Resonant electro-optic frequency comb


High-speed optical telecommunication is enabled by wavelength-division multiplexing, whereby hundreds of individually stabilized lasers encode information within a single-mode optical fibre. Higher bandwidths require higher total optical power, but the power sent into the fibre is limited by optical nonlinearities within the fibre, and energy consumption by the light sources starts to become a substantial cost factor1. Optical frequency combs have been suggested to remedy this problem by generating numerous discrete, equidistant laser lines within a monolithic device; however, at present their stability and coherence allow them to operate only within small parameter ranges2,3,4. Here we show that a broadband frequency comb realized through the electro-optic effect within a high-quality whispering-gallery-mode resonator can operate at low microwave and optical powers. Unlike the usual third-order Kerr nonlinear optical frequency combs, our combs rely on the second-order nonlinear effect, which is much more efficient. Our result uses a fixed microwave signal that is mixed with an optical-pump signal to generate a coherent frequency comb with a precisely determined carrier separation. The resonant enhancement enables us to work with microwave powers that are three orders of magnitude lower than those in commercially available devices. We emphasize the practical relevance of our results to high rates of data communication. To circumvent the limitations imposed by nonlinear effects in optical communication fibres, one has to solve two problems: to provide a compact and fully integrated, yet high-quality and coherent, frequency comb generator; and to calculate nonlinear signal propagation in real time5. We report a solution to the first problem.

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Fig. 1: Principles of generating WGM-based χ(2)-frequency combs.
Fig. 2: Theoretical scaling of sideband power and dispersion-induced breakdown of the comb.
Fig. 3: Experimental realization.

Change history

  • 10 May 2019

    Change history: In the Methods section of this Letter, there were formatting errors to the equations of motion using the Heisenberg picture; see accompanying Amendment for further details. This has been corrected online.


  1. 1.

    Kahn, J. M. & Miller, D. A. B. Communications expands its space. Nat. Photon. 11, 5–8 (2017).

    CAS  ADS  Article  Google Scholar 

  2. 2.

    Pfeifle, J. et al. Coherent terabit communications with microresonator Kerr frequency combs. Nat. Photon. 8, 375–380 (2014).

    CAS  ADS  Article  Google Scholar 

  3. 3.

    Ataie, V. et al. Ultrahigh count coherent WDM channels transmission using optical parametric comb-based frequency synthesizer. J. Lightwave Technol. 33, 694–699 (2015).

    ADS  Article  Google Scholar 

  4. 4.

    Marin-Palomo, P. et al. Microresonator-based solitons for massively parallel coherent optical communications. Nature 546, 274–279 (2017).

    CAS  ADS  Article  Google Scholar 

  5. 5.

    Temprana, E. et al. Overcoming Kerr-induced capacity limit in optical fiber transmission. Science 348, 1445–1448 (2015).

    CAS  ADS  Article  Google Scholar 

  6. 6.

    Mitchell, G. & Hodara, H. Review of the 2017 optical fiber communications (OFC) conference. Fiber Integr. Opt. 36, 101–103 (2017).

    ADS  Article  Google Scholar 

  7. 7.

    Imran, M., Anandarajah, P. M., Kaszubowska-Anandarajah, A., Sambo, N. & Poti, L. A survey of optical carrier generation techniques for terabit capacity elastic optical networks. IEEE Comm. Surv. Tutor. 20, 211–263 (2018).

    Article  Google Scholar 

  8. 8.

    Luo, L. W. et al. WDM-compatible mode-division multiplexing on a silicon chip. Nat. Commun. 5, 3069 (2014).

    ADS  Article  Google Scholar 

  9. 9.

    Holzwarth, R. et al. Optical frequency synthesizer for precision spectroscopy. Phys. Rev. Lett. 85, 2264–2267 (2000).

    CAS  ADS  Article  Google Scholar 

  10. 10.

    Liang, W. et al. High spectral purity Kerr frequency comb radio frequency photonic oscillator. Nat. Commun. 6, 7957 (2015).

    CAS  ADS  Article  Google Scholar 

  11. 11.

    Suh, M.-G. & Vahala, K. Gigahertz-repetition-rate soliton microcombs. Optica 5, 65–66 (2018).

    CAS  ADS  Article  Google Scholar 

  12. 12.

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

    CAS  ADS  Article  Google Scholar 

  13. 13.

    Herr, S. J. et al. Frequency comb up- and down-conversion in synchronously driven χ (2) optical microresonators. Opt. Lett. 43, 5745–5748 (2018).

    CAS  ADS  Article  Google Scholar 

  14. 14.

    Stefszky, M., Ulvila, V., Abdallah, Z., Silberhorn, C. & Vainio, M. Towards optical-frequency-comb generation in continuous-wave-pumped titanium-indiffused lithium-niobate waveguide resonators. Phys. Rev. A 98, 053850 (2018).

    CAS  ADS  Article  Google Scholar 

  15. 15.

