Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Integrated frequency-modulated optical parametric oscillator


Optical frequency combs have revolutionized precision measurement, time-keeping and molecular spectroscopy1,2,3,4,5,6,7. A substantial effort has developed around ‘microcombs’: integrating comb-generating technologies into compact photonic platforms5,7,8,9. Current approaches for generating these microcombs involve either the electro-optic10 or Kerr mechanisms11. Despite rapid progress, maintaining high efficiency and wide bandwidth remains challenging. Here we introduce a previously unknown class of microcomb—an integrated device that combines electro-optics and parametric amplification to yield a frequency-modulated optical parametric oscillator (FM-OPO). In contrast to the other solutions, it does not form pulses but maintains operational simplicity and highly efficient pump power use with an output resembling a frequency-modulated laser12. We outline the working principles of our device and demonstrate it by fabricating the complete optical system in thin-film lithium niobate. We measure pump-to-comb internal conversion efficiency exceeding 93% (34% out-coupled) over a nearly flat-top spectral distribution spanning about 200 modes (over 1 THz). Compared with an electro-optic comb, the cavity dispersion rather than loss determines the FM-OPO bandwidth, enabling broadband combs with a smaller radio-frequency modulation power. The FM-OPO microcomb offers robust operational dynamics, high efficiency and broad bandwidth, promising compact precision tools for metrology, spectroscopy, telecommunications, sensing and computing.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Frequency combs in the EO resonator and FM-OPO.
Fig. 2: The FM-OPO device.
Fig. 3: Pump-wavelength tuning of the FM-OPO.
Fig. 4: Power tunability of the FM-OPO.

Similar content being viewed by others


  1. Jones, D. J. et al. Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 288, 635–639 (2000).

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Udem, Th., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Diddams, S. A., Vahala, K. & Udem, T. Optical frequency combs: coherently uniting the electromagnetic spectrum. Science 369, eaay3676 (2020).

    Article  CAS  PubMed  Google Scholar 

  4. Coddington, I., Newbury, N. & Swann, W. Dual-comb spectroscopy. Optica 3, 414–426 (2016).

    Article  ADS  Google Scholar 

  5. 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  CAS  PubMed  Google Scholar 

  6. Picqué, N. & Hänsch, T. W. Frequency comb spectroscopy. Nat. Photon. 13, 146–157 (2019).

    Article  ADS  Google Scholar 

  7. Bao, C. et al. Architecture for microcomb-based GHz-mid-infrared dual-comb spectroscopy. Nat. Commun. 12, 6573 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555–559 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  9. Chang, L., Liu, S. & Bowers, J. E. Integrated optical frequency comb technologies. Nat. Photon. 16, 95–108 (2022).

    Article  ADS  CAS  Google Scholar 

  10. Zhang, M. et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator. Nature 568, 373–377 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Shen, B. et al. Integrated turnkey soliton microcombs. Nature 582, 365–369 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Siegman, A. E. Lasers (Univ. Science Books, 1986).

  13. Okawachi, Y. et al. Octave-spanning frequency comb generation in a silicon nitride chip. Opt. Lett. 36, 3398–3400 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Brasch, V. et al. Photonic chip–based optical frequency comb using soliton cherenkov radiation. Science 351, 357–360 (2016).

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  15. Jung, H., Xiong, C., Fong, K. Y., Zhang, X. & Tang, H. X. Optical frequency comb generation from aluminum nitride microring resonator. Opt. Lett. 38, 2810–2813 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Guidry, M. A., Lukin, D. M., Yang, K. Y., Trivedi, R. & Vučković, J. Quantum optics of soliton microcombs. Nat. Photon. 16, 52–58 (2021).

    Article  ADS  Google Scholar 

  17. Wang, C. et al. Monolithic lithium niobate photonic circuits for kerr frequency comb generation and modulation. Nat. Commun. 10, 978 (2019).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  18. Hu, Y. et al. High-efficiency and broadband on-chip electro-optic frequency comb generators. Nat. Photon. 16, 679–685 (2022).

