Threshold of complexity and Arnold tongues in Kerr ring microresonators

TL;DR

This paper investigates the complex instability regions, called Arnold tongues, in Kerr microresonators, revealing how they influence the threshold for sideband generation and the onset of complex dynamics.

Contribution

It develops a theoretical framework for understanding Arnold tongues and the threshold of complexity in Kerr microresonators, highlighting their role in instability and symmetry breaking.

Findings

Arnold tongues form narrow frequency and broad power regions in the parameter space.

Increasing pump power causes tongues to expand and intersect, indicating a threshold of complexity.

Synchronization and symmetry breaking occur within the tongues.

Abstract

We show that the threshold condition for two pump photons to convert into a pair of the sideband ones in Kerr microresonators with high-quality factors breaks the pump laser parameter space into a sequence of narrow in frequency and broad in power Arnold tongues. Instability tongues become a dominant feature in resonators with the finesse dispersion parameter close to and above one. As pump power is increased, the tongues expand and cross by forming a line of cusps, i.e., the threshold of complexity, where more sideband pairs become unstable. We elaborate theory for the tongues and threshold of complexity, and report the synchronisation and frequency-domain symmetry breaking effects inside the tongues.