a, Photograph of a MgF₂ reference microresonator. b, Photograph of a Si₃N₄ nonlinear microresonator. The insets show the cross-sectional profile of the fundamental mode of each microresonator. c, Concept of two-point OFD. d, OFD error signal generation and feedback control of the soliton microcomb. PD, photodetector.

Two-point OFD operations based on these two devices are described in Fig. 1c. Two lasers (f_A and f_B) are simultaneously stabilized to two modes of the MgF₂ microresonator. The spatial overlap between these modes provides common-mode noise rejection once the residual locking noise is below the thermal noise. It results in a mutual phase noise for f_B – f_A that is lower than that of each laser, and we use f_B – f_A as the frequency reference for further division. As shown in Fig. 1d, the microresonator is excited by a continuous-wave pump laser to generate a soliton microcomb with repetition frequency f_r. The reference lasers are combined with two adjacent comb lines indexed by m and n relative to the pump. The photodetected beatnotes are then downmixed to f_B – f_A – (m – n)f_r and locked to a local oscillator (LO) with frequency f_LO. This locking is commonly achieved by adjusting the pump frequency, which regulates f_r through the Raman-induced soliton self-frequency shift³⁷. Photodetection of the soliton pulse train provides the stabilized repetition frequency as

If the phase noise of the LO is not dominant, we can anticipate that the phase noise of f_r is reduced by a factor of (m – n)² compared with that of f_B – f_A.

Optical frequency references

We first characterize the performance of the frequency reference. To ensure stable operation, we enclose the MgF₂ microresonator in a metallic package with a tapered fibre coupler and a thermoelectric cooler (Fig. 2a). The packaging process does not affect the resonator’s Q factors, which can reach nearly 3 billion under near-critical coupling conditions. The Q factor and coupling can sustain for months without degradation, even in vibrational environments (Extended Data Fig. 1).

Fig. 2: Characterization of optical frequency references.

a, Photograph of the packaged MgF₂ reference microresonator. b, Typical transmission spectrum of resonance. The intrinsic quality factor Q_o is derived from Lorentzian fitting as 2.8 billion. c, Transmission spectra spanning more than the FSR. d, Measured relative frequency noise of the free-running and locked reference lasers. The simulated individual and relative thermorefractive noise of the references are also plotted, between which lies the regime accessible via common-mode noise rejection.

Two fibre lasers at wavelengths of 1,540 nm and 1,560 nm are stabilized to the MgF₂ microresonator using the Pound–Drever–Hall technique (Extended Data Fig. 2). Servo control is applied to the laser piezos and acousto-optic frequency shifters, providing a locking bandwidth of up to 300 kHz. Although the microresonator can support several transverse modes within an FSR, we stabilize the lasers to a pair of modes belonging to the same longitudinal mode family (Fig. 2c). The relative frequency noises of these lasers are characterized by using a multifrequency delayed self-heterodyne interferometer^38,39 (Methods). The relative frequency noise of the reference lasers is shown in Fig. 2d, where locking to the microresonator results in a noise reduction of more than 50 dB. In particular, the relative noise at offset frequencies ranging from 10 Hz to 1 kHz exhibits white noise characteristics, which is more than 10 dB below the thermorefractive noise of the microresonator. This behaviour indicates common-mode noise rejection, necessitating that both modes belong to the same longitudinal mode family. Consequently, the relative frequency noise between the two lasers within this frequency range is limited by residual noises in the Pound–Drever–Hall locking setup. An additional reduction of over 20 dB is anticipated by further minimizing these residual locking noises.

OFD

The detailed experimental setup to realize OFD is described in the Methods and Extended Data Fig. 3. The soliton microcomb exhibits a characteristic spectral envelope of sech² and a 3-dB bandwidth spanning over 30 nm (Fig. 3a). This bandwidth is sufficient to bridge the frequency gap between reference lasers (20 nm, or equivalently 2.5 THz), and dividing it to the 25-GHz repetition frequency should provide a noise reduction factor of 40 dB. The radio-frequency beatnotes of the free-running and stabilized soliton microcombs acquired with an electrical spectral analyser are compared in Fig. 3b,c. The former is susceptible to various technical noise sources, including noise transduced from the pump laser and temperature fluctuations within the microresonator, leading to a broader linewidth and frequency drift. By contrast, the repetition frequency of the stabilized soliton microcomb primarily follows the frequency references and exhibits a notable reduction in linewidth.

