Letter | Published:

Resonant electro-optic frequency comb

Abstract

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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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.

References

  1. 1.

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

  2. 2.

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

  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).

  4. 4.

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

  5. 5.

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

  6. 6.

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

  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).

  8. 8.

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

  9. 9.

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

  10. 10.

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

  11. 11.

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

  12. 12.

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

  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).

  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).

  15. 15.

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

  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).

  17. 17.

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

  18. 18.

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

  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).

  20. 20.

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

  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).

  22. 22.

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

  23. 23.

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

  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).

  25. 25.

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

  26. 26.

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

  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).

  28. 28.

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

  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).

  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).

  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).

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Acknowledgements

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.

Reviewer information

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.

Competing interests

The authors declare no competing interests.

Correspondence to Harald G. L. Schwefel.

Extended data figures and tables

  1. 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.

Supplementary information

  1. Supplementary Information

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

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About this article

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.
Extended Data Fig. 1: Experimental realization.

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