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  • Open Access

Enhanced soliton stability in bidirectionally coupled laser-microresonator systems

L. Bengel1,*, H. Peng2,*, B. de Rijk1, C. Koos2, and W. Reichel1,†

  • *These authors contributed equally to this work.
  • †Contact author: wolfgang.reichel@kit.edu

Phys. Rev. A 114, 053502 – Published 3 November, 2026

DOI: https://doi.org/10.1103/xw6j-58wy

Abstract

We investigate a bidirectionally coupled system consisting of a Kerr-nonlinear microresonator and a continuous-wave single-mode semiconductor laser. Inside the resonator, a forward-propagating and a backscattered field interact nonlinearly, while a fraction of the backscattered field is fed back into the laser cavity. We demonstrate in this paper that the interaction of the laser with the feedback opens up new ways of stabilizing solitons. Using numerical bifurcation analysis, we systematically identify existence and stability ranges of time-harmonic soliton states in the anomalous dispersion regime. We show that, in contrast with the unidirectional configuration, the bidirectional coupling introduces a dynamic self-correcting response of the laser frequency that stabilizes solitons. We further corroborate these enhanced stability properties through Monte Carlo time integrations of randomly perturbed soliton states, demonstrating a significantly larger basin of attraction for solitons in the bidirectional system, consistent with existing experimental observations.

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References (33)