Fig. 3: OFD characterization.

a, Optical spectra of the soliton microcomb and the reference lasers. b, Beatnote of the free-running soliton microcomb. c, Beatnote of the locked soliton microcomb. RBW, resolution bandwidth. d, Single-sideband phase noise of the free-running and locked beatnotes of the soliton microcomb. The projected contribution (scaled by 40 dB) from the optical frequency references is also plotted. The dashed black line indicates the timing jitter level of 1 as Hz^−1/2. The grey-shaded area represents the noise floor of the PNA during the measurement. e, Characterization of ADEV. Top: setup for referencing the OFD signals to clocks. Bottom: fractional ADEV of the clock reference (green), the original OFD signal (blue) and the OFD signal referenced to the clock (red). Measurements below and above 100-ms averaging time are performed using a PNA and a frequency counter, respectively. The vertical bars indicate the 1σ error of the fractional ADEV. TEC, thermoelectric cooler.

Figure 3d presents a more quantitative phase noise comparison. The stabilized repetition frequency’s phase noise aligns closely with the divided frequency references. Within an offset frequency range from 10 Hz to 1 kHz, OFD leads to a noise reduction exceeding 60 dB compared with the free-running case, following the 1/f² trend, where f is the offset frequency. A noise level of –85 dBc Hz^–1 at 10 Hz to –141 dBc Hz^–1 at 10-kHz offset frequency is achieved. Above the corner frequencies of approximately 300 kHz, its phase noise converges to the shot-noise-limited level of –152 dBc Hz^–1.

Figure 3e shows the fractional Allan deviation (ADEV) of the OFD-generated microwave signals. We observe that the ADEV reaches its minimum value of 6.5 × 10⁻¹³ at an averaging time of 50 ms. Beyond this point, the ADEV increases due to the long-term temperature drift of the MgF₂ microresonator. We implement a secondary feedback loop to suppress long-term frequency drifts. Once the primary feedback loop (the phase-locked loop (PLL) of the OFD) is engaged, the soliton beatnote is sent to a mixer along with a microwave synthesizer operating at 25 GHz to generate a low-frequency signal. This signal is then fed into a secondary PLL for active adjustments of the LO frequency of the primary PLL (f_LO in equation (1)) and the temperature of the reference microresonator (influencing f_B – f_A). By referencing the microwave synthesizer to an Rb clock and tuning the secondary PLL to respond only to low-frequency deviations, the long-term stability of the Rb clock is coherently transferred to the OFD-generated microwave without interfering with the short-term stability provided by the MgF₂ microresonator. Consequently, the hybrid system can surpass the performance of the clock reference below an averaging time of 100 ms, and then converge to the performance of the clock reference and achieve a minimum ADEV of 5.5 × 10⁻¹³ at an integration time of 3.2 s.

Anti-interference experiments

We compare the performance of our OFD system with a high-end electronic oscillator (Keysight PSG E8257D, referred to as PSG hereafter) as the LOs in three anti-interference experiments. The first objective is to test the anti-interference performance of the LOs under conditions of intense communication jamming⁴⁰, such as satellite communications disturbed by millimetre waves for 5G communications and autonomous vehicles (Fig. 4a). We start the experiments by upmixing a pair of frequency-close single-tone signals—one serving as the strong interference (–20 dBm) and the other as the weak information (–97 dBm)—with the local oscillation signal generated by PSG and OFD, respectively (Extended Data Fig. 5a). As shown in Fig. 4b, when PSG is used as the LO, the noise floor of the converted interference is so high that the information signal is drowned out. When shifting from PSG to OFD-based LO, a previously obscured information signal can be observed, attributed to the ultralow-phase-noise characteristics of the OFD-based LO. We then compare the signal-to-noise ratio of the information signals for the two cases at different frequency separations. In particular, our OFD system provides a 20-dB advantage over the PSG when the two signals are 10 kHz apart (Fig. 4c).

Fig. 4: Anti-interference experiments.

a, Conceptual diagram of an interfered communication channel. b, Electrical spectra of the signals after upconversion using PSG and OFD-based LOs. The black dashed line in the top panel indicates the inferred information signal. c, Differences in the signal-to-noise ratio (SNR) of the information signal for PSG and OFD-based LOs. The x axis is the frequency difference between the information and interference signals. d, Constellation diagram of interfered 64-QAM data transmission experiments using PSG and OFD-based LOs. The normalized symbol density is indicated by colour. e, Conceptual diagram of a Doppler radar. f, Electrical spectra of the echoes using PSG and OFD-based radar signals. The two targets move towards the receiver at 0.78 m s^–1 (left) and 1.05 m s^–1 (right).

