Universal dynamics and microwave control of programmable resonant electro-optic frequency combs

Nature Physics (2026)Cite this article Electro-optic frequency combs are foundational for applications in metrology and spectroscopy. Specifically, microresonator-based electro-optic combs are distinguished by efficient sideband generation, enabling high-performance integrated frequency references and pulse sources. However, the apparent simplicity of these devices, often described by the electro-optic modulation-induced coupling of nearest-neighbour cavity modes, has resulted in limited investigations of their fundamental physics, thereby restricting their full potential. Here we uncover the universal dynamics underpinning resonant electro-optic microcombs and characterize the full space of nonlinear optical states, controlled by modulation depth and optical detuning using the thin-film lithium niobate photonic platform. Furthermore, we design complex long-range couplings between cavity modes to realize programmable spectro-temporal shaping of the generated combs and pulses. We achieve three technological advances: repetition-rate flexibility, substantial comb bandwidth extension beyond traditional scaling laws and resonantly enhanced flat-top spectrum. Our results provide physical insights for synchronously driven cavity-based electro-optic systems broadly defined, and will enable electrically controlled and electrically enhanced comb generators for next-generation photonic applications.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutAll data needed to evaluate the conclusions in the paper are available via figshare at https://doi.org/10.6084/m9.figshare.31130746 (ref. 58).Li, J., Yi, X., Lee, H., Diddams, S. A. & Vahala, K. J. Electro-optical frequency division and stable microwave synthesis. Science 345, 309–313 (2014).Article ADS Google Scholar Karpiński, M., Jachura, M., Wright, L. J. & Smith, B. J. Bandwidth manipulation of quantum light by an electro-optic time lens. Nat. Photonics 11, 53–57 (2017).Article ADS Google Scholar Beha, K. et al. Electronic synthesis of light. Optica 4, 406 (2017).Article ADS Google Scholar Carlson, D. R. et al. Ultrafast electro-optic light with subcycle control. Science 361, 1358–1363 (2018).Article ADS Google Scholar Torres-Company, V. & Weiner, A. M. Optical frequency comb technology for ultra-broadband radio-frequency photonics.

