliton triggering and stabilization are performed using the frequency kick and capture-lock26 technique. A measured soliton spectrum generated using a 3-mm-diameter ring is shown in Fig. 3b (for Q characterization, see Supplementary Fig. 6). The spectral envelope exhibits a well-defined sech2 envelope. To confirm a stable repetition rate, the soliton pulse stream was detected and analysed using an electrical spectrum analyser. The electrical spectrum in Fig. 3b (right) gives a repetition rate near 21.2 GHz, and the resolution bandwidth of 1 kHz confirms pulse stream stability.

Acoustic confinement and Brillouin lasing

Apart from soliton microcombs, the stimulated Brillouin laser (SBL) is another device that has attracted considerable interest27,28. A key challenge for SBL operation is achieving simultaneous optical and acoustic waveguiding so as to enhance photon–phonon interactions—a feat hindered in conventional platforms by the low acoustic impedance of the silica cladding. Ge-silica PICs overcome this barrier through GeO2 doping, which reduces the longitudinal acoustic velocity of the waveguide core relative to the silica cladding, thereby enabling a fully transverse confined acoustic mode.

In the experiment, an approximately 25-mm-long waveguide is used to characterize the stimulated Brillouin scattering (SBS) gain spectrum and verify acoustical confinement by comparison to simulation. The waveguide core is 4 μm × 6 μm Ge-silica, with 15-μm thermal silicon oxide bottom cladding and 14-μm P2O5-doped silica upper cladding (the same cladding as shown in Fig. 2b, bottom right). Simulations of the normalized electric field and mechanical displacement distributions, shown in Fig. 3c, demonstrate simultaneous optical and acoustic wave confinement. Applying a pump–probe method (Methods), the SBS gain spectrum is obtained and agrees well with the simulation. The gain peak at 9.55 GHz has a full width at half maximum of 44.7 MHz, corresponding to a mechanical quality factor of about 210.

As a device demonstration, integrated Ge-silica resonators are used to generate a high-coherence Brillouin laser. To achieve phase matching for the Brillouin process near 1,550 nm, air-clad devices with diameters of approximately 20 mm were fabricated (for Q characterization, see Supplementary Fig. 7). Figure 3d (left) shows the optical spectrum of the lasing Stokes wave. The weaker pump signal peak in the spectrum arises from the need to collect the lasing Stokes wave in the propagation direction opposite to the pumping direction. Its strength is determined by residual reflection and backscattering in the measurement. The Brillouin lasing frequency shift is 9.68 GHz, which is lower than the typical 10.9 GHz shift observed in silica resonators18. Figure 3d (right) shows the microwave beatnote between the pump and Stokes waves, revealing its high coherence, as indicated by the high signal-to-noise ratio. This synergy of ultralow optical loss and engineered acoustic confinement unlocks low-noise Brillouin lasers for high-performance on-chip gyroscopes13, integrated microwave photonics and temperature/strain sensors.

LMA-enhanced hybrid-integrated low-noise laser

Narrow-linewidth lasers are pivotal for applications ranging from precision metrology to coherent optical communications. The recent integration of ultrahigh-Q microresonators with semiconductor diode lasers has markedly reduced the frequency noise of on-chip lasers and soliton microcombs by SIL4. The operational principle is shown in Fig. 4a. A resonant mode of the ultrahigh-Q microresonator acts as a frequency reference for stabilization, whereas backscattered light from the resonator provides optical feedback to narrow the linewidth of the diode laser. White frequency noise suppression scales quadratically with the quality factor (Q2) of the microresonator, whereas TRN scales inversely with the cavity mode volume. Here, TRN in the resonator mode is simulated using the commercial finite element analysis software COMSOL Multiphysics (Methods). The results, plotted in Fig. 4b, compare Ge-silica with low- and high-confinement Si3N4 resonators of identical diameters. Calculated mode areas are 28.06 μm2 (Ge-silica), 7.71 μm2 (thin Si3N4) and 1.33 μm2 (thick Si3N4). Owing to its substantially larger mode area, the Ge-silica platform has a greatly reduced TRN among the three integrated photonic systems.

