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The generation of spectrally pure microwave signals is a critical functionality in fundamental and applied sciences, including metrology and communications. Optical frequency combs enable the powerful technique of optical frequency division (OFD) to produce microwave oscillations of the highest quality1,2. Current implementations of OFD require multiple lasers, with space- and energy-consuming optical stabilization and electronic feedback components, resulting in device footprints incompatible with integration into a compact and robust photonic platform3,4,5. Here we demonstrate all-optical OFD on a photonic chip by synchronizing two distinct dynamical states of Kerr microresonators pumped by a single continuous-wave laser. The inherent stability of the terahertz beat frequency between the signal and idler fields of an optical parametric oscillator is transferred to a microwave frequency of a Kerr soliton comb, and synchronization is achieved via a coupling waveguide without the need for electronic locking. OFD factors of N = 34 and 468 are achieved for 227 GHz and 16 GHz soliton combs, respectively. In particular, OFD enables a 46 dB phase-noise reduction for the 16 GHz soliton comb, resulting in the lowest microwave noise observed in an integrated photonics platform. Our work represents a simple, effective approach for performing OFD and provides a pathway towards chip-scale devices that can generate microwave frequencies comparable to the purest tones produced in metrological laboratories.

Scheimpflug condition says the image plane is tilted as well. The tilted object and image planes become functions of y, so the Lensmaker's formula becomes f.

(a), Homodyne setup for thermal noise characterization of microresonators. DUT, device under test. (b), Measured thermal noise of the SiN device at room temperature (0V) and when a heating voltage is applied using a commercial arbitrary-waveform generator (1.3 V).

Rodrigues, J. R. et al. SiN-based waveguides with ultra-low thermo-optic effect. In Conference on Lasers and Electro-Optics (eds. Prasankumar, R., Tanabe, T., Brès, C. S. & Paiella, R.) SM4G.3 (Optica Publishing Group, 2022).

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Joshi, C. et al. Thermally controlled comb generation and soliton modelocking in microresonators. Opt. Lett. 41, 2565–2568 (2016).

Kalubovilage, M., Endo, M. & Schibli, T. R. X-Band photonic microwaves with phase noise below -180 dBc/Hz using a free-running monolithic comb. Opt. Express 30, 11266–11274 (2022).

Liu, F., Menyuk, C. R. & Chembo, Y. K. A stochastic approach to phase noise analysis for microwaves generated with Kerr optical frequency combs. Commun. Phys. 6, 117 (2023).

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Jang, J. K. et al. Observation of Arnold tongues in coupled soliton Kerr frequency combs. Phys. Rev. Lett. 123, 153901 (2019).

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The code used to plot the data is available in the Zenodo repository. Simulation code may be obtained from the authors upon reasonable request.

This work was performed in part at the Cornell Nano-Scale Facility, which is a member of the National Nanotechnology Infrastructure Network, supported by the NSF and in part at the CUNY Advanced Science Research Center NanoFabrication Facility. We acknowledge computing resources from Columbia University’s Shared Research Computing Facility project, which is supported by NIH Research Facility Improvement Grant 1G20RR030893-01 and associated funds from the New York State Empire State Development, Division of Science Technology and Innovation (NYSTAR) Contract C090171, both awarded 15 April 2010. We thank T. Schibli, Y. Levin, K. Bergman and M. Hattink for helpful discussions. This work was supported by Defense Advanced Research Projects Agency of the US Department of Defense (Grant No. HR0011-22-2-0007), Army Research Office (ARO) (Grant No. W911NF-21-1-0286) and Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-20-1-0297).

Djordjevic, S. S. et al. CMOS-compatible, athermal silicon ring modulators clad with titanium dioxide. Opt. Express 21, 13958–13968 (2013).

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JE Langer · 2011 · 16 — Recommendations for FNA biopsy should not be based on the presence of hypofunctioning regions on 123 I scan without sonographic confirmation.

Supplementary Figs. 1–3 and sections I–IV regarding theoretical model and numerical simulations: I, Schawlow–Townes linewidth of optical parametric oscillator; II, Classical phase-noise sources of optical parametric oscillator; III, Numerical model of synchronization; IV, Design example of the athermal waveguide.

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EDFA, erbium-doped fibre amplifier; WDM, wavelength division multiplexer. Two near-identical spiral resonators are used for OPO and soliton-comb generation, respectively. The output of the OPO chip is combined with the pump for the soliton chip via a fibre-based WDM to facilitate synchronization.

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Zhao, Y., Jang, J.K., Beals, G.J. et al. All-optical frequency division on-chip using a single laser. Nature 627, 546–552 (2024). https://doi.org/10.1038/s41586-024-07136-2

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Godey, C., Balakireva, I. V., Coillet, Aurélien & Chembo, Y. K. Stability analysis of the spatiotemporal lugiato-lefever model for kerr optical frequency combs in the anomalous and normal dispersion regimes. Phys. Rev. A 89, 063814 (2014).

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Y.Z., Y.O. and A.L.G conceived the project. Y.Z. and J.K.J. performed the theoretical analysis. Y.Z., J.K.J. and G.J.B. performed the experiment. Y.Z., J.K.J., Y.O. and A.L.G. performed the data analysis with input from all authors. X.J. and K.J.M. fabricated the silicon-nitride devices under the supervision of M.L. Y.Z., J.K.J. and A.L.G. wrote the manuscript with feedback from all authors. M.L. and A.L.G. supervised the project.

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Nature thanks Olivier Llopis, Florian Sedlmeir and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Present address: John Hopcroft Center for Computer Science, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, China

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Sun, S. et al. Integrated optical frequency division for microwave and mmwave generation. Nature https://doi.org/10.1038/s41586-024-07057-0 (2024).