Laser Photonics Rev. 8, 368–393 (2014).Article ADS Google Scholar Parriaux, A., Hammani, K. & Millot, G. Electro-optic frequency combs. Adv. Opt. Photonics 12, 223 (2020).Article ADS Google Scholar Metcalf, A. J., Torres-Company, V., Leaird, D. E. & Weiner, A. M. High-power broadly tunable electrooptic frequency comb generator. IEEE J. Sel. Top. Quantum Electron. 19, 231–236 (2013).Article ADS Google Scholar Kobayashi, T., Sueta, T., Cho, Y. & Matsuo, Y. High-repetition-rate optical pulse generator using a Fabry–Perot electro-optic modulator. Appl. Phys. Lett. 21, 341–343 (1972).Article ADS Google Scholar Ho, K.-P. & Kahn, J. M. Optical frequency comb generator using phase modulation in amplified circulating loop. IEEE Photonics Technol. Lett. 5, 721–725 (1993).Article ADS Google Scholar Kourogi, M., Enami, T. & Ohtsu, M. A monolithic optical frequency comb generator. IEEE Photonics Technol. Lett. 6, 214–217 (1994).Article ADS Google Scholar Saitoh, T. et al. Modulation characteristic of waveguide-type optical frequency comb generator. J. Light. Technol. 16, 824–832 (1998).Article ADS Google Scholar Rueda, A., Sedlmeir, F., Kumari, M., Leuchs, G. & Schwefel, H. G. L. Resonant electro-optic frequency comb. Nature 568, 378–381 (2019).Article ADS Google Scholar Buscaino, B., Zhang, M., Loncar, M. & Kahn, J. M. Design of efficient resonator-enhanced electro-optic frequency comb generators. J. Light. Technol. 38, 1400–1413 (2020).Article ADS Google Scholar Kourogi, M., Nakagawa, K. & Ohtsu, M. Wide-span optical frequency comb generator for accurate optical frequency difference measurement. IEEE J. Quantum Electron. 29, 2693–2701 (1993).Article ADS Google Scholar Xiao, S., Hollberg, L., Newbury, N. R. & Diddams, S. A. Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator. Opt. Express 16, 8498 (2008).Article ADS Google Scholar Wang, K. et al. Generating arbitrary topological windings of a non-Hermitian band. Science 371, 1240–1245 (2021).Article ADS Google Scholar Kim, S., Krasnok, A. & Alù, A. Complex-frequency excitations in photonics and wave physics. Science 387, eado4128 (2025).Article Google Scholar Del’Haye, P. et al. Optical frequency comb generation from a monolithic microresonator. Nature 450, 1214–1217 (2007).Article ADS Google Scholar Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, eaan8083 (2018).Article Google Scholar Zhu, D. et al. Integrated photonics on thin-film lithium niobate. Adv. Opt. Photonics 13, 242 (2021).Article ADS Google Scholar Boes, A. et al. Lithium niobate photonics: unlocking the electromagnetic spectrum. Science 379, eabj4396 (2023).Article ADS Google Scholar Hu, Y. et al. Integrated electro-optics on thin-film lithium niobate. Nat. Rev. Phys. 7, 237–254 (2025).Article Google Scholar Xu, M. et al. Dual-polarization thin-film lithium niobate in-phase quadrature modulators for terabit-per-second transmission. Optica 9, 61 (2022).Article ADS Google Scholar Shen, M. et al. Photonic link from single-flux-quantum circuits to room temperature. Nat. Photonics 18, 371–378 (2024).Article ADS Google Scholar Feng, H. et al. Integrated lithium niobate microwave photonic processing engine. Nature 627, 80–87 (2024).Article ADS Google Scholar Hu, Y. et al. Integrated lithium niobate photonic computing circuit based on efficient and high-speed electro-optic conversion. Nat. Commun. 16, 8178 (2025).Article ADS Google Scholar Song, Y. et al. Integrated electro-optic digital-to-analogue link for efficient computing and arbitrary waveform generation. Nat. Photonics 19, 1107–1115 (2025).Article ADS Google Scholar Zhang, M. et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator. Nature 568, 373–377 (2019).Article ADS Google Scholar Hu, Y., Reimer, C., Shams-Ansari, A., Zhang, M. & Loncar, M. Realization of high-dimensional frequency crystals in electro-optic microcombs. Optica 7, 1189 (2020).Article ADS Google Scholar Hu, Y. et al. High-efficiency and broadband on-chip electro-optic frequency comb generators. Nat. Photonics 16, 679–685 (2022).Article ADS Google Scholar Zhang, J. et al. Ultrabroadband integrated electro-optic frequency comb in lithium tantalate. Nature 637, 1096–1103 (2025).Article ADS Google Scholar Lei, T. et al. Strong-coupling and high-bandwidth cavity electro-optic modulation for advanced pulse-comb synthesis. Light Sci. Appl. 14, 373 (2025).Article ADS Google Scholar Godey, C., Balakireva, I. V., Coillet, A. & 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).Article ADS Google Scholar Sounas, D. L. & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photonics 11, 774–783 (2017).Article ADS Google Scholar Yu, M. et al. Integrated electro-optic isolator on thin-film lithium niobate. Nat. Photonics 17, 666–671 (2023).Article ADS Google Scholar Millot, G. et al. Frequency-agile dual-comb spectroscopy. Nat. Photonics 10, 27–30 (2016).Article ADS Google Scholar Hu, Y. et al. Mirror-induced reflection in the frequency domain. Nat. Commun. 13, 6293 (2022).Article ADS Google Scholar Song, Y., Hu, Y., Lončar, M. & Yang, K. Hybrid Kerr–electro-optic frequency combs on thin-film lithium niobate. Light Sci. Appl. 14, 270 (2025).Article ADS Google Scholar Hu, Y. et al. On-chip electro-optic frequency shifters and beam splitters. Nature 599, 587–593 (2021).Article ADS Google Scholar Tusnin, A. K., Tikan, A. M. & Kippenberg, T. J. Nonlinear states and dynamics in a synthetic frequency dimension. Phys. Rev. A 102, 023518 (2020).Article ADS Google Scholar Zhang, H. et al. On-demand tailoring soliton patterns through intracavity spectral phase programming. Nat. Commun. 16, 4710 (2025).Article ADS Google Scholar Li, M. et al. Integrated Pockels laser. Nat. Commun. 13, 5344 (2022).Article ADS Google Scholar Holzgrafe, J. et al. Cavity electro-optics in thin-film lithium niobate for efficient microwave-to-optical transduction. Optica 7, 1714 (2020).Article ADS Google Scholar Guo, Q. et al. Ultrafast mode-locked laser in nanophotonic lithium niobate. Science 382, 708–713 (2023).Article ADS Google Scholar Lucas, E., Yu, S.-P., Briles, T. C., Carlson, D. R. & Papp, S. B. Tailoring microcombs with inverse-designed, meta-dispersion microresonators. Nat. Photonics 17, 943–950 (2023).Article ADS Google Scholar Moille, G., Lu, X., Stone, J., Westly, D. & Srinivasan, K. Fourier synthesis dispersion engineering of photonic crystal microrings for broadband frequency combs. Commun. Phys. 6, 144 (2023).Article Google Scholar Javid, U. A. et al. Chip-scale simulations in a quantum-correlated synthetic space. Nat. Photonics 17, 883–890 (2023).Article ADS Google Scholar Wang, K., Dutt, A., Wojcik, C. C. & Fan, S. Topological complex-energy braiding of non-Hermitian bands. Nature 598, 59–64 (2021).Article ADS Google Scholar Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics 11, 752–762 (2017).Article ADS Google Scholar Zhu, X. et al. Twenty-nine million intrinsic Q -factor monolithic microresonators on thin-film lithium niobate. Photonics Res. 12, A63 (2024).Article Google Scholar Suh, M.-G. & Vahala, K. Gigahertz-repetition-rate soliton microcombs. Optica 5, 65 (2018).Article ADS Google Scholar Xue, S. et al. Full-spectrum visible electro-optic modulator. Optica 10, 125 (2023).Article ADS Google Scholar Suh, M.-G., Yang, Q.-F., Yang, K. Y., Yi, X. & Vahala, K. J. Microresonator soliton dual-comb spectroscopy. Science 354, 600–603 (2016).Article ADS Google Scholar Shams-Ansari, A. et al. Thin-film lithium-niobate electro-optic platform for spectrally tailored dual-comb spectroscopy. Commun. Phys. 5, 88 (2022).Article Google Scholar Cundiff, S. T. & Weiner, A. M. Optical arbitrary waveform generation. Nat. Photonics 4, 760–766 (2010).Article ADS Google Scholar Fülöp, A. et al. High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators. Nat. Commun. 9, 1598 (2018).Article ADS Google Scholar Jørgensen, A. A. et al. Petabit-per-second data transmission using a chip-scale microcomb ring resonator source. Nat. Photonics 16, 798–802 (2022).Article ADS Google Scholar Song, Y. Universal dynamics and microwave control of programmable resonant electro-optic frequency combs. figshare https://doi.org/10.6084/m9.figshare.31130746.v1 (2026).Download referencesWe thank N. Achuthan, R. Cheng, T. Ge, B. Grinkemeyer, J. Fang, E. Hu, K. Powell, S. Rajabali, D. Renaud, N. Rivera, T. Rosenbaum, U. Senica, A. Shams-Ansari, A. Shelton, J. Sloan, H. Warner, C. Xin, Z. Yuan and X. Zuo for discussions. We thank T. Chen (Flexcompute), K. Richard, N. Hoffman and M. Roberts (Keysight Technologies, Inc.) for technical support. The device fabrication in this work was performed at the Harvard University Center for Nanoscale Systems, a member of the National Nanotechnology Coordinated Infrastructure Network, which is supported by the US National Science Foundation under NSF award no. ECCS-2025158.

