Dissipative Kerr Soliton Self-Balancing from Kerr-Induced Synchronization

Integrated frequency comb sources are a key enabling technology for frequency metrology applications. Their on-chip integration promises to bring metrology capacity outside of the lab, particularly since they can operate at low continuous-wave pump laser power in the dissipative Kerr soliton (DKS) regime. Yet, such small foot-print and low power comes at a cost: higher noise and overall lower comb power. In particular, this translates to highly challenging detection and locking of the carrier-envelope offset, necessary for complete stabilization of the comb. Recently, Kerr-induced synchronization (KIS) of a DKS to a reference laser has been demonstrated as a tool for passive all-optical stabilization of DKS microcombs, with fundamental modification to the DKS and microcomb properties. Here, we demonstrate that the combination of additional power from the reference laser (now part of the DKS) and the KIS phase locking that pins the repetition rate together fundamentally alter the DKS, forcing an energy redistribution to maintain its center of mass. We demonstrate this self-balancing effect theoretically, which in a pure quadratic dispersion resonator leads to reference-dependent recoil. With higher-order dispersion through which the DKS yields phase-matched dispersive waves (DWs), we demonstrate that self-balancing increases the DW radiation, experimentally showing a 22 dB increase of comb teeth at 780 nm in an octave-spanning microcomb for efficient deployable carrier-envelope offset detection.

💡 Research Summary

Integrated microresonator frequency combs based on dissipative Kerr solitons (DKS) promise low‑power, chip‑scale metrology, but their small footprint and modest pump power lead to weak comb lines and poor signal‑to‑noise ratios, making carrier‑envelope‑offset (CEO) detection especially difficult. Kerr‑induced synchronization (KIS) – the injection of a second “reference” laser into the same resonator that hosts the DKS – has recently been shown to passively lock the soliton’s repetition rate to the frequency difference between the two pumps. This paper uncovers a previously unreported consequence of KIS: the soliton undergoes a self‑balancing process that conserves its spectral center of mass (SCM) despite the asymmetric energy added by the reference pump.

In the simplest case of a resonator with only second‑order (quadratic) dispersion, the authors model the system with a multi‑pump Lugiato‑Lefever equation (MLLE) and apply standard soliton perturbation theory. They treat loss, pump terms, and the reference field as small perturbations to the nonlinear Schrödinger equation. By assuming that only the soliton amplitude, position, central frequency (spectral recoil µ_r), and phase evolve, they derive an analytical condition for stationary KIS operation. The condition shows that, while the repetition rate remains fixed (ν_KIS_rep = (ν_pmp – ν_ref)/M), the soliton must acquire a spectral recoil µ_r that exactly compensates the momentum introduced by the reference pump. The recoil follows a sech(·)·tanh(·) dependence on the reference mode number µ_s and is independent of the reference pump power, predicting an optimal µ_s for maximal recoil. Numerical simulations of the full MLLE confirm this trend, demonstrating that the soliton indeed shifts its spectrum opposite to the reference pump without changing its repetition rate. This “self‑balancing” is fundamentally different from Raman‑induced recoil or recoil caused by higher‑order dispersion, which always accompany a repetition‑rate shift.

When third‑order (or higher) dispersion is present, the DKS can phase‑match to a cavity mode far from the pump, generating a dispersive wave (DW). The authors extend the MLLE to include a D₃ term, repeat the perturbative analysis, and find that the soliton now has two degrees of freedom to conserve its SCM: spectral recoil and enhanced DW emission. The reference pump’s asymmetric energy injection forces the soliton to increase DW power on the side opposite the reference, thereby preserving the overall spectral momentum.

Experimentally, the team uses a Si₃N₄ microring resonator with an octave‑spanning comb. A primary pump around 1550 nm and a reference laser near 780 nm are injected. In the KIS regime the repetition rate remains unchanged, yet the high‑frequency DW at 780 nm grows by 22 dB compared with the single‑pump case. Spectral measurements confirm that this enhancement is not due to simple four‑wave mixing between the two pumps; rather, it originates from the soliton’s intrinsic self‑balancing response. The boosted DW provides a strong, coherent line suitable for f‑2 f interferometry, enabling robust CEO detection even with the low on‑chip pump power typical of integrated DKS sources.

The paper’s contributions are threefold: (1) identification of a new soliton self‑balancing mechanism triggered by KIS, (2) analytical and numerical demonstration that the mechanism yields a predictable spectral recoil and, in the presence of higher‑order dispersion, a substantial increase in DW power, and (3) experimental verification of a 22 dB DW boost that directly facilitates CEO detection in chip‑scale microcombs. By showing that KIS can simultaneously lock the repetition rate, preserve the soliton’s spectral momentum, and amplify useful spectral components without additional electronic feedback, the work opens a pathway toward fully integrated, low‑noise, broadband frequency combs for portable metrology, remote sensing, and optical communications. Future directions include multi‑reference‑laser schemes for tailored DW spectra, real‑time CEO feedback using the self‑balancing dynamics, and exploration of the effect in other material platforms (e.g., AlN, LiNbO₃) where higher‑order dispersion can be engineered.