Fig. 4: Hybrid integration of diode laser and germano-silicate device.

a, Schematic of SIL of the diode laser using external ultrahigh-Q microring. b, Simulated TRN spectra. Mode areas are 28.06 μm2, 7.71 μm2 and 1.33 μm2 for Ge-silica, thin Si3N4 and thick Si3N4, respectively. c, Single sideband frequency noise of SIL laser, indicating a Hz-level fundamental linewidth (FL). Inset, the image of a 1,550-nm DFB laser and integrated Ge-silica microring (indicated in false colour). d, Narrow-linewidth lasers at red, green and violet wavelengths, realized by SIL of Fabry–Pérot (FP) diode lasers to microrings. The fundamental linewidths are 15 Hz at 632 nm, 12 Hz at 512 nm and 90 Hz at 444 nm. e, Comparison of the fundamental linewidths of integrated lasers with state-of-the-art Si3N4 platforms30,31.

As a demonstration of this hybrid-integrated low-noise laser based on our platform, a commercial C-band DFB laser is endfire-coupled to the bus waveguide of a Ge-silica resonator chip with Q factor exceeding 100 million (Fig. 4c, inset, in which the microring resonator and bus waveguide are indicated in false colour). The laser chip, which is mounted on a thermoelectric cooler to avoid long-term drift, is able to deliver power of >100 mW at 1,548 nm. Optical feedback is provided to the laser by backward Rayleigh scattering in the microresonator, which spontaneously aligns the laser frequency to the nearest resonator mode. In experiments, as the phase accumulated in the feedback is critical to determining the stability of injection locking, the feedback phase is controlled by adjusting the air gap between the chips. At a specific phase detuning, a soliton crystal comb29 is generated (Supplementary Fig. 8a). The pump line of the comb output is filtered and directed to a self-heterodyne setup for frequency-noise characterization. The SIL operation boosts the laser coherence, with the frequency noise spectrum shown in Fig. 4c and achieves a Hz-level fundamental linewidth resulting from a 46-dB noise reduction compared with the free-running DFB laser. In the data, the increasing frequency noise at high-offset frequency is an artefact of spontaneous noise from the DFB laser and can be eliminated by out-coupling from a drop waveguide4.

The narrow-linewidth lasers are further extended into the visible spectrum by SIL of commercially available multimode Fabry–Pérot diode lasers to high-Q microrings. Under SIL, the devices become single mode with high side-mode-suppression ratios (Supplementary Fig. 8b). Also, fundamental linewidths of 15 Hz at 632 nm, 12 Hz at 512 nm and 90 Hz at 444 nm are achieved (Fig. 4d). Compared with state-of-the-art integrated lasers30,31, the Ge:silica platform provides more than 20 dB improvement in fundamental linewidth across the visible spectrum (Fig. 4e), holding the potential to redefine performance benchmarks in integrated visible photonics14.

Discussion

In summary, we have developed a Ge-silica ultralow-loss platform that markedly advances integrated photonics (see detailed comparison between Ge-silica and the state-of-the-art low-loss Si3N4 in Supplementary Table 1). This new platform has achieved a >10 dB improvement in both the violet wavelength range and anneal-free Q. The unique material and geometric properties of these waveguides enable dispersion engineering for soliton microcomb generation, simultaneous confinement of acoustic and optical modes, and suppression of thermal refractive noise. They also maintain ultrahigh Q factors in both polarizations, and enhance power-handling abilities for high-power mode-locked lasers. Moreover, the photosensitivity of Ge-silica32 allows UV-written optical gratings for applications forming the basis of fibre Bragg gratings in photonic systems. By contrast, the small index contrast of Ge:silica on silica leads to larger bending losses, which limit integration density. These can be mitigated by using 3D integration, increasing Ge doping or operating at shorter wavelengths. On account of the quadratic33 and cubic dependence34 of nonlinearity on optical Q factor, the low nonlinearity of silica can be readily compensated by exploiting ultrahigh-Q devices. Moreover, electro-optic tuning can be enabled through heterogeneous integration with lithium niobate or lithium tantalate.

The surface-tension-induced smoothness of the waveguides bypasses Rayleigh scattering loss limitations, greatly extending integrated photonics at shorter operational wavelengths. Specifically, by integrating visible diode lasers with ultralow-loss Ge-silica resonators, Hz-level, narrow-linewidth lasers31 and microcombs35 are possible in the visible band. With further development in deposition and fabrication techniques, the Ge-silica PICs hold the potential to reach their material-limited waveguide loss of 0.2 dB km−1 (corresponding to a microresonator Q factor of >100 billion). This fibre-like optical loss for PICs would revolutionize certain fibre-based technologies by moving their manufacture to CMOS foundries, including solid-state gyroscopes, advanced frequency comb technology for precision portable clocks, large-scale low-loss circuits for quantum computing, high-power amplifiers and mode-locked lasers.

