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Tailoring microcombs with inverse-designed, meta-dispersion microresonators

Nature Photonics volume 17, pages 943–950 (2023)Cite this article

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Abstract

Nonlinear wave mixing in optical microresonators offers new perspectives to generate compact optical-frequency microcombs, which enable an ever-growing number of applications. Microcombs exhibit a spectral profile that is primarily determined by their microresonator’s dispersion. One example is the sech2 spectrum of dissipative Kerr solitons under anomalous group-velocity dispersion. Here we introduce an inverse-design approach to spectrally shape microcombs, by optimizing an arbitrary meta-dispersion in a resonator. By incorporating the system’s governing equation into a genetic algorithm, we are able to efficiently identify a dispersion profile that produces a microcomb closely matching a user-defined target spectrum, such as spectrally flat combs or near-Gaussian pulses. We show a concrete implementation of these intricate optimized dispersion profiles, using selective bidirectional-mode hybridization in photonic-crystal resonators. Moreover, we fabricate and explore several microcomb generators with such flexible ‘meta’ dispersion control. Their dispersion is not only controlled by the waveguide composing the resonator, but also by a corrugation inside the resonator, which geometrically controls the spectral distribution of the bidirectional coupling in the resonator. This approach provides programmable mode-by-mode frequency splitting and thus greatly increases the design space for controlling the nonlinear dynamics of optical states such as Kerr solitons.

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Fig. 1: Concept of microcomb inverse design via meta-dispersion engineering.
Fig. 2: Dispersion optimization for comb shaping.
Fig. 3: Meta-dispersion in PhCRs.
Fig. 4: Examples of meta-dispersion in PhCR.
Fig. 5: Comb generation in meta-dispersion PhCRs.
Fig. 6: Numerical simulation of comb states.

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Data availability

The data and code used to produce the figures of this manuscript are available on Zenodo at https://doi.org/10.5281/zenodo.7998103.

Code availability

The code for the genetic algorithm implementation used to perform the dispersion optimization is available at https://github.com/ErwanLucas/inverseLLE.

References

  1. Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, eaan8083 (2018).

    Google Scholar 

  2. Lugiato, L. A. & Lefever, R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987).

    ADS  MathSciNet  Google Scholar 

  3. Coen, S., Randle, H. G., Sylvestre, T. & Erkintalo, M. Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model. Opt. Lett. 38, 37–39 (2013).

    ADS  Google Scholar 

  4. Spencer, D. T. et al. An optical-frequency synthesizer using integrated photonics. Nature 557, 81–85 (2018).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  6. Trocha, P. et al. Ultrafast optical ranging using microresonator soliton frequency combs. Science 359, 887–891 (2018).

    ADS  Google Scholar 

  7. Suh, M.-G. & Vahala, K. J. Soliton microcomb range measurement. Science 359, 884–887 (2018).

    ADS  Google Scholar 

  8. Riemensberger, J. et al. Massively parallel coherent laser ranging using a soliton microcomb. Nature 581, 164–170 (2020).

    ADS  Google Scholar 

  9. Drake, T. E. et al. Terahertz-rate Kerr-microresonator optical clockwork. Phys. Rev. X 9, 031023 (2019).

    Google Scholar 

  10. Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nat. Photon. 4, 471–476 (2010).

    ADS  Google Scholar 

  11. Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2013).

    ADS  Google Scholar 

  12. Lorenc, D., Velic, D., Markevitch, A. & Levis, R. Adaptive femtosecond pulse shaping to control supercontinuum generation in a microstructure fiber. Opt. Commun. 276, 288–292 (2007).

    ADS  Google Scholar 

  13. Sigmund, O. On the usefulness of non-gradient approaches in topology optimization. Struct. Multidiscipl. Optim. 43, 589–596 (2011).

    MathSciNet  MATH  Google Scholar 

  14. Jensen, J. & Sigmund, O. Topology optimization for nano-photonics. Laser Photon. Rev. 5, 308–321 (2011).

    ADS  Google Scholar 

  15. Genty, G. et al. Machine learning and applications in ultrafast photonics. Nat. Photon. 15, 91–101 (2021).

    ADS  Google Scholar 

  16. Joannopoulos, J. D., Villeneuve, P. R. & Fan, S. Photonic crystals: putting a new twist on light. Nature 386, 143–149 (1997).

    ADS  Google Scholar 

  17. Molesky, S. et al. Inverse design in nanophotonics. Nat. Photon. 12, 659–670 (2018).

    ADS  Google Scholar 

  18. Yu, Z., Cui, H. & Sun, X. Genetically optimized on-chip wideband ultracompact reflectors and Fabry-Perot cavities. Photon. Res. 5, B15–B19 (2017).

    Google Scholar 

  19. Ahn, G. H. et al. Photonic inverse design of on-chip microresonators. ACS Photonics 9, 1875–1881 (2022).

    Google Scholar 

  20. Yu, S.-P. et al. Spontaneous pulse formation in edgeless photonic crystal resonators. Nat. Photon. 15, 461–467 (2021).

    ADS  Google Scholar 

  21. Lu, X., Rao, A., Moille, G., Westly, D. A. & Srinivasan, K. Universal frequency engineering tool for microcavity nonlinear optics: multiple selective mode splitting of whispering-gallery resonances. Photon. Res. 8, 1676 (2020).

    Google Scholar 

  22. 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, 1–11 (2023).

    Google Scholar 

  23. Zhang, C., Kang, G., Wang, J., Pan, Y. & Qu, J. Inverse design of soliton microcomb based on genetic algorithm and deep learning. Opt. Express 30, 44395–44407 (2022).