    Article  ADS  CAS  Google Scholar 

  19. Yu, M. et al. Integrated femtosecond pulse generator on thin-film lithium niobate. Nature 612, 252–258 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  20. Diddams, S. A., Ma, L.-S., Ye, J. & Hall, J. L. Broadband optical frequency comb generation with a phase-modulated parametric oscillator. Opt. Lett. 24, 1747–1749 (1999).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Esteban-Martin, A., Samanta, G. K., Devi, K., Kumar, S. C. & Ebrahim-Zadeh, M. Frequency-modulation-mode-locked optical parametric oscillator. Opt. Lett. 37, 115–117 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Okawachi, Y. et al. Competition between Raman and Kerr effects in microresonator comb generation. Opt. Lett. 42, 2786–2789 (2017).

    Article  CAS  PubMed  Google Scholar 

  23. Boes, A. et al. Lithium niobate photonics: Unlocking the electromagnetic spectrum. Science 379, eabj4396 (2023).

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Wang, C. et al. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 562, 101–104 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Li, M. et al. Lithium niobate photonic-crystal electro-optic modulator. Nat. Commun. 11, 4123 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  26. Jankowski, M. et al. Ultrabroadband nonlinear optics in nanophotonic periodically poled lithium niobate waveguides. Optica 7, 40–46 (2020).

    Article  ADS  CAS  Google Scholar 

  27. Hwang, A. Y. et al. Mid-infrared spectroscopy with a broadly tunable thin-film lithium niobate optical parametric oscillator. Optica 10, 1535–1542 (2023).

    Article  ADS  CAS  Google Scholar 

  28. Park, T. et al. High-efficiency second harmonic generation of blue light on thin-film lithium niobate. Opt. Lett. 47, 2706–2709 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Kashiwazaki, T. et al. Continuous-wave 6-dB-squeezed light with 2.5-THz-bandwidth from single-mode PPLN waveguide. APL Photon. 5, 036104 (2020).

    Article  ADS  CAS  Google Scholar 

  30. Nehra, R. et al. Few-cycle vacuum squeezing in nanophotonics. Science 377, 1333–1337 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Lu, J. et al. Ultralow-threshold thin-film lithium niobate optical parametric oscillator. Optica 8, 539–544 (2021).

    Article  ADS  Google Scholar 

  32. McKenna, T. P. et al. Ultra-low-power second-order nonlinear optics on a chip. Nat. Commun. 13, 4532 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  33. Ledezma, L. et al. Octave-spanning tunable infrared parametric oscillators in nanophotonics. Sci. Adv. 9, eadf9711 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Li, M. et al. Integrated Pockels laser. Nat. Commun. 13, 5344 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  35. Stokowski, H. S. et al. Integrated quantum optical phase sensor in thin film lithium niobate. Nat. Commun. 14, 3355 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  36. Luke, K. et al. Wafer-scale low-loss lithium niobate photonic integrated circuits. Opt. Exp. 28, 24452–24458 (2020).

    Article  CAS  Google Scholar 

  37. Li, Z. et al. High density lithium niobate photonic integrated circuits. Nat. Commun. 14, 4856 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  38. Xue, X., Zheng, X. & Zhou, B. Super-efficient temporal solitons in mutually coupled optical cavities. Nat. Photon. 13, 616–622 (2019).

    Article  ADS  CAS  Google Scholar 

  39. Helgason, Ó. B. et al. Power-efficient soliton microcombs. Preprint at (2022).

  40. Li, J. et al. Efficiency of pulse pumped soliton microcombs. Optica 9, 231–239 (2022).

    Article  ADS  Google Scholar 

  41. Harris, S. E. & Targ, R. FM oscillation of the He-Ne laser. Appl. Phys. Lett. 5, 202–204 (1964).

    Article  ADS  CAS  Google Scholar 

  42. Kuizenga, D. & Siegman, A. FM-laser operation of the Nd:YAG laser. IEEE J. Quantum Electron. 6, 673–677 (1970).

    Article  ADS  CAS  Google Scholar 

  43. Eckardt, R. C., Nabors, C. D., Kozlovsky, W. J. & Byer, R. L. Optical parametric oscillator frequency tuning and control. J. Opt. Soc. Am. B 8, 646–667 (1991).

    Article  ADS  CAS  Google Scholar 

  44. Ling, J. et al. Self-injection locked frequency conversion laser. Laser Photon. Rev. 17, 2200663 (2023).

    Article  ADS  Google Scholar 

  45. Op de Beeck, C. et al. III/V-on-lithium niobate amplifiers and lasers. Optica 8, 1288–1289 (2021).

    Article  ADS  Google Scholar 

  46. Del’Haye, P. et al. Phase-coherent microwave-to-optical link with a self-referenced microcomb. Nat. Photon. 10, 516–520 (2016).

    Article  ADS  Google Scholar 

  47. Mishra, J. et al. Ultra-broadband mid-infrared generation in dispersion-engineered thin-film lithium niobate. Opt. Exp. 30, 32752–32760 (2022).

    Article  CAS  Google Scholar 

  48. Celik, O. T. et al. High-bandwidth CMOS-voltage-level electro-optic modulation of 780 nm light in thin-film lithium niobate. Optics Express 30, 23177–23186 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  49. Sordillo, L. A. & Sordillo, P. P. (eds) Short-Wavelength Infrared Windows for Biomedical Applications (SPIE Press, 2022).

  50. Willer, U., Saraji, M., Khorsandi, A., Geiser, P. & Schade, W. Near- and mid-infrared laser monitoring of industrial processes, environment and security applications. Opt. Lasers Eng. 44, 699–710 (2006).

    Article  Google Scholar 

  51. Goldenstein, C. S., Spearrin, R., Jeffries, J. B. & Hanson, R. K. Infrared laser-absorption sensing for combustion gases. Prog. Energy Combust. Sci. 60, 132–176 (2017).

    Article  Google Scholar 

  52. Martin, A. et al. Photonic integrated circuit-based FMCW coherent LiDAR. J. Lightwave Technol. 36, 4640–4645 (2018).

    Article  ADS  CAS  Google Scholar 

Download references


This work was supported by the US government through the Defense Advanced Research Projects Agency Young Faculty Award and Director’s Fellowship (YFA, grant no. D19AP00040), the LUMOS programme (grant no. HR0011-20-2-0046), the US Department of Energy (grant no. DE-AC02-76SF00515) and the Q-NEXT NQI Center; the US Air Force Office of Scientific Research provided an MURI grant (grant no. FA9550-17-1-0002, received by A.H.S.-N.). We thank NTT Research for their financial and technical support. H.S.S. acknowledges support from the Urbanek Family Fellowship, and V.A. was partially supported by the Stanford Q-Farm Bloch Fellowship Program and the Max Planck Society Sabbatical Fellowship Award. This work was also performed at the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-2026822. We also acknowledge the Q-NEXT DOE NQI Center and the David and Lucille Packard Fellowship for their support. D.J.D. and A.Y.H. acknowledge support from the NSF GRFP (grant no. DGE-1656518). H.S.S. and V.A. thank K. Multani and C. Sarabalis for their discussions and technical support. A.H.S.-N. thanks J. M. Kahn and S. E. Harris for their discussions.

Author information

Authors and Affiliations



A.H.S.-N. and H.S.S. conceived the device and H.S.S. designed the photonic integrated circuit. H.S.S., C.L., M.J. and T.P.M. developed the essential components of the photonic circuit. H.S.S., T.P. and A.Y.H. fabricated the device. H.S.S., V.A. and O.T.C. developed the fabrication process. M.M.F. and A.H.S.-N. provided experimental and theoretical support. H.S.S., T.P. and D.J.D. performed the experiments. H.S.S., A.Y.H., T.P. and D.J.D. analysed the data. H.S.S. and A.H.S.-N. wrote the paper. H.S.S., V.A. and A.H.S.-N. developed the experiment. H.S.S., D.J.D. and A.H.S.-N. developed the numerical and analytical models. A.H.S.-N. supervised all efforts.

