We show that in the Kerr-Induced Synchronization (KIS) regime, an external reference pump laser allows for the control of the opposite (in frequency) Dispersive Wave (DW) power and frequency, through self-balancing of the cavity soliton. We report an increase of more than 20~dB of the DW of an octave-spanning comb at 780 nm, with a reference pump in the telecom C-band, while tuning of the DW over three comb teeth. Our work paves the way for significant improvement of the carrier-envelope offset frequency detection of octave-spanning combs.
Shandilya et al. (2024) studied this question.