We then replace the single-tone information signal with communication data in the 64-QAM (QAM, quadrature amplitude modulation) format, with a symbol rate of 50 kBd to imitate a real communication scenario (Extended Data Fig. 5b). The frequency gap between the information and interference signals is 35 kHz. The upmixed information signal is analysed using a vector signal analyser for constellation diagram construction and error vector magnitude (EVM) measurement. As shown in Fig. 4d, using the PSG-based LO yields an EVM of 12.06%, exceeding the 8% threshold for standard 64-QAM telecommunication. By contrast, using the OFD-based LO yields an EVM of only 4.38%, maintaining an adequate signal fidelity under heavy jamming due to its lower phase noise. These experimental results suggest that our system can outperform table-top electronic microwave oscillators in the quest for robust communication systems.

OFD can also enhance Doppler radar systems that harvest the velocity of moving targets by Doppler shift (Fig. 4e). When the carrier frequency is set to 25 GHz, a velocity of 1 m s^–1 only induces a Doppler shift up to 167 Hz. Detecting objects with such slow speed from strong static background reflections necessitates radar signals with ultralow phase noise at low offset frequencies. We evaluate the sensitivities of Doppler radars using signals provided by OFD and PSG. A rectangular reflector placed near the transmitting and receiving antennas serves as the static background, whereas a small object mounted on a rotational stage acts as the target (Extended Data Fig. 5c). Two targets with different rotation radii (0.89 m/1.2 m) are tested in sequence, with the rotation speed set to 50° s^–1. As shown in Fig. 4f, both targets are detectable only when using the OFD-based radar signal, owing to its substantially lower noise floor at low offset frequencies. Moreover, the rest of the equally spaced spurious signals are introduced by the a.c. utility power at 50 Hz.

Performance of an integrated optoelectronic oscillator⁹, OEwaves OE3700 X-band optoelectronic oscillator (*), a Brillouin laser oscillator in silica¹⁰, a Brillouin laser oscillator in Si₃N₄ (ref. ¹¹), a self-injection-locked-laser-based oscillator¹², a free-running microcomb in Si₃N₄ (ref. ⁵⁶), a free-running microcomb in MgF₂ (ref. ³²), a free-running microcomb in silica³³, an optical parametric oscillator in Si₃N₄-referenced microcomb in Si₃N₄ (ref. ⁵⁷), a Si₃N₄-coil-cavity-referenced microcomb in Si₃N₄ (ref. ²⁴), a mini-Fabry–Pérot-cavity-referenced microcomb in Si₃N₄ (ref. ²³) and a MgF₂-microresonator-referenced microcomb in Si₃N₄ (this work) are compared. All of the phase noise is scaled to a 10-GHz carrier frequency. The grey-shaded area indicates the noise performance of commercial electronics (PSG). The dashed black line indicates the timing jitter level of 1 as Hz^−1/2.

Although state-of-the-art one-point OFD systems provide more than an order of magnitude lower timing noise using self-referenced table-top optical frequency combs¹⁷, such a configuration can also be potentially implemented in microcombs through a combination of dispersion engineering and efficient pumping schemes^42,43. Additionally, optimizing the residual amplitude modulation in the phase modulator may improve common-mode noise rejection, potentially providing over 20-dB lower timing noise (Fig. 2d).

Further integration of the OFD system is viable. By leveraging thin-film lithium niobate technology⁴⁴, key components such as phase modulators⁴⁵ and acousto-optic modulators⁴⁶ can be implemented on chips. Integrated lasers^11,29,47 and soliton microcombs^{29,48,49,50,51} with competitive noise performance have also been recently demonstrated, and their low noise amplification for photodetection can be realized using erbium-doped waveguide amplifiers⁵². In addition, electro-optic comb generators can also be chosen as the frequency divider such that the desired microwaves can be directly read out from the driving voltage-controlled oscillator¹⁶. As for the optical references, integrated waveguide couplers have been developed to interface with ultrahigh-Q crystalline microresonators^53,54. They should enable laser self-injection locking to the microresonators, such that the Pound–Drever–Hall locking setup can be eliminated to reduce the form factors and electrical power consumption⁵⁵. These advances would extend the impact of OFD technologies to consumer markets such as high-resolution radars for autonomous vehicles and transceivers for high-speed wireless communications, providing exceptional performance, compact size, robust operation and mass production. They can also facilitate many scientific tasks, including very long baseline interferometry for space-based radio astronomy and high-fidelity manipulation of superconducting qubits.