Recent advances in realizing optical frequency combs using nonlinear parametric processes in integrated photonic resonators have revolutionized on-chip optical clocks, spectroscopy and multichannel optical communications. At the same time, the introduction of topological physics in photonic systems has allowed the design of photonic devices with novel functionalities and inherent robustness against fabrication disorders. Here we use topological design principles to theoretically propose the generation of optical frequency combs and temporal dissipative Kerr solitons in a two-dimensional array of coupled ring resonators that creates a synthetic magnetic field for photons and exhibits topological edge states. We show that these topological edge states constitute a travelling-wave super-ring resonator that leads to the generation of coherent nested optical frequency combs, as well as the self-formation of nested temporal solitons and Turing rolls that are remarkably phase-locked over more than 40 rings. Moreover, we show that the topological nested solitons are robust against defects in the lattice, and a single nested soliton achieves a mode efficiency of over 50%, an order of magnitude higher than single-ring frequency combs. Our topological frequency comb works in a parameter regime that can be readily accessed using existing low-loss integrated photonic platforms like silicon nitride.
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Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).
Cundiff, S. T. & Ye, J. Colloquium: femtosecond optical frequency combs. Rev. Mod. Phys. 75, 325–342 (2003).
Diddams, S. A., Vahala, K. & Udem, T. Optical frequency combs: coherently uniting the electromagnetic spectrum. Science 369, eaay3676 (2020).
Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555–559 (2011).
Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, eaan8083 (2018).
Pasquazi, A. et al. Micro-combs: a novel generation of optical sources. Phys. Rep. 729, 1–81 (2018).
Gaeta, A. L., Lipson, M. & Kippenberg, T. J. Photonic-chip-based frequency combs. Nat. Photon. 13, 158–169 (2019).
Del’Haye, P. et al. Optical frequency comb generation from a monolithic microresonator. Nature 450, 1214–1217 (2007).
Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2013).
Jang, J. K. et al. Synchronization of coupled optical microresonators. Nat. Photon. 12, 688–693 (2018).
Tikan, A. et al. Emergent nonlinear phenomena in a driven dissipative photonic dimer. Nat. Phys. 17, 1–7 (2021).
Helgason, Ó. B. et al. Dissipative solitons in photonic molecules. Nat. Photon. 15, 305–310 (2021).
Vasco, J. & Savona, V. Slow-light frequency combs and dissipative Kerr solitons in coupled-cavity waveguides. Phys. Rev. Appl. 12, 064065 (2019).
Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).
Khanikaev, A. B. & Shvets, G. Two-dimensional topological photonics. Nat. Photon. 11, 763–773 (2017).
Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).
Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).
Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).
Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).
Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).
St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photon. 11, 651–656 (2017).
Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).
Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).
Yang, Z. et al. Mode-locked topological insulator laser utilizing synthetic dimensions. Phys. Rev. X 10, 011059 (2020).
Cheng, X. et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater. 15, 542–548 (2016).
Zhao, H. et al. Non-Hermitian topological light steering. Science 365, 1163–1166 (2019).
Barik, S. et al. A topological quantum optics interface. Science 359, 666–668 (2018).
Shalaev, M. I., Walasik, W., Tsukernik, A., Xu, Y. & Litchinitser, N. M. Robust topologically protected transport in photonic crystals at telecommunication wavelengths. Nat. Nanotechnol. 14, 31–34 (2019).
Gao, X. et al. Dirac-vortex topological cavities. Nat. Nanotechnol. 15, 1012–1018 (2020).
Lu, L., Gao, H. & Wang, Z. Topological one-way fiber of second Chern number. Nat. Commun. 9, 5384 (2018).
Mittal, S., Goldschmidt, E. A. & Hafezi, M. A topological source of quantum light. Nature 561, 502–506 (2018).
Mittal, S., Orre, V. V., Goldschmidt, E. A. & Hafezi, M. Tunable quantum interference using a topological source of indistinguishable photon pairs. Nat. Photon. 15, 542–548 (2021).
Blanco-Redondo, A., Bell, B., Oren, D., Eggleton, B. J. & Segev, M. Topological protection of biphoton states. Science 362, 568–571 (2018).
Kruk, S. et al. Nonlinear light generation in topological nanostructures. Nat. Nanotechnol. 14, 126–130 (2019).
Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y. Nonlinear topological photonics. Appl. Phys. Rev. 7, 021306 (2020).
Lumer, Y., Plotnik, Y., Rechtsman, M. C. & Segev, M. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905 (2013).
Ablowitz, M. J., Curtis, C. W. & Ma, Y.-P. Linear and nonlinear traveling edge waves in optical honeycomb lattices. Phys. Rev. A 90, 023813 (2014).
Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117, 143901 (2016).
Mukherjee, S. & Rechtsman, M. C. Observation of Floquet solitons in a topological bandgap. Science 368, 856–859 (2020).
Xue, X., Wang, P.-H., Xuan, Y., Qi, M. & Weiner, A. M. Microresonator Kerr frequency combs with high conversion efficiency. Laser Photon. Rev. 11, 1600276 (2017).
Bao, H. et al. Laser cavity-soliton microcombs. Nat. Photon. 13, 384–389 (2019).
Xue, X., Zheng, X. & Zhou, B. Super-efficient temporal solitons in mutually coupled optical cavities. Nat. Photon. 13, 616–622 (2019).
Leykam, D., Mittal, S., Hafezi, M. & Chong, Y. D. Reconfigurable topological phases in next-nearest-neighbor coupled resonator lattices. Phys. Rev. Lett. 121, 023901 (2018).
Mittal, S., Orre, V. V., Leykam, D., Chong, Y. D. & Hafezi, M. Photonic anomalous quantum Hall effect. Phys. Rev. Lett. 123, 043201 (2019).
Chembo, Y. K. & Yu, N. Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators. Phys. Rev. A 82, 033801 (2010).
Chembo, Y. K. & Menyuk, C. R. Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators. Phys. Rev. A 87, 053852 (2013).
Hansson, T., Modotto, D. & Wabnitz, S. On the numerical simulation of Kerr frequency combs using coupled mode equations. Opt. Commun. 312, 134–136 (2014).
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).
Kues, M. et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546, 622–626 (2017).
Reimer, C. et al. High-dimensional one-way quantum processing implemented on d-level cluster states. Nat. Phys. 15, 148–153 (2019).
Carusotto, I. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020).
Kollár, A. J., Fitzpatrick, M. & Houck, A. A. Hyperbolic lattices in circuit quantum electrodynamics. Nature 571, 45–50 (2019).
This research was supported by the Air Force Office of Scientific Research Multi-University Research Initiative (AFOSR-MURI grant no. FA9550-16-1-0323), Office of Naval Research Multi-University Research Initiative (ONR-MURI grant no. N00014-20-1-2325), United States Army Research Laboratory grant no. W911NF1920181 and NSF grant no. PHY1820938. Y.K.C. was supported by the Air Force Office of Scientific Research (AFOSR grant no. FA9550-20-1-0357).
S.M. and M.H. have filed a provisional patent based on the results reported in this manuscript.
Peer review information Nature Physics thanks Vittorio Peano and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary Figs. 1–7 and Sections 1–8.
Circulation of a single nested soliton around the lattice.
Circulation of two nested solitons around the lattice.
Robustness of nested solitons against defects in the lattice.
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Mittal, S., Moille, G., Srinivasan, K. et al. Topological frequency combs and nested temporal solitons. Nat. Phys. 17, 1169–1176 (2021). https://doi.org/10.1038/s41567-021-01302-3
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