Universal threshold and Arnold tongues in Kerr ring microresonators

TL;DR

This paper uncovers the existence of Arnold tongues in Kerr ring microresonators, revealing how instability boundaries create resonance domains that influence frequency and power thresholds, with implications for laser stability and side-band generation.

Contribution

It introduces the concept of Arnold tongues in Kerr microresonators and details the universal threshold, advancing understanding of instability boundaries in these systems.

Findings

Identification of Arnold tongues between thresholds

RF spectra show transition between locked and unlocked regimes

Universal threshold estimates provided

Abstract

We report that an instability boundary of a single-mode state in Kerr ring microresonators with ultrahigh quality factors breaks the parameter space span by the pump laser power and frequency into a sequence of narrow in frequency and broad in power resonance domains - Arnold tongues. Arnold resonances are located between the Lugiato-Lefever (lower) and universal (higher) thresholds. Pump power estimates corresponding to the universal threshold are elaborated in details. RF-spectra generated within the tongues reveal a transition between the repetition-rate locked and unlocked regimes of the side-band generation.