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Topological temporally mode-locked laser

Abstract

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 (https://doi.org/10.6084/m9.figshare.25050494). 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.

References

  1. Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y. Nonlinear topological photonics. Appl. Phys. Rev. 7, 021306 (2020).

    Article  ADS  Google Scholar 

  2. Jürgensen, M., Mukherjee, S. & Rechtsman, M. C. Quantized nonlinear Thouless pumping. Nature 596, 63–67 (2021).

    ADS  Google Scholar 

  3. Parto, M. et al. Edge-mode lasing in 1D topological active arrays. Phys. Rev. Lett. 120, 113901 (2018).

    ADS  Google Scholar 

  4. Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).

    Google Scholar 

  5. Contractor, R. et al. Scalable single-mode surface-emitting laser via open-Dirac singularities. Nature 608, 692–698 (2022).

    ADS  Google Scholar 

  6. Longhi, S. Non-Hermitian topological phase transition in PT-symmetric mode-locked lasers. Opt. Lett. 44, 1190–1193 (2019).

    ADS  Google Scholar 

  7. Yang, Z. et al. Mode-locked topological insulator laser utilizing synthetic dimensions. Phys. Rev. X 10, 011059 (2020).

    Google Scholar 

  8. Zykin, A. Y., Skryabin, D. V. & Kartashov, Y. V. Topological solitons in arrays of modelocked lasers. Opt. Lett. 46, 2123 (2021).

    ADS  Google Scholar 

  9. Tusnin, A. K., Tikan, A. M. & Kippenberg, T. J. Dissipative Kerr solitons at the edge state of the Su-Schrieffer-Heeger model. J. Phys. Conf. Ser. 2015, 012159 (2021).

    Google Scholar 

  10. Tikan, A. et al. Protected generation of dissipative Kerr solitons in supermodes of coupled optical microresonators. Sci. Adv. 8, eabm6982 (2022).

    Google Scholar 

  11. Fan, Z., Puzyrev, D. N. & Skryabin, D. V. Topological soliton metacrystals. Commun. Phys. 5, 248 (2022).

  12. Mittal, S., Moille, G., Srinivasan, K., Chembo, Y. K. & Hafezi, M. Topological frequency combs and nested temporal solitons. Nat. Phys. 17, 1169–1176 (2021).

    Google Scholar 

  13. Haus, H. A. Mode-locking of lasers. IEEE J. Sel. Top. Quant. 6, 1173–1185 (2000).

    Google Scholar 

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

    Google Scholar 

  15. Dutt, A. et al. Creating boundaries along a synthetic frequency dimension. Nat. Commun. 13, 3377 (2022).

    ADS  Google Scholar 

  16. Li, G. et al. Direct extraction of topological Zak phase with the synthetic dimension. Light Sci. Appl. 12, 81 (2023).

    ADS  Google Scholar 

  17. Leefmans, C. et al. Topological dissipation in a time-multiplexed photonic resonator network. Nat. Phys. 18, 442–449 (2022).

    Google Scholar 

  18. Parto, M., Leefmans, C., Williams, J., Nori, F. & Marandi, A. Non-Abelian effects in dissipative photonic topological lattices. Nat. Commun. 14, 1440 (2023).

    ADS  Google Scholar 

  19. Gong, Z. et al. Topological phases of non-Hermitian systems. Phys. Rev. X 8, 031079 (2018).

    Google Scholar 

  20. Kawabata, K., Shiozaki, K., Ueda, M. & Sato, M. Symmetry and topology in non-Hermitian physics. Phys. Rev. X 9, 041015 (2019).

    Google Scholar 

  21. Yao, S. & Wang, Z. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett. 121, 086803 (2018).

    ADS  Google Scholar 

  22. Zhang, K., Yang, Z. & Fang, C. Correspondence between winding numbers and skin modes in non-Hermitian systems. Phys. Rev. Lett. 125, 126402 (2020).

    ADS  MathSciNet  Google Scholar 

  23. Hatano, N. & Nelson, D. R. Vortex pinning and non-Hermitian quantum mechanics. Phys. Rev. B 56, 8651–8673 (1997).

    ADS  Google Scholar 

  24. Hatano, N. & Nelson, D. R. Non-Hermitian delocalization and eigenfunctions. Phys. Rev. B 58, 8384–8390 (1998).

    ADS  Google Scholar 

  25. Quinlan, F., Ozharar, S., Gee, S. & Delfyett, P. J. Harmonically mode-locked semiconductor-based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources. J. Opt. A 11, 103001 (2009).

    ADS  Google Scholar 

  26. Harvey, G. T. & Mollenauer, L. F. Harmonically mode-locked fiber ring laser with an internal Fabry–Perot stabilizer for soliton transmission. Opt. Lett. 18, 107–109 (1993).

    ADS  Google Scholar 

  27. Pottiez, O. et al. Experimental study of supermode noise of harmonically mode-locked erbium-doped fibre lasers with composite cavity. Opt. Commun. 202, 161–167 (2002).

    ADS  Google Scholar 

  28. Srinivasan, S. et al. Harmonically Mode-locked hybrid silicon laser with intra-cavity filter to suppress supermode noise. IEEE J. Sel. Top. Quant. 20, 8–15 (2014).

    Google Scholar 

  29. Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).

    ADS  MathSciNet  Google Scholar 

  30. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).

    ADS  Google Scholar 

  31. Yin, C., Jiang, H., Li, L., Lü, R. & Chen, S. Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems. Phys. Rev. A 97, 052115 (2018).

    ADS  Google Scholar 

  32. Weidemann, S. et al. Topological funneling of light. Science 368, 311–314 (2020).

    ADS  MathSciNet  Google Scholar 

  33. Xiao, L. et al. Non-Hermitian bulk–boundary correspondence in quantum dynamics. Nat. Phys. 16, 761–766 (2020).

    Google Scholar 

  34. Liu, Y. G. N. et al. Complex skin modes in non-Hermitian coupled laser arrays. Light Sci. Appl. 11, 336 (2022).

    ADS  Google Scholar 

  35. Wang, K. et al. Generating arbitrary topological windings of a non-Hermitian band. Science 371, 1240–1245 (2021).

    ADS  Google Scholar 

  36. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    ADS  Google Scholar 

  37. Longhi, S. Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model. Phys. Rev. B 103, 144202 (2021).

    ADS  Google Scholar 

  38. Tzortzakakis, A. F., Makris, K. G. & Economou, E. N. Non-Hermitian disorder in two-dimensional optical lattices. Phys. Rev. B 101, 014202 (2020).

    ADS  Google Scholar 

  39. Luo, X., Ohtsuki, T. & Shindou, R. Universality classes of the Anderson transitions driven by non-Hermitian disorder. Phys. Rev. Lett. 126, 090402 (2021).

    ADS  Google Scholar 

  40. Weidemann, S., Kremer, M., Longhi, S. & Szameit, A. Coexistence of dynamical delocalization and spectral localization through stochastic dissipation. Nat. Photon. 15, 576–581 (2021).

    ADS  Google Scholar 

  41. Lin, Q. et al. Observation of non-Hermitian topological Anderson insulator in quantum dynamics. Nat. Commun. 13, 3229 (2022).

    ADS  Google Scholar 

  42. Song, Y. et al. Two-dimensional non-Hermitian skin effect in a synthetic photonic lattice. Phys. Rev. Appl. 14, 064076 (2020).

    ADS  Google Scholar 

  43. Roy, A., Parto, M., Nehra, R., Leefmans, C. & Marandi, A. Topological optical parametric oscillation. Nanophotonics 11, 1611–1618 (2022).

    Google Scholar 

  44. Roy, A. et al. Temporal walk-off induced dissipative quadratic solitons. Nat. Photon. https://doi.org/10.1038/s41566-021-00942-4 (2022).

  45. Marandi, A., Wang, Z., Takata, K., Byer, R. L. & Yamamoto, Y. Network of time-multiplexed optical parametric oscillators as a coherent Ising machine. Nat. Photon. 8, 937–942 (2014).

    ADS  Google Scholar 

  46. Englebert, N., Mas Arabí, C., Parra-Rivas, P., Gorza, S.-P. & Leo, F. Temporal solitons in a coherently driven active resonator. Nat. Photon. 15, 536–541 (2021).

    ADS  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

Authors

Contributions

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). https://doi.org/10.1038/s41567-024-02420-4

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