Optical frequency combs, characterized by their precisely spaced, sharp spectral lines that serve as a ‘frequency ruler’ for light, are indispensable tools in numerous fields, from precision metrology and atomic clocks to high-capacity telecommunications and molecular spectroscopy^3,4,5,6,7. Fuelled by their potential practical applications, the drive to miniaturize frequency combs into chip-scale integrated devices, known as microcombs, has recently accelerated at a remarkable pace⁸. Conventional optical frequency combs, produced through mode-locked lasers and synchronously pumped optical parametric oscillators (OPOs)^1,2, are large and require substantial infrastructure, such as complex feedback systems or high-power lasers. As a result, their cost is high, and their use outside laboratory settings is limited. Two principal methods for creating integrated frequency comb sources suitable for smaller, deployable devices have been explored in response. The first involves third-order χ⁽³⁾ or Kerr optical nonlinearity, with successful demonstrations in materials such as silica, silicon nitride, aluminium nitride, silicon carbide and lithium niobate (LN)^{13,14,15,16,17}. The second strategy uses the electro-optic (EO) effect, which has been realized in resonant (Fig. 1a) and non-resonant integrated thin-film LN devices^10,18,19. Despite these remarkable advances, EO and Kerr combs face several challenges. These combs are often limited in their efficiency, exhibit a strong pump background, suffer from limited tunability and display an exponentially decreasing comb line intensity for the lines distant from the pump. Moreover, Kerr frequency combs demand sophisticated control and become substantially more challenging to operate at a smaller free spectral range (FSR).

a, In a standard EO comb, an optical resonator conducts EO modulation on a single laser pump. This results in an output of equally spaced lines with intensities that decay exponentially. b, The FM-OPO uses the second harmonic (SH) as a pump and emits light at the fundamental frequency. An EO modulator couples the neighbouring cavity modes, creating an evenly distributed output comb. c, The microscope image shows a thin-film LN chip housing eight FM-OPO devices. One device has a footprint of around 1 × 10 mm² (highlighted with a dashed rectangle). FH, fundamental harmonic. Scale bar, 2 mm.

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In this study, we propose and demonstrate a previously unknown type of microcomb that combines the advantages of both EO and Kerr combs, merging nonlinear optical processes with EO modulation in an integrated device. Specifically, our structure accommodates both optical parametric amplification and phase modulation within a single cavity, thereby facilitating the generation of a frequency-modulated optical parametric oscillator^20,21 (FM-OPO; Fig. 1b). Remarkably, unlike in conventional Kerr and EO combs, the dynamics in our system do not result in pulse formation, making the output more closely resemble that of a frequency-modulated laser. In contrast to a serrodyne approach, the radio-frequency (RF) modulation we use has only a single Fourier component. This strategy maintains the operational simplicity characteristic of EO combs while achieving substantially broader bandwidths than those attainable through modulation alone. Furthermore, our technique gives rise to a flat-top output comb with most lines within 3 dB of the mean, an optimal spectral distribution for many applications, while avoiding unwanted nonlinearities that manifest at large pulse peak powers²². Finally, the FM-OPO exhibits impressive efficiency, converting a substantial fraction of the pump light into comb lines while demanding only modest RF power inputs for operation.

To demonstrate the integrated FM-OPO, we turn to thin-film LN for its strong second-order optical nonlinearity and EO effect. Thin-film LN has recently emerged as a platform for integrated nanophotonics²³ through demonstrations of efficient EO modulators^24,25, EO combs^10,18, periodically poled LN waveguides for frequency conversion^26,27,28, quantum light generation^29,30, resonant second-harmonic generation and OPOs^31,32,33, and integration with complex photonic integrated circuits for applications such as laser control³⁴ and quantum measurements³⁵. The above demonstrations are either based on the EO effect that transfers energy between optical modes separated by the RF frequency or the χ⁽²⁾ nonlinearity that can provide broadband gain. Combining these two distinct capabilities forms the foundation for the integrated FM-OPO. Moreover, our choice of LN is motivated by its strong potential for large-scale manufacturability as evidenced by efforts now pursued in industry^36,37.