    ADS  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  25. Lobanov, V. E., Lihachev, G., Kippenberg, T. J. & Gorodetsky, M. Frequency combs and platicons in optical microresonators with normal GVD. Opt. Express 23, 7713–7721 (2015).

    ADS  Google Scholar 

  26. Yu, S.-P., Lucas, E., Zang, J. & Papp, S. B. A continuum of bright and dark-pulse states in a photonic-crystal resonator. Nat. Commun. 13, 3134 (2022).

    ADS  Google Scholar 

  27. Holland, J. H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence (MIT Press, 1992).

  28. Kumar, M., Husain, M., Upreti, N. & Gupta, D. Genetic algorithm: review and application. SSRN Electron. J. https://ssrn.com/abstract=3529843 (2010).

  29. Coen, S. & Erkintalo, M. Universal scaling laws of Kerr frequency combs. Opt. Lett. 38, 1790–1792 (2013).

    ADS  Google Scholar 

  30. 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).

    ADS  Google Scholar 

  31. Helgason, Ó. B. et al. Dissipative solitons in photonic molecules. Nat. Photon. 15, 305–310 (2021).

    ADS  Google Scholar 

  32. Skryabin, D. V. Hierarchy of coupled mode and envelope models for bi-directional microresonators with Kerr nonlinearity. OSA Continuum 3, 1364–1375 (2020).

    Google Scholar 

  33. Jung, H. et al. Tantala Kerr nonlinear integrated photonics. Optica 8, 811–817 (2021).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  35. Herr, T. et al. Mode spectrum and temporal soliton formation in optical microresonators. Phys. Rev. Lett. 113, 123901 (2014).

    ADS  Google Scholar 

  36. Herr, T. et al. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nat. Photon. 6, 480–487 (2012).

    ADS  Google Scholar 

  37. Li, Q. et al. Stably accessing octave-spanning microresonator frequency combs in the soliton regime. Optica 4, 193–203 (2017).

    ADS  Google Scholar 

  38. Gao, M. et al. Probing material absorption and optical nonlinearity of integrated photonic materials. Nat. Commun. 13, 3323 (2022).

    ADS  Google Scholar 

  39. Ji, Q.-X. et al. Engineered zero-dispersion microcombs using CMOS-ready photonics. Optica 10, 279–285 (2023).

    ADS  Google Scholar 

  40. Wang, H. et al. Dirac solitons in optical microresonators. Light Sci. Appl. 9, 205 (2020).

    ADS  Google Scholar 

  41. Fan, S. Sharp asymmetric line shapes in side-coupled waveguide-cavity systems. Appl. Phys. Lett. 80, 908–910 (2002).

    ADS  Google Scholar 

  42. Gorodetsky, M. L., Pryamikov, A. D. & Ilchenko, V. S. Rayleigh scattering in high-Q microspheres. J. Opt. Soc. Am. B 17, 1051–1057 (2000).

    ADS  Google Scholar 

  43. Hansson, T., Modotto, D. & Wabnitz, S. On the numerical simulation of Kerr frequency combs using coupled mode equations. Opt. Commun. 312, 134–136 (2014).

    ADS  Google Scholar 

  44. Gnan, M. et al. Closure of the stop-band in photonic wire Bragg gratings. Opt. Express 17, 8830–8842 (2009).

    ADS  Google Scholar 

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Acknowledgements

E.L. acknowledges support from the Swiss National Science Foundation (SNSF) under contract no. 191705. This research was funded by the DARPA PIPES programme under HR0011-19-2-0016 and the AFOSR FA9550-20-1-0004 project no. 19RT1019 and NIST.

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Author notes

  1. Erwan Lucas

    Present address: Laboratoire ICB, UMR CNRS 6303, Dijon, France

Authors and Affiliations

  1. Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO, USA

    Erwan Lucas, Su-Peng Yu, Travis C. Briles, David R. Carlson & Scott B. Papp

  2. Department of Physics, University of Colorado, Boulder, CO, USA

    Erwan Lucas, Su-Peng Yu & Scott B. Papp

  3. Octave Photonics, Louisville, CO, USA

    David R. Carlson

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Contributions

E.L. implemented the optimization algorithm, performed the experiments and analysed the data. E.L. and S.-P.Y. contributed to the numerical simulations and resonators design. T.C.B. and D.R.C. fabricated the microresonators. E.L. wrote the manuscript, with input from all authors. S.B.P. supervised the project.

Corresponding authors

Correspondence to Erwan Lucas or Scott B. Papp.

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Competing interests

D.R.C. is a cofounder of Octave Photonics. The remaining authors declare no competing interests.

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Peer review information

Nature Photonics thanks Victor Torres-Company and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 PhC and mode splitting calibration.

Measured mode splitting of the target mode as a function of corrugation amplitude ρPhC (single frequency PhC), measured across 114 resonators. The inset shown an extended range of ρPhC.

Extended Data Fig. 2 Effect of distributing the PhC pattern along the ring perimeter.

(a) Measured mode splitting distribution with various amount of chirping applied to the corrugation pattern. The design target is the Gaussian distribution shown in black. (b-d) Spatial profiles of the designed corrugations. (a) Without chirp, the splitting distribution is distorted and even inverted. The effect is avoided by chirping the pattern.

Supplementary information

Supplementary Information

Supplementary sections 1-4 and Figs. 1–3.

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Lucas, E., Yu, SP., Briles, T.C. et al. Tailoring microcombs with inverse-designed, meta-dispersion microresonators. Nat. Photon. 17, 943–950 (2023). https://doi.org/10.1038/s41566-023-01252-7

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