Methods

High-quality upper silica cladding deposition

The upper cladding of these germano-silicate resonators was deposited by ICP-PECVD (Unaxis VLR) at 250 °C using a deuterated silane based precursor and oxygen plasma. To reduce the losses due to the stress optic effect of the cladding, while also repairing the solarization of the germano-silicate due to direct plasma exposure, the devices studied underwent a 20-min 1,000 °C rapid thermal anneal between each deposition of 500 nm of cladding. As a test, we deposited a 6-μm thickness upper cladding (Extended Data Fig. 2a), observing complete filling of the coupling gap. This encapsulation effectively protects the device from environmental contamination, enabling the maintenance of ultrahigh Q up to 160 million (Extended Data Fig. 2b) over several months. It is noted that the original Q factor before cladding deposition was measured at approximately 250 million. This decrease in Q factor with upper cladding, partial Q recovery through thermal treatment, yet never fully recovering the original Q values, is consistent with what was previously observed in ULL silicon nitride in ref. 51, in which the same ICP-PECVD system was used. The possible solutions to this would be to switch to a deposition type that avoids exposure to a plasma or using better precursors, such as low-pressure chemical vapour deposition or tetraethoxysilane PECVD52.

Brillouin gain spectrum measurements and simulations

To achieve high sensitivity, we use a dual-intensity-modulation pump–probe technique53. The test device has a 14-μm-thick 1.5 mol% P2O5-doped silica upper cladding, designed to fully confine both optical and acoustic fields. This slightly phosphorus-doped silica layer was deposited by PECVD, chosen for its ability to rapidly produce thick, stress-free films. Post-cladding characterization shows waveguide propagation loss below 0.5 dB m−1 and edge coupling loss of 1.4 dB per facet. The SBS gain characterization uses counterpropagating pump and probe lasers injected through facet couplers, with both lasers operating near 1,560 nm. The pump laser is intensity-modulated at a frequency of 10 MHz and the probe laser is intensity-modulated at a frequency of 10.075 MHz. The transmission signal of the probe laser is routed to a lock-in amplifier for gain measurement, using a 75-kHz reference beatnote of the two modulation frequencies. The SBS gain spectrum is obtained by frequency-scanning the probe laser over a 20 GHz range from red- to blue-detuning relative to the fixed pump frequency. Both optical and acoustic fields are calculated using the finite element method based on the model described in ref. 54. The material properties used in the simulation are as follows: refractive index of 1.478, 1.451 and 1.449; density of 2,750, 2231 and 2,200 kg m−3; Poisson’s ratio of 0.180, 0.166 and 0.170; Young’s modulus of 64.8, 72.6 and 73.0 GPa; Brillouin linewidth of 59 MHz, 28 MHz and 17 MHz; and photoelastic coefficient p12 of 0.2373, 0.2264 and 0.2260, for Ge-silica (core), P-silica (upper cladding) and thermally grown silica (bottom cladding), respectively.

TRN simulations

The TRN in Fig. 4b of Ge-silica, thin SiN and thick SiN are numerically simulated in a finite element solver (COMSOL Multiphysics) using a model based on the fluctuation-dissipation theorem55. For each of the three materials, the simulation is based on a ring microresonator with a diameter of 3 mm. The rectangular waveguide dimensions of the Ge-silica, thin SiN and thick SiN microresonators are 12 μm × 4 μm, 8 μm × 0.1 μm and 2 μm × 0.8 μm, respectively (width × height). These dimensions of thin SiN and thick SiN are taken from refs. 4,56. The Ge-silica waveguide is air-cladded, whereas the thin and thick SiN waveguides have silica cladding. Material parameters used in the simulation are as follows: for Ge-silica, the thermo-optic coefficient 1.27 × 10−5 K−1, heat conductivity 1.38 W m−1 K−1, heat capacity 740 J kg−1 K−1, density 2.2 × 103 kg m−3; for SiN, the thermo-optic coefficient 2.45 × 10−5 K−1, heat conductivity 30 W m−1 K−1, heat capacity 800 J kg−1 K−1, density 3.29 × 103 kg m−3; for the silica cladding of the SiN waveguide, the thermo-optic coefficient 1.2 × 10−5 K−1, heat conductivity 1.38 W m−1 K−1, heat capacity 740 J kg−1 K−1, density 2.2 × 103 kg m−3. The ambient temperature is set at 300 K.

Data availability

The data presented in the main text are available from Zenodo57. All other data are available from the corresponding authors upon request.

Code availability

The codes used in the study are available from the corresponding authors upon request.

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