Both Kerr and EO comb generation fundamentally rely on mode locking, which subsequently leads to the formation of pulses. However, this process inherently introduces a strong frequency-dependent variation in the intensity of the comb lines that decay exponentially with their offset from the centre. Another considerable challenge posed by pulse formation is the inefficient use of pump power, as a continuous-wave pump overlaps only with a small part of the circulating field. Recent advancements have started to address this issue, mainly by exploiting auxiliary resonances^18,38,39 and using pulsed pumps⁴⁰. Finally, pulse formation leads to large intracavity peak powers that can engage other unwanted nonlinearities and make comb formation challenging in integrated platforms²². We discover here that incorporating parametric gain into an EO-modulated cavity leads to a frequency comb without necessitating pulse formation. Our device demonstrates high efficiency, reduced pump background, and spectral flatness. In contrast to the extensive engineering and operation dynamics required for similar results by the Kerr combs, the FM-OPO offers an alternative versatile solution. Moreover, unlike pure EO combs, the FM-OPO requires only modest RF power, enabling scalability and applications in deployable sensors. Despite the modulation being close to the cavity resonance mode spacing, the dynamics of our system strikingly resemble those of a frequency-modulated laser^12,41,42. As in a frequency-modulated laser, we will see that the optical frequency of the signal is swept across a bandwidth BW at the rate of the RF modulation Ω.

We first consider the situation without any modulation. We assume that we operate the OPO non-degenerately so that it emits signal and idler tones at mode number offsets ±n_osc from a central mode with frequency ω₀ close to half of the pump frequency ω_p/2. As we introduce RF modulation at frequency Ω characterized by a mode-coupling rate M, these signal and idler tones are simultaneously subject to gain and modulation. The pairing of these effects around the signal and idler creates conditions that mirror the dynamics of a frequency-modulated laser, in which phase-insensitive gain and modulation coexist.

In a frequency-modulated laser, the limiting behaviour that prevents mode locking arises from a detuning between the FSR of the cavity and the drive frequency Ω. The frequency-modulated laser then transitions to chaotic and mode-locked states as this detuning is reduced and the bandwidth is increased to approach the gain bandwidth of the medium or a limit set by the cavity dispersion¹². The oscillation bandwidth of the FM-OPO is limited by the dispersion of the cavity, characterized by mode frequencies ω_n = ω₀ + ζ₁ × n + ζ₂/2 × n², where ζ₁ and ζ₂ are the cavity FSR near ω₀ and the second-order dispersion, respectively. Under the regime considered, our device avoids the transition to mode-locking behaviour. The signal and idler modes are far separated and experience local FSRs near ±n_osc that differ from each other by 2n_oscζ₂. Moreover, the parametric nature of the process necessitates the simultaneous formation of combs at both signal and idler frequencies. Therefore, in the assumed non-degenerate regime, there is always effectively a drive detuning when we consider both signal and idler combs. This results in dynamics that closely mirror those of a frequency-modulated laser with detuned driving, in which continuous frequency sweeping is observed rather than pulse formation. The effective bandwidth is given by

where Γ is the modulation index, and the signal and idler tones are frequency modulated as \({a}_{{\rm{s,i}}}(t)\approx {A}_{{\rm{s,i}}}{{\rm{e}}}^{-{\rm{i}}{\omega }_{{\rm{i}}}t}{{\rm{e}}}^{\mp {\rm{i}}\varGamma \sin (\varOmega t)}{{\rm{e}}}^{{\rm{i}}{\omega }_{{\rm{p}}}t/2}\). The bandwidth formula aligns well with the established expression for the frequency-modulated laser bandwidth BW ∝ MΩ/(Ω − FSR) (ref. ¹²), with the correspondence being that the frequency-modulated laser detuning Ω − FSR is replaced by the detuning n_oscζ₂ between the drive and local FSR in the FM-OPO. Finally, we note that there are conditions for which the above analysis no longer holds, for example, at (near-)degenerate OPO operation leading to smaller n_osc, at substantially larger M or for dispersion-engineered waveguides that may match the local signal or idler FSRs. Bulk phase-modulated OPOs have already been demonstrated^20,21. In contrast to the FM laser, the FM bandwidth and the gain bandwidth of the FM-OPO are both defined through dispersion engineering. We leave the engineering and study of the dynamics of integrated phase-modulated OPOs in a wider set of operating regimes to future work.

