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Tailoring microcombs with inverse-designed, meta-dispersion microresonators


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

Code availability

The code for the genetic algorithm implementation used to perform the dispersion optimization is available at


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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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Authors and Affiliations



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

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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).

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