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Topological frequency combs and nested temporal solitons


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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Fig. 1: Working of the topological frequency comb.
Fig. 2: Operation of topological comb in the regimes of Turing rolls and chaos.
Fig. 3: Operation of topological comb in the regime of a nested solitons.
Fig. 4: Robustness of the topological comb.
Fig. 5: Qualitative phase diagram of the topological frequency comb.

Data availability

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.

Code availability

The codes that support the findings of this study are available from the corresponding author upon reasonable request.


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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).

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Authors and Affiliations



S.M. and M.H. conceived the idea. S.M. performed the numerical simulations, analysed the data and wrote the manuscript with inputs from M.H., Y.K.C., G.M. and K.S. M.H. supervised the project.

Corresponding author

Correspondence to Sunil Mittal.

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Competing interests

S.M. and M.H. have filed a provisional patent based on the results reported in this manuscript.

Additional information

Peer review informationNature Physics thanks Vittorio Peano and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–7 and Sections 1–8.

Supplementary Video 1

Circulation of a single nested soliton around the lattice.

Supplementary Video 2

Circulation of two nested solitons around the lattice.

Supplementary Video 3

Robustness of nested solitons against defects in the lattice.

Source data

Source Data Fig. 2

Raw data for line plots in Fig. 2a,c,g,h.

Source Data Fig. 3

Raw data for line plots in Fig. 3b,i,j.

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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).

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