We demonstrate an optical frequency comb generator based on an FM-OPO integrated on a chip (Fig. 1c). The device evenly distributes 11 mW of optical power over 200 comb lines using 140 mW of C-band optical pump power and 200 mW of RF modulation power. Comb lines are spaced by about 5.8 GHz. We base our device on a racetrack resonator in thin-film LN on an insulator with intrinsic quality factors of around Q_i ≈ 10⁶. This resonator holds within it an EO modulator, an optical parametric amplifier and a high-efficiency wavelength-selective coupler that nearly fully transmits the 780 nm pump while keeping the C-band excitation within the cavity. Figure 2a shows a schematic of the device, whereas Fig. 2b shows a microscope image of a single FM-OPO device. The coupler enables our device to operate as a doubly resonant OPO in which the pump passes through the optical parametric amplifier but is non-resonant in the cavity. One straight section has gold electrodes patterned next to it, enabling EO modulation of the cavity (Fig. 2b, left inset). The other straight section of the cavity is a periodically poled LN waveguide that provides parametric gain when pumped with the second harmonic (see Fig. 2b, right inset, for a second-harmonic microscope picture of the poled thin-film LN). In the Methods section, we describe the design and characterization of the waveguides and cavity in detail.

a, The device features a racetrack resonator with an intracavity waveguide coupler, which allows only the fundamental harmonic to resonate while enabling the second harmonic to traverse the device once. The straight section of one racetrack contains a periodically poled waveguide for second-order optical nonlinearity, whereas the other couples to microwaves through on-chip electrodes. A single-pass waveguide on the same chip generates the pump of the OPO at the second-harmonic frequency, which is separated from the input C-band laser light using a series of filters. b, The microscope image shows the FM-OPO racetrack resonator, with the centre removed for clarity. The dark lines represent integrated waveguides. The yellow structure atop the racetrack is a gold microelectrode slot waveguide that links with microwaves. The SEM micrograph in the left inset depicts the waveguide between the electrodes. The bottom of the racetrack is periodically poled, as shown in the second-harmonic microscope image of the poled film in the second inset. The waveguide circuit in the bottom-right corner is a pump-filtering section after the second-harmonic generation (SHG) waveguide. c, The output spectrum of the FM-OPO produces approximately 200 unique oscillator modes at the signal and idler frequencies using about 140 mW of input optical power and 200 mW of RF power. The dark-blue line represents a coupled-mode theory simulation result. The bottom-right inset magnifies into the flat area of the comb, whereas the top-right inset shows an RF power spectral density (PSD) of the FM-OPO output, detected using a fast photodiode with peaks at multiples of the cavity FSR. CME, coupled-mode equation; OPA, optical parametric amplification; PPLN, periodically poled LN. Scale bars, 200 μm (b, main image); 10 μm (b, left inset); and 20 μm (b, right inset).

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We generate the 780-nm pump on the same chip in a separate periodically poled LN waveguide by second-harmonic generation. We filter out the original pump field through three on-chip filters of the same design as the intracavity coupler. The high second-harmonic generation efficiency enables us to achieve considerable optical pump powers using only a standard commercial C-band laser. Figure 2c shows an example FM-OPO output spectrum when the device is pumped with around 140 mW of fundamental-harmonic optical power (corresponding to around 100 mW of second-harmonic power) and 200 mW of RF power, equivalent to about 4.5 V peak voltage. We plot an EO comb generated using the same RF power within the same cavity in grey for comparison. We observe a flat comb formation around signal and idler wavelengths and no substantial background from the pump. The measured output aligns with our coupled-mode theory model (thick dark-blue line) described below. The bottom-right inset in Fig. 2c shows individual lines in a flat spectrum spaced by around 5.8 GHz. The observed contrast of around 15 dBm between maxima and minima results from the limited resolution of the optical spectrum analyser rather than the nature of the FM-OPO. The top-right inset in Fig. 2c shows the result of collecting the output using a fast photodetector and an RF spectrum analyser. In the RF spectrum, we observe narrow lines spaced by the multiples of the cavity FSR, resulting from the FM-OPO sweeping over a frequency-dependent output coupler (see the Methods for details).

