Versatile optical frequency division with Kerr-induced synchronization at tunable microcomb synthetic dispersive waves

Kerr-induced synchronization (KIS) provides a key tool for the control and stabilization of a dissipative Kerr soliton (DKS) frequency comb, enabled by the capture of a comb tooth by an injected reference laser. Efficient KIS relies on large locking bandwidth, meaning both the comb tooth and intracavity reference power need to be sufficiently large. Although KIS can theoretically occur at any comb tooth, large modal separations from the main pump to achieve large optical frequency division factors are often difficult or unfeasible due to cavity dispersion. While tailoring the dispersion to generate dispersive waves can support on-resonance KIS far from the main pump, this approach restricts synchronization to specific wavelengths. Here we demonstrate an alternative KIS method that allows efficient synchronization at arbitrary modes by multi-pumping a microresonator. This creates a multicolour DKS with a main and an auxiliary comb, the latter enabling the creation of a synthetic dispersive wave. As cross-phase modulation leads to a unique group velocity for both the soliton comb and the auxiliary comb, repetition rate disciplining of the auxiliary comb through KIS automatically controls the DKS microcomb. We explore this colour-KIS phenomenon theoretically and experimentally, showing control and tuning of the soliton microcomb repetition rate, resulting in optical frequency division independent of the main pump noise properties.