Dynamics of driven dissipative temporal solitons in an intracavity phase trap

Englebert et al. Light: Science & Applications (2026)15:117 https://doi.org/10.1038/s41377-025-02147-8 www.nature.com/lsa ARTICLE Open Access Dynamics of driven dissipative temporal solitons in an intracavity phase trap Nicolas Englebert 1,2 , Corentin Simon 1 , Carlos Mas Arabí 1,3 , François Leo 1 and Simon-Pierre Gorza 1✉ 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Abstract Temporal cavity solitons are ultrashort optical pulses circulating in driven Kerr resonators. Their intrinsic stability and ability to generate coherent broadband frequency combs have led to breakthroughs in fields such as sensing, metrology, and signal synthesis. However, this robustness limits control over soliton dynamics and constrains comb characteristics. Here, we demonstrate that stationary and moving trapping potentials, generated through intracavity phase modulation, provide unprecedented control over cavity soliton properties. We theoretically show that, for deep potentials, the soliton spectral shift and repetition rate tuning range are primarily limited by a Hopf bifurcation, and reveal the role of dissipation in soliton dynamics. Using a fibre resonator, we observe stable blue- and red-shifted solitons up to 0.4 times their spectral width, at least an order of magnitude larger than with external phase modulation of the drive. We also investigate the interplay between the trapping potential and stimulated Raman scattering, showing that Raman self-frequency shift can be fully compensated, extending the existence range of cavity solitons. Our results provide a new means for stabilising or rapidly tuning the repetition rate of Kerr combs over a wide range, broadening the applications of Kerr frequency combs. Introduction Dissipative solitons are a fascinating class of localised structures that emerge in non-conservative systems1–4. They are uniquely determined by the system parameters to achieve a double balance: between dissipation and gain, and between dispersion and nonlinearity5. The latter ensures the invariance of nonlinear waves during propagation, endowing them with particle-like behaviour. Among optical dissipative solitons, temporal cavity solitons (CSs) are sechtype pulses propagating endlessly in coherently driven Kerr resonators6–9. The remarkable stability of the emitted output pulse train has led to growing interest in CSs over the last decade, driving progress in diverse applications such as distance measurement10, high-resolution spectroscopy11, telecommunications12, and astronomy13. Meanwhile, considerable efforts have been devoted to controlling the properties of cavity solitons11,14–16, notably through Correspondence: Simon-Pierre Gorza () 1 Service OPERA-Photonics, Université libre de Bruxelles (U.L.B.), 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Brussels, Belgium 2 Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Full list of author information is available at the end of the article modulations of the driving field’s phase17–20 and amplitude21–24. An appealing alternative approach would be to leverage the interaction between solitons and an intracavity phase modulation (IPM), which acts as an external potential for the nonlinear waves25–28. The interplay between solitons and a potential was extensively studied for conservative solitons (see e.g., refs. 29–31 and references therein), as well as for dissipative solitons in active mode-locked lasers32,33. Yet, the frequency constraint and phase locking of CSs to the coherent driving wave make these solitons more susceptible to perturbations affecting the delicate double balance. This raises the question of the effectiveness of intracavity phase traps in controlling and manipulating cavity solitons. In our work, we theoretically and experimentally explore the interaction between coherently driven cavity solitons and trapping potentials. Specifically, we derive the properties and existence range of cavity solitons synchronised to drifting IPMs. We demonstrate that the trapping enables the robust manipulation of the CS centre frequency and the output soliton comb repetition rate over a larger tuning range than established methods. As an application of the CS frequency control, we study the © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Englebert et al. Light: Science & Applications (2026)15:117 Page 2 of 10 Theoretical analysis We first theoretically analyse the impact of a real potential (V), such as that generated by IPM, on the existence and stability of CSs. The starting point is the driven-dissipative nonlinear Schrödinger equation, also known as the Lugiato-Levefer equation (LLE), a meanfield model that describes remarkably well the dynamics of coherently driven passive Kerr resonators35–37. It is here generalised to include a potential term. As such, it can be seen as the driven-dissipative Gross-Pitaevskii equation. It reads in dimensionless form (see Supplementary Information section A for the normalisation)28,38: 
 ∂Aðt; τÞ ∂ ∂2 ¼ iS þ ½Δ þ V ðτ Þ  i  j Aj2 þ i d þ i 2 A ∂t ∂τ ∂τ ð1Þ where t is the (slow) time associated with the round-trip evolution of the electric field envelope Aðt; τÞ of a wave propagating in a dispersive resonator with anomalous group-velocity dispersion and focusing Kerr nonlinearity. τ is a (fast) time variable defined in a co-moving reference frame in which V ðτÞ is assumed stationary with time t. S d Potential drift d<0 b c Power V τ) ' +V( Power Fast time (τ) Blue-shift Red-shift Driving :>0 := 0 Frequency :<0 ΩSL 17.5 = 7.5 ΩDL Frequency 5 35 = 15 Frequency ΩH2 10 Ω1 Stable cavity soliton 2.5 ΩH1 0 0 5 π2S 2 Δ LLE = DL 8 50 100 150 200 Absolute drift velocity µdµ a d>0 Absolute frequency shift µ:µ i Power Results is the driving amplitude and Δ is the normalised phase detuning from the closest resonance. d is a drift coefficient that accounts for a non-zero group velocity at the driving frequency in the co-moving reference frame. Dissipative Kerr cavity solitons are stationary solutions localised along the fast time τ. They are sustained by th (...truncated)