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Topological temporally mode-locked laser


Mode-locked lasers play a crucial role in modern science and technology. They are essential to the study of ultrafast and nonlinear optics, and they have applications in metrology, telecommunications and imaging. Recently, there has been interest in studying topological phenomena in mode-locked lasers. From a fundamental perspective, such study promises to reveal nonlinear topological physics, and from a practical perspective it may lead to the development of topologically protected short-pulse sources. Despite this promising outlook, the interplay between topological photonic lattices and laser mode-locking has not been studied experimentally. In this work, we theoretically propose and experimentally realize a topological temporally mode-locked laser. We demonstrate a nonlinearity-driven non-Hermitian skin effect in a laser cavity and observe the robustness of the laser against disorder-induced localization. Our experiments demonstrate fundamental point-gap topological physics that was previously inaccessible to photonics experiments, and they suggest potential applications of our mode-locked laser to sensing, optical computing and robust topological frequency combs. The experimental architecture employed in this work also provides a template for studying topology in other mode-locked photonic sources, including dissipative cavity solitons and synchronously pumped optical parametric oscillators.

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Fig. 1: Topological temporal mode-locking.
Fig. 2: Nonlinearity-driven NHSE in a topological mode-locked laser.
Fig. 3: Topological winding in a topological mode-locked laser.
Fig. 4: Robustness against disorder-induced localization.
Fig. 5: Robustness against disorder-induced localization.

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Data availability

The data used to generate the plots and results in this paper are available on figshare ( Source data are provided with this paper. All other data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code used to generate the plots and simulation results in this paper is available from the corresponding author upon reasonable request.


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We are grateful to K. Vahala and L. Wu for lending equipment useful to this work. We thank D. Nelson and N. Hatano for their comments on this work. The authors acknowledge support from NSF Grants No. 1846273 and 1918549 and AFOSR Award No. FA9550-20-1-0040. F.N. is supported in part by the Office of Naval Research (ONR), Japan Science and Technology Agency (JST) (via the Quantum Leap Flagship Program (Q-LEAP) and the Moonshot R&D Grant No. JPMJMS2061) and the Asian Office of Aerospace Research and Development (AOARD) (via Grant No. FA2386-20-1-4069). We wish to thank NTT Research for their financial and technical support.

Author information

Authors and Affiliations



C.R.L. and A.M. conceived the idea. C.R.L., A.D. and J.W. constructed the experimental setup. C.R.L. developed the theory, performed the simulations and experiments, and analysed the data. M.P. assisted with the simulations and the experiments. G.H.Y.L. helped to improve the experimental procedures. F.N. provided additional insight and guidance. A.M. supervised the project. All authors discussed the results and contributed to the writing of the paper.

Corresponding author

Correspondence to Alireza Marandi.

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Competing interests

A.M. has a financial interest in PINC Technologies Inc., which is developing photonic integrated nonlinear circuits. The other authors declare no competing interests.

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Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Topological Temporal Mode-Locking With a Hatano-Nelson Lattice.

(a) Heat map of our mode-locked laser’s output for 500 roundtrips. Here our laser’s intracavity couplings implement the Hatano-Nelson model with periodic boundary conditions. (b) A similar heat map, but now where the laser’s couplings implement a boundary in the Hatano-Nelson lattice. The data used to generate the heat maps in (a) and (b) are also used to generate the plots in Fig. 3. Note that the pulses in these heat maps are broadened for visibility.

Supplementary information

Supplementary Information

Supplementary Sections 1–9 and Figs. 1–26.

Source data

Source Data Fig. 2

Source data for Fig. 2c.

Source Data Fig. 3

Source data for Fig. 3a,d.

Source Data Fig. 5

Source data for Fig. 5a–d.

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Leefmans, C.R., Parto, M., Williams, J. et al. Topological temporally mode-locked laser. Nat. Phys. 20, 852–858 (2024).

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