Self-locking of the frequency comb repetition rate in microring resonators with higher order dispersions

We predict that the free spectral range (FSR) of the soliton combs in microring resonators can self-lock through the back-action of the Cherenkov dispersive radiation on its parent soliton under the conditions typical for recent experiments on the generation of the octave wide combs. The comb FSR in the self-locked state remains quasi-constant over sufficiently broad intervals of the pump frequencies, implying that this effect can be potentially used as the comb self-stabilisation technique. The intervals of self-locking form a sequence of the discrete plateaus reminiscent to other staircase-like structures known in the oscillator synchronisation research. We derive a version of the Adler equation for the self-locking regime and confirm that it is favoured by the strong overlap between the soliton and the dispersive radiation parts of the comb signal.