Funding National Research Foundation of Korea, funded by the Korean government, NRF-2022M3K4A1094782 (Y.S., X.L., M.Y., M.L.).

Air Force Office of Scientific Research, FA955024PB004 (Y.S.).

Air Force Office of Scientific Research, FA9550-23-1-0333 (M.L.). US Department of Defense, FA9453-23-C-A039 (M.L.).

Amazon Web Services, A50791 (M.H., M.L.). US National Science Foundation, OMA-2138068 (N.S.). US National Science Foundation, OMA-2137723 (M.Y.). US National Science Foundation, EEC-1941583 (J.Y., N.S.). US National Aeronautics and Space Administration, 80NSSC22K0262 (N.S.). US Department of the Navy, N6833522C0413 (X.Z.).

National Science Foundation of China, NSFC-12474321 (T.L., Y.H.). Rubicon postdoctoral fellowship from the Dutch Research Council, 019.231EN.011 (A.C.).

Swiss National Science Foundation, Postdoc.Mobility, 222257 (G.H.). Behring Foundation and CAPES-Fulbright (L.M.). A*STAR NSS(PhD) scholarship (S.L.).These authors contributed equally: Yunxiang Song, Tianqi Lei.John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USAYunxiang Song, Andrea Cordaro, Michael Haas, Guanhao Huang, Xudong Li, Shengyuan Lu, Letícia Magalhães, Jiayu Yang, Matthew Yeh, Xinrui Zhu, Neil Sinclair & Marko LončarState Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing, ChinaTianqi Lei, Yanyun Xue, Qihuang Gong & Yaowen HuSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarY.H., M.L., Y.S. and T.L. conceived the project. Y.S. performed the experiments and fabricated the devices. Y.S. designed the devices with Y.H. assisting. Y.S. and T.L. performed the simulations with Y.X. assisting. A.C., M.H., G.H., X.L., S.L., L.M., J.Y., M.Y., X.Z. and N.S. helped with all aspects of the project. Y.S., T.L., Y.X., Y.H. and M.L. interpreted and analysed the data. Y.S. and M.L. wrote the manuscript with contributions from all authors. M.L., Y.H. and Q.G. supervised the project.Correspondence to Yaowen Hu or Marko Lončar.M.L. is involved in developing lithium niobate technologies at HyperLight Corporation. The other authors declare no competing interests.Nature Physics thanks Huihui Lu and Johann Riemensberger for their contribution to the peer review of this work. Peer reviewer reports are available.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Discussion and Figs. 1–17.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsSong, Y., Lei, T., Xue, Y. et al. Universal dynamics and microwave control of programmable resonant electro-optic frequency combs. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03198-3Download citationReceived: 08 June 2025Accepted: 28 January 2026Published: 12 March 2026Version of record: 12 March 2026DOI: https://doi.org/10.1038/s41567-026-03198-3Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative