# Controlling Frequency Comb Line Spacing Via Symmetry Broken Faticons

Lewis Hill, Erwan Lucas, Alekhya Ghosh, Juan Diego Mazo Vásquez, Julius T Gohsrich, Arghadeep Pal, Haochen Yan, Pascal Del'haye, Gian-Luca Oppo, Stéphane Coen, et al.

► To cite this version:

Lewis Hill, Erwan Lucas, Alekhya Ghosh, Juan Diego Mazo Vásquez, Julius T Gohsrich, et al. Controlling Frequency Comb Line Spacing Via Symmetry Broken Faticons. 2025 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Jun 2025, Munich, Germany. pp.1-1, 10.1109/CLEO/Europe-EQEC65582.2025.11111585. [https://hal-05405326v1](https://hal.science/hal-05405326v1)

HAL Id: hal-05405326

Submitted on 9 Dec 2025

**HAL** is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire **HAL**, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Controlling Frequency Comb Line Spacing Via Symmetry Broken Faticons

Lewis Hill¹, Erwan Lucas², Alekhya Ghosh¹,³, Juan Diego Mazo Vásquez¹,³, Julius T. Gohsrich¹,³, Arghadeep Pal¹,³, Haochen Yan¹,³, Pascal Del'Haye¹,³, Gian-Luca Oppo⁴, Stéphane Coen⁵,⁶, Flore K. Kunst¹,³, and Julien Fatome²

1. Max Planck Institute for the Science of Light, Staudtstr. 2, 91058 Erlangen, Germany

2. Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS-UBE, Dijon, France

3. Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, Germany

4. SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK

5. Department of Physics, University of Auckland, Auckland, New Zealand

6. The Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand

Recently, a novel temporal structure known as the faticon has been identified within ring resonators composed of Kerr materials [1]. An example of a faticon is shown in Fig. 1(a), where its unique structure is seen to depend on two interlocked field components, $|E_{\pm}|^2$. These components co-propagate within the ring resonator but exhibit left- and right-circular polarizations, respectively. Faticons were initially predicted through a coupled set of (normalized) Lugiato-Lefever equations and have since been experimentally observed [1]. A key mechanism enabling the existence of a faticon is the spontaneous symmetry breaking (SSB) of light [2-5], wherein the symmetry between the two field components' intensities $|E_+|^2$ and $|E_-|^2$ spontaneously breaks ($|E_+|^2 \neq |E_-|^2$) due to an infinitesimal change in a system parameter, such as the cavity detuning $\theta$.

Our recent further investigation into faticon structures has revealed an intriguing phenomenon - a higher-order SSB. This additional symmetry breaking is easiest seen between the peak powers of the two underlying faticon field components themselves, as illustrated in Fig. 1(b). The result of this peak-power SSB is a dynamic interplay between the symmetry-broken peaks, leading to a "chasing" effect between the two components, shown in Fig. 1(c-h). This chasing effect causes the faticon to either decelerate or accelerate, settling into a new constant propagation velocity within the ring. Remarkably, the change in faticon propagation speed is directly linked to the degree of peak-power symmetry breaking, allowing controlled tuning of the round-trip time in the resonator. This, in turn, enables precise variation of the faticon's repetition rate and the corresponding frequency comb line spacing.

<figure><img src="image_2.png" /><figcaption>**Fig. 1** (a) Example of a symmetric faticon fast-time structure in a Kerr ring resonator. (b) Scan of the cavity detuning parameter for a fixed input pump, showing the peak power of the two field components that comprise the faticon. A spontaneous symmetry-breaking bifurcation occurs between the field components at approximately $\theta = 8.325$. (c-h) Slow-time evolutions for initial conditions of a symmetric faticon at a cavity detuning value within the symmetry-breaking region ($\theta = 8.375$, as indicated in (b)). (c-e) Evolution of the field components $|E_+|^2$ and $|E_-|^2$ in (c) and (d), respectively, with their combined profile in (e). Symmetry breaking in the instance of (c-e) favors $|E_+|^2$, here resulting in a slower propagation velocity of the faticon relative to the cavity reference frame. (f-h) Similar evolution but with symmetry breaking favoring $|E_-|^2$, leading to an increased propagation velocity relative to the cavity reference frame.</figcaption></figure>

## References

[1] E. Lucas et al. "Polarization faticons: Chiral localized structures in self-defocusing Kerr resonators", arXiv:2412.05116 (2024)

[2] L. Hill et al. "Effects of self-and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators", Phys. Rev. A 101, 013823 (2020)

[3] B. Garbin et al. "Asymmetric balance in symmetry breaking", Phys. Rev. Research 2, 023244 (2020)

[4] G. N. Campbell et al. "Frequency comb enhancement via the self-crystallization of vectorial cavity solitons", Optics Express Vol. 32, Issue 21, pp. 37691-37702 (2024)

[5] A. Ghosh et al. "Phase Symmetry Breaking of Counterpropagating Light in Microresonators for Switches and Logic Gates", arXiv:2407.16625 (2024)