Corresponding author

Correspondence to Amir H. Safavi-Naeini.

Ethics declarations

Competing interests

A.H.S.-N., H.S.S. and A.Y.H. are inventors of a patent application that covers the concept and implementation of the frequency-modulated optical parametric oscillator and its applications. The other authors declare no competing interests.

Peer review

Peer review information

Nature thanks Laura Sinclair and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Periodically poled lithium niobate waveguide design.

a, Schematic of a periodically poled lithium niobate waveguide, waveguide dimensions are: ridge height h = 300 nm, slab height s = 200 nm, width w = 1200 nm, cladding thickness c = 700 nm, poling period Λ = 3.7 μm. Thin-film lithium niobate is bonded to a 2 μm thick silicon dioxide layer and clad with a PECVD layer of SiO2. An eigenmode solution at 1550 nm is overlaid with the waveguide schematic. b, Effective index bands for various waveguide modes in our waveguide geometry. The blue line highlights the fundamental TE mode. We compensate for the effective index mismatch Δneff between the fundamental and second harmonic with periodic poling of the film. c, SEM micrograph of a chromium electrode patterned on a thin-film-LN chip for poling. d, Second harmonic microscope picture of periodically poled thin-film LN. Black areas on the left and right correspond to Cr electrodes. Oblong, grayscale shapes between the finger electrodes are inverted crystal domains. White areas of the inverted domains correspond to the full-depth poling of the film.

Source data

Extended Data Fig. 2 Fabrication process of the photonic integrated circuit.

a, We start our fabrication process with a thin-film of lithium niobate on insulator. b, Next, we deposit a 100 nm protective layer of SiO2, pattern Cr electrodes, and pole the LN by applying high voltage pulses. c-d, We remove the SiO2 and Cr afterward and etch waveguides into the LN film through argon ion-mill dry etching. e-f, After the waveguide fabrication, we pattern gold electrodes with the liftoff process and clad the entire structure with SiO2. g, Finally, we pattern vias in the SiO2 layer to access the metal electrodes.

Extended Data Fig. 3 Experimental setup for the FM-OPO characterization.

We characterize our devices with a C-band tunable laser that we amplify with an erbium-doped fiber amplifier (EDFA), yielding up to 1 W of optical power. We control the power going to the chip with a variable optical attenuator (VOA) and calibrate that power by splitting around 5% of laser into a power meter (PM). We control the polarization with a fiber polarization controller (FPC) and inject the light into a cleaved chip facet with a lensed fiber. We drive the FM-OPO with an RF source connected to an amplifier. We place a circulator before the chip to avoid reflections returning to the source. Any RF reflections are passed to termination through a 20 dB attenuator. We characterize the output of our devices by splitting the FH and SH light using a dichroic mirror. Both wavelengths are passed through VOAs for power control and measured with calibrated avalanche photodetectors (APDs). Finally, we split part of the FH light into an optical spectrum analyzer and a fast photodiode.

Extended Data Fig. 4 Intracavity coupler characterization.

a, Broadband transmission spectrum of a snail resonator with a straight section length of 2 mm. We observe mode contrast changing from under-coupled at 1500 nm to critically coupled at around 1550 nm to over-coupled at 1580 nm. b, Device measurement scheme, we probe a cavity with an internal coupler using an evanescent coupler feed waveguide. c, Zoom into a single cavity mode around 1585 nm, fitting a Lorentzian lineshape (solid blue line) reveals an intrinsic quality factor (Qi) of around 2.5 million and extrinsic quality factor (Qe) of around 800,000. d, Intrinsic and extrinsic quality factors as a function of wavelength. We distinguish between the Qi and Qe by observing the wavelength dependence. Qi peaks at around 1580 nm, where the intracavity coupler transmits all the light, thus forming a low-loss cavity. Qe decreases with wavelength because modes become less confined and can couple stronger to neighboring waveguides. The region where Qi ≈ Qe around 1552 nm is ambiguous; we report the same average number for both Qi and Qe there.

