Dissipative Kerr Soliton Self-Balancing from Kerr-Induced Synchronization

TL;DR

This work shows that Kerr-induced synchronization (KIS) between a primary pump and a reference laser in a microresonator induces a self-balancing mechanism that conserves the soliton’s spectral center of mass even as intracavity energy becomes asymmetric. Using the multi-pump Lugiato-Lefever framework and soliton perturbation theory, the authors derive analytic expressions for spectral recoil in purely quadratic dispersion and show how higher-order dispersion enables dispersive-wave (DW) enhancement through energy reallocation, without altering the repetition rate. They demonstrate, both numerically and experimentally, that injecting the reference pump can boost high-frequency DW power by up to 22 dB in an octave-spanning microcomb, with a linear dependence on reference power, thereby improving CEO detection without compromising comb coherence. This self-balancing mechanism offers a new route for energy management in DKSs, enabling targeted spectral enhancement and robust field-deployable metrology with on-chip microcombs.

Abstract

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.

Figures (4)

• Figure 1: Soliton self-balancing mechanism through spectral energy redistribution under Kerr-induced synchronization---(a--c) Pure quadratic dispersion case.a The DKS frequency comb centers on the main pump. The equivalent lever diagram represents conservation of the center of mass, which in the single-pump case corresponds to equal weight at equal distance from the center (i.e., the main pump). b In the KIS regime, however, the reference pump becomes part of the DKS and adds asymmetric energy, creating a nonphysical imbalance. c Because the repetition rate is pinned by the main and reference pumps, the DKS cannot compensate for the energy imbalance through temporal drift. The sole degree of freedom available to the DKS is to shift its center of mass, resulting in recoil. (d--f) Higher-order dispersion case.d If the resonator exhibits at least a tertiary dispersion term, the DKS becomes phase-matched to at least one azimuthal mode of the cavity, leading to dispersive wave emission and creating a natural imbalance, hence an intrinsic recoil for center-of-mass conservation. e Similarly, in the KIS regime the reference pump adds an energy imbalance. f The DKS now possesses another degree of freedom to compensate for the reference energy. While it still compensates via recoil, it also increases its dispersive wave emission, enhancing the dispersive wave mode away from the reference mode. DW: dispersive wave.
• Figure 2: Self-balancing in a pure quadratic integrated dispersion microresonator. (a) Simulated spectra with (blue) and without (purple) KIS. FWM: four-wave mixing. (b) Spectral recoil that occurs due to KIS. When the reference pump is used to synchronize the DKS on one side of the spectrum, a spectral recoil occurs and the spectral center of mass is shifted in the opposite direction. (c) Comparison of simulated and analytically calculated spectral recoil at varying reference pump mode numbers and amplitudes. The simulated spectral recoil (circular markers) follow the analytically calculated $\sech(\cdot)\tanh(\cdot)$ trend (dotted lines). The maximal spectral recoil is obtained at the same $\mu_\mathrm{ref}$ for all reference pump amplitudes.
• Figure 3: Demonstration of self-balancing effect in the presence of a single DW. (a) Comparison of the frequency comb spectra with (blue) and without (purple) KIS. In the absence of KIS, the peak of the spectrum is offset from $\mu=0$ due to a spectral recoil resulting from the presence of a DW. When a reference pump is injected at the frequency of the comb line at $\mu_{\rm ref}=-20$, the soliton enters the KIS regime and experiences a spectral recoil in a manner identical to what was shown in the pure-quadratic case. (b) The KIS-induced spectral recoil opposes the recoil due to the DW and cancels each other out, leaving the resulting spectrum nearly symmetric around $\mu=0$. (c) Apart from the spectral recoil, the self-balancing effect leads to a significant increase in the power of the comb lines around the DW mode. (d) Change in the DW power as a function of the mode at which the reference pump is injected, for different reference pump powers. The circular points show results obtained from the MLLE and dotted lines are fits to the analytical expression obtained in \ref{['eq:delta_dw_power']}. A clear peak exists at the same $\mu_{\rm ref}$ regardless of the power of the reference pump and the DW power decreases monotonically away from this peak, clearly demonstrating that the DW enhancement in the presence of the reference pump is not due to simple four-wave mixing between the main and reference pumps. (e) The ratio of the DW power and the reference pump power as a function of the reference pump mode number, indicating the efficiency of DW enhancement due to the self-balancing effect. The ratio increases monotonically with $\mu_{\rm ref}$ in agreement with \ref{['eq:self_balancing_D3']}.
• Figure 4: Numerical and experimental demonstration of DW power enhancement due to self-balancing. (a) Numerically calculated spectra with (blue) and without (purple) KIS, demonstrating that the injection of the reference pump at the low-frequency DW leads to a proportional increase in the high-frequency DW power $\Delta P_\mathrm{DW}$ on the other side of the spectrum. (b) The change in the high-frequency DW power is linearly proportional to the change in the comb tooth power where the reference pump is injected, as predicted analytically. (c) Experimental spectra with (blue) and without (purple) KIS showing that the injection of the reference pump at the low-frequency DW leads to a ≈22 enhancement of the high-frequency DW. (d) Experimental measurement of the high frequency DW power against reference power. The uncertainty are within the marker size. At low reference pump power, the DW power increases linearly with the reference pump power, as predicted analytically and verified numerically in (c).