    Leo, F. et al. Frequency-comb formation in doubly resonant second-harmonic generation. Phys. Rev. A 93, 043831 (2016).

    ADS  Article  Google Scholar 

  16. 16.

    Torres-Company, V. & Weiner, A. M. Optical frequency comb technology for ultra-broadband radio-frequency photonics. Laser Photonics Rev. 8, 368–393 (2014).

    ADS  Article  Google Scholar 

  17. 17.

    Kovacich, R. P., Sterr, U. & Telle, H. R. Short-pulse properties of optical frequency comb generators. Appl. Opt. 39, 4372–4376 (2000).

    CAS  ADS  Article  Google Scholar 

  18. 18.

    Beha, K. et al. Electronic synthesis of light. Optica 4, 406–411 (2017).

    CAS  ADS  Article  Google Scholar 

  19. 19.

    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).

    CAS  ADS  Article  Google Scholar 

  20. 20.

    Pozar, D. M. Microwave Engineering 4th edn (Wiley, Hoboken, 2011).

    Google Scholar 

  21. 21.

    Ilchenko, V. S., Savchenkov, A. A., Matsko, A. B. & Maleki, L. Whispering-gallery-mode electro-optic modulator and photonic microwave receiver. J. Opt. Soc. Am. B 20, 333–342 (2003).

    CAS  ADS  Article  Google Scholar 

  22. 22.

    Tsang, M. Cavity quantum electro-optics. Phys. Rev. A 81, 063837 (2010).

    ADS  Article  Google Scholar 

  23. 23.

    Hobbs, P. Building Electro-Optical Systems: Making It all Work (Wiley, Hoboken, 2011).

    Google Scholar 

  24. 24.

    Strekalov, D. V., Marquardt, C., Matsko, A. B., Schwefel, H. G. L. & Leuchs, G. Nonlinear and quantum optics with whispering gallery resonators. J. Opt. 18, 123002 (2016).

    ADS  Article  Google Scholar 

  25. 25.

    Strekalov, D. V. et al. Microwave whispering-gallery resonator for efficient optical up-conversion. Phys. Rev. A 80, 033810–033815 (2009).

    ADS  Article  Google Scholar 

  26. 26.

    Rueda, A. et al. Efficient microwave to optical photon conversion: an electro-optical realization. Optica 3, 597–604 (2016).

    CAS  ADS  Article  Google Scholar 

  27. 27.

    Botello, G. S. et al. Sensitivity limits of millimeter-wave photonic radiometers based on efficient electro-optic upconverters. Optica 5, 1210–1219 (2018).

    ADS  Article  Google Scholar 

  28. 28.

    Breunig, I. Three-wave mixing in whispering gallery resonators. Laser Photonics Rev. 10, 569–587 (2016).

    CAS  ADS  Article  Google Scholar 

  29. 29.

    Mandel, L. & Wolf, E. Optical Coherence and Quantum Optics 1st edn (Cambridge Univ. Press, Cambridge, 1995).

  30. 30.

    Law, C. K. Effective hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium. Phys. Rev. A 49, 433–437 (1994).

    CAS  ADS  Article  Google Scholar 

  31. 31.

    Zelmon, D. E., Small, D. L. & Jundt, D. Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol. % magnesium oxide-doped lithium niobate. J. Opt. Soc. Am. B 14, 3319–3322 (1997).

    CAS  ADS  Article  Google Scholar 

  32. 32.

    Li, J., Lee, H., Yang, K. Y. & Vahala, K. J. Sideband spectroscopy and dispersion measurement in microcavities. Opt. Express 20, 26337–26344 (2012).

    ADS  Article  Google Scholar 

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This work was supported by the Marsden Fund Council and Julius von Haast Fellowship from government funding, managed by Royal Society Te Apārangi of New Zealand, and the Max Planck Institute for the Science of Light, Erlangen, Germany.

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Nature thanks Pauline Kuo and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information




A.R. and F.S. performed all of the experiments and developed the theory. A.R. performed the theoretical and numerical modelling. H.G.L.S. proposed the experiment and supervised the project. A.R., F.S., M.K., G.L. and H.G.L.S. wrote the manuscript. All authors contributed to discussing and interpreting the results.

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Correspondence to Harald G. L. Schwefel.

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Extended data figures and tables

Extended Data Fig. 1 Experimental realization.

a, COMSOL simulation of the 3D copper microwave cavity. The colour bar indicates the microwave electrical field distribution inside the microcavity. In the side and top view, the localization close to the rim of the WGM is apparent. Dashed lines indicate the diameter of the WGM. The microwave field is coupled through a pin coupler to the WGM. b, Top and bottom halves of the copper cavity. The lithium niobate WGM resonator is mounted in the top half and the silicon prism in the bottom half.

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Supplementary Information

This file contains Supplementary Sections A-E, including Supplementary Figures 1-2 and Supplementary References.

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Rueda, A., Sedlmeir, F., Kumari, M. et al. Resonant electro-optic frequency comb. Nature 568, 378–381 (2019).

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