  1. P. Marin-Palomo, J. N. Kemal, T. J. Kippenberg, W. Freude, S. Randel, and C. Koos, Performance of chip-scale optical frequency comb generators in coherent WDM communications, Opt. Express 28, 12897 (2020).
  2. Q.-X. Ji, W. Zhang, A. Savchenkov, P. Liu, S. Sun, W. Jin, J. Guo, J. Peters, L. Wu, A. Feshali, M. Paniccia, V. Ilchenko, J. Bowers, A. Matsko, and K. Vahala, Dispersive-wave-agile optical frequency division, Nat. Photon. 19, 624 (2025).
  3. X. Jin, Z. Xie, X. Zhang, H. Hou, B. Wu, F. Zhang, X. Zhang, L. Chang, Q. Gong, and Q.-F. Yang, Microresonator-referenced soliton microcombs with zeptosecond-level timing noise, Nat. Photon. 19, 630 (2025).
  4. S. Sun, B. Wang, K. Liu, M. W. Harrington, F. Tabatabaei, R. Liu, J. Wang, S. Hanifi, J. S. Morgan, M. Jahanbozorgi, Z. Yang, S. M. Bowers, P. A. Morton, K. D. Nelson, A. Beling, D. J. Blumenthal, and X. Yi, Integrated optical frequency division for microwave and mmWave generation, Nature (London) 627, 540 (2024).
  5. Y. Zhao, J. K. Jang, G. J. Beals, K. J. McNulty, X. Ji, Y. Okawachi, M. Lipson, and A. L. Gaeta, All-optical frequency division on-chip using a single laser, Nature (London) 627, 546 (2024).
  6. D. Drayss, D. Fang, C. Füllner, G. Lihachev, T. Henauer, Y. Chen, H. Peng, P. Marin-Palomo, T. Zwick, W. Freude, T. J. Kippenberg, S. Randel, and C. Koos, Non-sliced optical arbitrary waveform measurement (OAWM) using soliton microcombs, Optica 10, 888 (2023).
  7. D. Fang, D. Drayss, H. Peng, G. Lihachev, C. Füllner, A. Kuzmin, P. Marin-Palomo, P. Matalla, P. Kharel, R. N. Wang, J. Riemensberger, M. Zhang, J. Witzens, J. C. Scheytt, W. Freude, S. Randel, T. J. Kippenberg, and C. Koos, 320 GHz photonic-electronic analogue-to-digital converter (ADC) exploiting Kerr soliton microcombs, Light: Sci. Appl. 14, 241 (2025).
  8. H. Peng, Y. Chen, D. Fang, C. Bremauer, G. Lihachev, D. Drayss, J. Riemensberger, A. Sherifaj, M. Lu, A. Voloshin, S. T. Skacel, M. Lauermann, T. Zwick, W. Freude, S. Randel, T. J. Kippenberg, and C. Koos, Optical arbitrary waveform generation (OAWG) using self-injection-locked RF-synchronized Kerr soliton microcombs, in CLEO 2025, Technical Digest Series (Optica Publishing Group, Washington, DC, 2025), paper SS164_1.
  9. H. Peng, L. Schmitz, D. Drayss, Y. Zheng, V. Lauinger, B. Geiger, Y. Xu, D. Fang, W. Freude, S. Randel, K. Yvind, L. Schmalen, M. Pu, and C. Koos, 400 GBd 32QAM transmission using RF-synchronized dark-soliton microcombs for optical arbitrary waveform generation (OAWG), in 2025 European Conference on Optical Communications (ECOC) (IEEE, Piscataway, NJ, 2025), pp. 1–4.
  10. J. Liu, G. Huang, R. N. Wang, J. He, A. S. Raja, T. Liu, N. J. Engelsen, and T. J. Kippenberg, High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits, Nat. Commun. 12, 2236 (2021).
  11. X. Ji, X. Li, Z. Qiu, R. N. Wang, M. Divall, A. Gelash, G. Lihachev, and T. J. Kippenberg, Deterministic soliton microcombs in Cu-free photonic integrated circuits, Nature (London) 646, 843 (2025).
  12. H.-J. Chen, K. Colburn, P. Liu, H. Yan, H. Hou, J. Ge, J.-Y. Liu, P. Lehan, Q.-X. Ji, Z. Yuan, D. Bouwmeester, C. Holmes, J. Gates, H. Blauvelt, and K. Vahala, Towards fibre-like loss for photonic integration from violet to near-infrared, Nature (London) 649, 338 (2026).
  13. B. Shen, L. Chang, J. Liu, H. Wang, Q.-F. Yang, C. Xiang, R. N. Wang, J. He, T. Liu, W. Xie, J. Guo, D. Kinghorn, L. Wu, Q.-X. Ji, T. J. Kippenberg, K. Vahala, and J. E. Bowers, Integrated turnkey soliton microcombs, Nature (London) 582, 365 (2020).
  14. C. Xiang, J. Liu, J. Guo, L. Chang, R. N. Wang, W. Weng, J. Peters, W. Xie, Z. Zhang, J. Riemensberger, J. Selvidge, T. J. Kippenberg, and J. E. Bowers, Laser soliton microcombs heterogeneously integrated on silicon, Science 373, 99 (2021).
  15. G. Lihachev, W. Weng, J. Liu, L. Chang, J. Guo, J. He, R. N. Wang, M. H. Anderson, Y. Liu, J. E. Bowers, and T. J. Kippenberg, Platicon microcomb generation using laser self-injection locking, Nat. Commun. 13, 1771 (2022).
  16. A. S. Raja, A. S. Voloshin, H. Guo, S. E. Agafonova, J. Liu, A. S. Gorodnitskiy, M. Karpov, N. G. Pavlov, E. Lucas, R. R. Galiev, A. E. Shitikov, J. D. Jost, M. L. Gorodetsky, and T. J. Kippenberg, Electrically pumped photonic integrated soliton microcomb, Nat. Commun. 10, 680 (2019).
  17. A. S. Voloshin, N. M. Kondratiev, G. V. Lihachev, J. Liu, V. E. Lobanov, N. Y. Dmitriev, W. Weng, T. J. Kippenberg, and I. A. Bilenko, Dynamics of soliton self-injection locking in optical microresonators, Nat. Commun. 12, 235 (2021).
  18. H. Wang, B. Shen, Y. Yu, Z. Yuan, C. Bao, W. Jin, L. Chang, M. A. Leal, A. Feshali, M. Paniccia, J. E. Bowers, and K. Vahala, Self-regulating soliton switching waves in microresonators, Phys. Rev. A 106, 053508 (2022).
  19. S. Deshmukh, T. M. Schneider, and A. Tikan, Bifurcation structure of soliton self-injection locking in microresonators, Opt. Lett. 51, 4817 (2026).
  20. L. A. Lugiato and R. Lefever, Spatial dissipative structures in passive optical systems, Phys. Rev. Lett. 58, 2209 (1987).
  21. M. Haelterman, S. Trillo, and S. Wabnitz, Dissipative modulation instability in a nonlinear dispersive ring cavity, Opt. Commun. 91, 401 (1992).
  22. N. M. Kondratiev, V. E. Lobanov, A. V. Cherenkov, A. S. Voloshin, N. G. Pavlov, S. Koptyaev, and M. L. Gorodetsky, Self-injection locking of a laser diode to a high-Q WGM microresonator, Opt. Express 25, 28167 (2017).
  23. J. Gärtner, P. Trocha, R. Mandel, C. Koos, T. Jahnke, and W. Reichel, Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory, Phys. Rev. A 100, 033819 (2019).
  24. P. Parra-Rivas, D. Gomila, L. Gelens, and E. Knobloch, Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion, Phys. Rev. E 98, 042212 (2018).
  25. P. Parra-Rivas, D. Gomila, L. Gelens, and E. Knobloch, Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion, Phys. Rev. E 97, 042204 (2018).
  26. L. Bengel, Stability of solitary wave solutions in the Lugiato–Lefever equation, Z. Angew. Math. Phys. 75, 130 (2024).
  27. L. Bengel and B. de Rijk, Existence and stability of soliton-based frequency combs in the Lugiato–Lefever equation, Phys. D 483, 134922 (2025).
  28. C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, 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).
  29. M. Stanislavova and A. G. Stefanov, Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides, J. Math. Phys. 59, 101502 (2018).
  30. A. E. Ulanov, T. Wildi, N. G. Pavlov, J. D. Jost, M. Karpov, and T. Herr, Synthetic reflection self-injection-locked microcombs, Nat. Photon. 18, 294 (2024).
  31. L. Bengel, Codes to “Enhanced soliton stability in bi-directionally coupled laser-microresonator systems”, Radar, , 2026, 10.35097/ccmqsda449ghm9k6.
  32. H. Uecker, D. Wetzel, and J. D. M. Rademacher, pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems, Numer. Math. Theory Methods Appl. 7, 58 (2014).
  33. H. Kielhöfer, Bifurcation Theory, 2nd ed., Applied Mathematical Sciences (Springer, New York, 2012), Vol. 156, pp. viii+398.

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