We can understand nearly all the salient features of the observed spectra in the context of an approximate time-domain coupled-mode theory analysis. We also use this formulation to derive the formula for the comb bandwidth shown in equation (1), which agrees well with observations 4b. We define mode amplitudes a_n to represent the field amplitudes for the nth mode around the fundamental-harmonic frequency, where n = 0 corresponds to the fundamental mode closest to half of the pump frequency. In this context, b represents the amplitude of the second-harmonic pump field. Each mode n has a natural frequency given by the cavity dispersion with ζ₁/2π ≈ 5.8 GHz and ζ₂/2π ≈ −11 kHz corresponding to the cavity FSR and the second-order dispersion, respectively. Other key parameters include the laser drive detuning Δ ≡ ω_p/2 − ω₀, and the RF drive detuning from the FSR δ ≡ Ω − ζ₁. The mode coupling due to modulation M, which is proportional to the RF drive voltage, and the nonlinear coupling rate g provide the critical ingredients for realizing the comb dynamics. We also include the loss rates of the considered field amplitudes, κ_a,n and κ_b. The rate κ_b corresponds to that of an extremely lossy single-pass ‘cavity’ and enables us to approximate our DRO in this coupled-mode theory formulation. We derive all of the model parameters from independent simulations, as well as experimental and theoretical analysis (refer to the Methods section and Supplementary Information for more details). The resulting coupled-mode equations are

There are two main approximations in these equations. First, we represent the pump field as the excitation of a very lossy mode b, solutions involving substantial spatial variations of the pump field along the waveguide cannot be represented accurately by this model. Second, we include only coupling between modes n and −n—we ignore the weaker coupling between modes with nearby n numbers. For example, coupling between n and −n + 1 can be present and may become stronger as a function of pump wavelength. Tuning the pump wavelength and consequently the detuning Δ over a cavity FSR changes the mode pairs that are amplified (Fig. 3a). The device parameters are shown in Extended Data Table 1.

a, We examine the pump-wavelength tuning of a doubly resonant OPO. The blue traces relate to optical spectrum analyser measurements. The output wavelength of the DRO is determined by the frequency matching between the signal and idler modes with respect to the pump. The thin grey lines, recurring every 1/2 free spectral range, correspond to the theoretical model. b, The pump-wavelength tuning of the FM-OPO aligns with the pure OPO trend. However, the entire frequency-modulated clusters of modes tune synchronously along the energy-conservation lines. For both a and b, one division on the y axis corresponds to a 50-dB change in the detected optical power for each optical spectrum analyser trace.

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We tune the output wavelength in the FM-OPO through small adjustments to the pump wavelength, enabling the output to span the full range of the gain spectrum. This tuning is predominantly influenced by the cavity dispersion, mirroring the characteristics observed in an unmodulated OPO^32,43. We show the OPO tuning behaviour in Fig. 3a. The blue traces correspond to measurements with an optical spectrum analyser, whereas the grey lines present the predicted tuning behaviour based on the waveguide dispersion. The FM-OPO exhibits a similar tuning pattern, as shown in Fig. 3b. Here, the comb clusters closely follow the expected tuning. By adjusting the pump wavelength by 23  pm (or 2.9 GHz), which equates to half of the FSR of the cavity, we can access bandwidth of approximately 70 nm (or 8.7 THz) for both FM-OPO and OPO.