Source data

Extended Data Fig. 5 Second-order dispersion characterization of the optical cavity.

a, We characterize the second-order dispersion by probing the snail cavity with a broadband tunable C-band laser. We use a similar input setup to the one in Fig. 3 with an additional power splitter connected to a fiber MZI and detector, which serve as wavelength calibration. We collect the light with a setup with a VOA and an InGaAs APD. b, Measured free spectral range of the cavity as a function of wavelength. We find mode locations and fit a line to extract the second-order dispersion parameter of around ζ2/2π ≈ −11 kHz.

Source data

Extended Data Fig. 6 Characterization of the second-order optical nonlinearity.

a, Experimental setup for the second harmonic generation measurement. We use a similar input setup as in Fig. 3 and drive a periodically poled LN waveguide with a tunable C-band laser. We collect the output light into a fiber and split it with a dichroic mirror between two avalanche photodetectors (APDs) for FH and SH light characterization. b, Example second harmonic generation transfer function measured at pump power of about PFH ≈ 200 μW. c, Measured second harmonic generation output power as a function of pump power. The quadratic fit yields a normalized efficiency of around η ≈ 1,500 %/Wcm2. The inset shows a microscope picture of bright second harmonic light scattered at the output facet of the chip and collected into a lensed fiber.

Source data

Extended Data Fig. 7 Characterization of the electro-optic coupling to the snail resonator.

a, Experimental setup. We use a similar input path as in Fig. 3 and drive the device with a tunable C-band laser. In addition, we deliver RF signals from the source in the same way as in Fig. 3, except we do not use the microwave amplifier. We collect the light into an InGaAs avalanche photodiode (APD) through a variable optical attenuator (VOA). b, Normalized transmission of a single cavity mode with (orange) and without RF drive (blue). Solid lines correspond to fitting the model. We drive the cavity with peak voltage of around VP ≈ 4.5 V for the modulated dataset. c, Fitted electro-optic coupling M/2π as a function of peak modulation voltage. We extract M0 from curves like the ones in Fig. 7b and fit a line to find M0/2π ≈ 60 MHz/V.

Source data

Extended Data Fig. 8 RF and optical spectra generated by the FM-OPO.

a, Measured RF spectra generated by the FM-OPO as a function of the RF drive strength. b, Zoom-into the first sideband around 5.78 GHz shows additional features not predicted by our simple model, likely arising from the multi-cluster behavior at high RF power. c, Simulated RF spectra generated by an FM-OPO coupled to a wavelength-dependent output coupler. d, Full optical spectrum analyzer spectra of the generated FM-OPO combs, partially plotted in Fig. 4a. e, Maximum spectral coverage of the FM-OPO, observed with around 1.2 W RF drive power.

Source data

Extended Data Fig. 9 FM-OPO tuning with laser and RF detuning.

a, Transmission of the leakage fundamental pump to the snail port of the resonator, corresponding to the OPO output in b. b, Pump-wavelength tuning of the OPO in a nondegenerate regime, the output wavelength tuning curves repeat with a period of 1/2 FSR with respect to the pump wavelength. c, -d, Pump-wavelength tuning of the FM-OPO driven with M/2π ≈ 100 MHz, and 510 MHz, respectively. All measurements in b, c, and d correspond to pumping the device with about 140 mW of optical power. The faint line in the center of each colormap corresponds to the FH pump leakage into the cavity. e, FM-OPO can be driven with the RF frequency on resonance with the cavity FSR near degeneracy (Ω = ζ1) or detuned (Ω − ζ1 = δ ≠ 0). f, Tuning of the FM-OPO comb spectrum with RF detuning δ. g, Total integrated comb power as a function of RF frequency and detuning δ.

Source data

Extended Data Table 1 Summary of the FM-OPO device parameters

Supplementary information

Supplementary Information

This file contains a detailed theory of the FM-OPO operation.

Peer Review File

Source data

Rights and permissions

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 permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stokowski, H.S., Dean, D.J., Hwang, A.Y. et al. Integrated frequency-modulated optical parametric oscillator. Nature 627, 95–100 (2024).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing