Self-organization of cavity solitons in Brillouin-Kerr ring resonators

Abstract

We report on the interaction between stimulated Brillouin scattering and temporal cavity solitons in doubly resonant ring resonators. Our experiments are performed in coherently driven passive optical-fibre resonators. We demonstrate that the interplay between four-wave mixing and cascade Brillouin lasing spontaneously generates patterns of CSs on a temporal grid at twice the Brillouin-shift. These patterns are shown to be highly stable owing to a long-range locking mechanism mediated by the acoustic oscillation generated by the solitons. We introduce a unified mean-field model of the cavity to describe the dynamics between the coupled forward and backward waves under coherent driving. This model reproduces very well the experiments and explains the paracrystalline structures of the soliton pattern. Our findings significantly advance the understanding of hybrid Brillouin-Kerr optical frequency combs.

Figures (4)

• Figure 1: Space–time schematic representation of the trailing tail formation behind a CS. The CS locally excites an acoustic wave with the Brillouin impulse response $h_b(t)$, upon which $S_1$ is scattered, resulting in the generation of a decaying trailing wave pinned to the soliton.
• Figure 2: (a) Transmitted ($P_F$) and backward ($P_B$) signals when scanning the frequency of a laser over multiple resonances (forward detuning scan rate $\qty{2.3}{\radian / \milli \second}$). The transmission shows the expected tilted nonlinear resonance, followed by a single soliton step. (b) Close-up view of a single resonance. This step co-exists with a weak backward Brillouin lasing signal. (c) Dynamics of the output forward signal, recorded with a high-bandwidth oscilloscope after filtering the CW driving component. The formation dynamics of individual solitons are visible in the zoomed-in view (d). (e,f) The simulation with our mean-field model [Eqs.\ref{['eq1']}-\ref{['eq2']}] reproduces very well the whole dynamics ($\qty{2.3}{\radian / \milli \second}$). Raman interaction, which slightly bends CS's trajectory in panel (d), is not included in the simulation for simplicity.
• Figure 3: (a) Oscilloscope measurements at the cavity output showing the long-term stability of the soliton pattern ($\delta\approx0.49$). (b) Optical spectrum measured in the through port of the cavity coupler, after pump filtering. Light blue, high resolution (RBW = $\qty{0.16}{\pico \meter}$) and, dark blue, low resolution (RBW = $\qty{30}{\pico \meter}$). (c) Same for the backward signal at high resolution. (d) Radiofrequency spectrum corresponding to (b) (different realization). Inset: fine teeth structure of the wide comb. (e) Zoom around one RF tooth.
• Figure 4: (a) Simulation of a CS showing its oscillation induced by the drifting modulated background from the $S_0-S_2$ beating. Inset: soliton peak power variation. (b) Experimental measurement of the oscillation of the CSs. Each point of the scatter plot corresponds to a single CS. (c) Simulated intracavity power for spontaneously generated CSs, after numerical filtering of $S_2$. The weak modulation at $2\nu_b$, stationary in the CSs reference frame and responsible for their locking, can be seen. (d) Theoretical soliton drift induced by the interaction between a CS located at $\tau=0$ and $S_1$, computed from Eqs. \ref{['eq1']}-\ref{['eq2']} (solid lines). Stable equilibrium points are indicated. The dashed line shows our simplified analytical model of the drift, fitted to the experimental CS positions. (e) Reconstructed cumulated drift from the fitted model and experimental CSs positions computed from the oscilloscope trace recorded over a round-trip once the pattern is stabilized. (f) Distribution of the experimental delay between two consecutive solitons, separated by a single ($n=1$) or multiple ($n>1$) lattice period $1/2\nu_b = \qty{46.1}{\pico \second}$.