We measure the spectra generated by the FM-OPO using an optical spectrum analyser. We find that the device operates continuously and robustly in a non-degenerate mode at around n_osc ≈ 800. In this regime, we expect equation (1) to hold to high accuracy. We pump the device at 1,554 nm with about 140 mW. We step the EO coupling rate of the 5.8-GHz EO modulation between 0 MHz and around 510 MHz by varying the RF power supplied to the chip. As shown in Fig. 4a, we observe a frequency comb develop. Several additional comb clusters labelled (−n_osc + 1, n_osc) and (−n_osc + 1, n_osc + 1) appear at a drive exceeding M/2π ≈ 360 MHz. Although the single-cluster comb states that are generated for M below 250 MHz are easier to understand and model, and will likely be more useful in a practical system, we also present the states that arise at larger values of M, and that result in multiple FM-OPO clusters. These are predicted by our theoretical analysis and described in more detail in the Methods. We plot only the signal combs (blue detuned) and omit the idler combs (red detuned) for clarity; we provide full spectra in Extended Data Fig. 8. The measured spectral peak at around 1,554 nm corresponds to a slight leakage of the original fundamental-harmonic pump into the cavity. We count the number of generated lines within the 3 dB bandwidth of the mean comb power and plot this in Fig. 4b. We observe good agreement between the data, numerical solution of the coupled-mode equations (2) and (3) (blue-shaded region) and the analytical expression for the FM-OPO given by equation (1) (dashed line). At the highest EO modulation rate of around 1.2 W, we observe more than 1,000 comb lines oscillating together within −30 dB from the flat-top mean power (see Extended Data Fig. 8e for the full spectrum).

a, Evolution of combs with the EO drive. As the EO coupling increases, we observe comb growth and the emergence of secondary combs that couple (−n_osc + m, n_osc) modes, aligning with several grey lines in Fig. 3. We combine high-resolution (approximately 20 pm) measurements from areas with detectable signals and low-resolution readings from the rest of the range. We primarily focus on the signal around 1,515 nm for simplicity. The peak around 1,554 nm is because of a minor leakage of the initial pump into the cavity. b, The maximum count of individual oscillating lines in the FM-OPO as a function of EO coupling. The faint blue region corresponds to the prediction from the coupled-mode theory. We plot the comb count predicted with the FM-OPO theory with a dashed line. c, We measure the depletion of the FM-OPO optical pump of around 93%, corresponding to the conversion efficiency of around 34%. The inset shows the normalized second-harmonic generation pump (orange) and FM-OPO (blue) when changing the pump wavelength at M/2π ≈ 30 MHz. The contrast between the second-harmonic maximum and minimum defines depletion. d, The output power of the pure OPO as a function of the pump power at the fundamental-harmonic frequency. The pump initially generates a second harmonic in a single-pass waveguide that later drives the OPO. A line fitting to the data shows a nonlinear coupling rate g/2π of approximately 12 kHz. We describe the displayed measurement and simulation uncertainties in the Methods.

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The FM-OPO operates with high efficiency, converting around 34% of the input second-harmonic light into comb lines. First, the intracavity conversion efficiency is high, exceeding 90%, based on the pump depletion measurement in Fig. 4c. We chose to use depletion because it is self-calibrating and enables us to calculate the efficiency based on the contrast between the measured maxima and minima of the normalized second-harmonic power (see the Supplementary Information for details), visible when tuning the pump wavelength, as shown in the inset. Next, the intracavity comb is out-coupled with the cavity escape efficiency η_a ≈ 0.36, which limits the total efficiency of our device. Note that the depletion and the conversion efficiency do not depend on the RF drive strength. However, the efficiency depends on the optical pump power and is maximized at around four times the threshold. The output power of the FM-OPO resembles a typical behaviour of an unmodulated OPO in Fig. 4d, in which we observe a threshold of about 47 mW second-harmonic power and nonlinear coupling rate g/2π ≈ 12 kHz, lower than the predicted 67 kHz, which we attribute to operating at non-perfect phase matching Δk ≠ 0. The low power requirements of our device enable direct integration with chip-based lasers^35,44,45 to build self-contained comb generators.

We have successfully demonstrated a new type of integrated comb generator and established its fundamental operating principles. Our device demonstrates exceptional brightness, flatness and efficiency while retaining robust operational dynamics. Increasing the bandwidth and using the nonlinearities of LN will enable f−2f locking⁴⁶, leading to a truly coherent frequency comb in the stricter sense. Group velocity matching signal and idler will enable engineering parametric gain bandwidth to cover as much as 3–4 μm (ref. ⁴⁷), expanding the use of the FM-OPO in mid-infrared spectroscopy. Given that our initial demonstration still has the potential for marked improvements in optical bandwidth by dispersion engineering, RF power consumption by resonant enhancement and optical conversion efficiency by improved out-coupling, this breakthrough opens the door to a new class of deployable optical frequency combs. For the application of these combs to the problems of spectroscopy, the versatility of the LN material platform allows for spectral coverage from blue light⁴⁸ into the mid-infrared^27,47, enabling their use in fields such as medical diagnostics⁴⁹, process control in agriculture, food production and various industrial sectors^50,51. Although the comb teeth spacing of our current devices is around 5.8 GHz, our platform can achieve an FSR of 50 GHz to meet telecom standards and even exceed 100 GHz, given established modulators²⁴. Therefore, we anticipate flat-top combs generated with FM-OPOs to find applications as sources in fibre communication systems. Moreover, they are invaluable for ranging applications using FMCW LiDAR⁵².

Device design and fabrication

We design our waveguide geometry to maximize the normalized efficiency and interaction rate. Extended Data Fig. 1a shows a schematic of the periodically poled, X-cut LN waveguide. We chose the ridge height h = 300 nm, slab thickness s = 200 nm, top width w = 1.2 μm and SiO₂ cladding thickness c = 700 nm. We find the guided modes by numerically solving Maxwell’s equations with a finite-element solver (COMSOL). Extended Data Fig. 1a shows the E_x field distribution for a mode at 1,550 nm. Extended Data Fig. 1b presents the bands of the effective index as a function of wavelength in our waveguide geometry. The blue line highlights the fundamental transverse electric mode we use in our nonlinear waveguide and EO modulator. The difference between the effective index at the fundamental and second-harmonic frequency Δn_eff results in phase mismatch that we compensate for with periodic poling with a period of around Λ = λ_SH/Δn_eff = 3.7 μm. The LN waveguide forms a racetrack resonator with an intracavity directional coupler designed to close the resonator for the fundamental harmonic but ensures that the second-harmonic pump does not circulate. We call this design a ‘snail resonator’. All the waveguide bends are defined by Euler curves to minimize light scattering between straight and bent waveguide sections.

We periodically pole the thin-film LN before the waveguide fabrication by patterning chromium finger electrodes on top of an insulating SiO₂ layer. Extended Data Fig. 1c shows a scanning electron microscope (SEM) micrograph of a poling electrode. Next, we apply short pulses on the order of 1 kV to invert the ferroelectric domains and then verify the poling with a second-harmonic microscope. Extended Data Fig. 1d shows a periodically poled film. In the second-harmonic microscope picture, the black areas on the sides of the image correspond to the metal electrodes. The oblong shapes stretching between fingers correspond to the inverted LN domains. White regions at the centre of the inverted domains correspond to the poling that extends throughout the full depth of the thin-film LN. We pattern the critical waveguides within the fully poled film regions by aligning the electron-beam lithography mask in the waveguide patterning step.

Extended Data Fig. 2 presents the fabrication process flow. We start with a thin-film LN on an insulator chip (Extended Data Fig. 2a). We use 500 nm LN film bonded to around 2 μm of SiO₂ on a silicon handle wafer (from NanoLN). Then, we deposit about 100 nm of silicon dioxide using plasma-enhanced chemical vapour deposition (PlasmaTherm Shuttlelock PECVD System), which serves as a protective layer and prevents leakage current during poling. We pattern 100 nm thick chromium electrodes (evaporated with Kurt J. Lesker e-beam evaporator) on top of the insulating layer through electron-beam lithography (JEOL 6300-FS, 100-kV) and lift-off process and apply short voltage pulses to invert the LN domains (Extended Data Fig. 2b). Next, we remove the chromium and SiO₂ layers with chromium etchant and buffered oxide etchant to obtain a poled thin-film LN chip (Extended Data Fig. 2c). We follow with waveguide patterning using JEOL 6300-FS electron-beam lithography and hydrogen silsesquioxane mask (FOx-16). We transfer the mask to the LN material using dry etching with an argon ion mill (Extended Data Fig. 2d). After the waveguide fabrication, we pattern another lift-off mask with electron-beam lithography to pattern electrodes for our EO modulators (Extended Data Fig. 2e). We use 200 nm of gold with a 15-nm chromium adhesion layer evaporated with the e-beam evaporator. We clad the entire chip with a layer of 700-nm thick SiO₂ deposited with a high-density plasma chemical vapour deposition using PlasmaTherm Versaline HDP CVD System (Extended Data Fig. 2f) and open vias to access electrodes using inductively coupled plasma reactive ion etching (Extended Data Fig. 2g). We finish preparing the chip facets for light coupling by stealth dicing with a DISCO DFL7340 laser saw.

Experimental setup

We characterize the FM-OPO and OPO response of our devices using the setup in Extended Data Fig. 3. We colour-code the paths intended to use with various signals: light orange corresponds to the fundamental-harmonic light (around 1,500–1,600 nm), the blue path corresponds to the second-harmonic (around 750–800 nm), and green corresponds to the RF signals. We drive our devices with a tunable C-band laser (Santec TSL-550, 1,480–1,630 nm) that we amplify with an erbium-doped fibre amplifier to around 1 W. We attenuate the optical power most of the time. We control the optical power to the chip with an MEMS variable optical attenuator (from OZ Optics) and calibrate the power using a 5% tap and a power meter (Newport 918D-IR-OD3R). The wavelength of the laser is controlled in a feedback loop using a wavelength meter (Bristol Instruments 621B-NIR). The light then passes through a fibre polarization controller and couples to the chip facet through a lensed fibre. We deliver RF signals to the chip through a ground–signal–ground probe (GGB Industries Picoprobe 40A). We use Keysight E8257D PSG Analog Signal Generator as an RF source and amplify it with a high-power amplifier (Mini-Circuits ZHL-5W-63-S+). We place a circulator before the chip to avoid any reflections into the source and terminate the reflected port after passing it through a 20-dB attenuator.

The generated light is split between two paths with a 1,000-nm short-pass dichroic mirror (Thorlabs DMSP1000). The two paths are connected to the InGaAs and Si avalanche photodiodes (Thorlabs APD410A and Thorlabs APD410) to detect the fundamental- and second-harmonic power, respectively. VOAs precede both avalanche photodiodes (APDs) to avoid saturation and increase the dynamic range of the measurements (HP 8156A and Thorlabs FW102C). Part of the fundamental-harmonic path splits into an optical spectrum analyser (Yokogawa AQ6370C) and a fast photodetector (New Focus 1554-B-50), the response of which is characterized by an RF spectrum analyser (Rohde & Schwarz FSW26).

Intracavity coupler characterization

We characterize the performance of the intracavity coupler using a smaller racetrack resonator with a 2-mm straight section. Extended Data Fig. 4a shows the normalized transmission of the cavity (Extended Data Fig. 4b). The variation in intrinsic and extrinsic quality factors changes cavity-mode contrast across the wavelength range. This results in a transition from an undercoupled cavity at 1,500 nm to critically coupled at 1,550 nm and overcoupled at 1,580 nm. We confirm this by fitting the quality factors for all modes. For instance, in Fig. 4c, we find Q_i ≈ 2.5 × 10⁶ and Q_e ≈ 0.8 × 10⁶. Extended Data Fig. 4d plots the quality factors against wavelength, highlighting a Q_i peak near 1,580 nm, corresponding to the maximum coupler transmission. We use the same coupler in the FM-OPO resonator, but we increase the straight section length to 10 mm, resulting in flattened Q_i wavelength dependence.