Threshold of complexity and Arnold tongues in Kerr-ring microresonators

Dmitry Skryabin, Zhiwei Fan, Alberto Villois, Danila Puzyrev

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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.
Original languageEnglish
Article numberL011502
JournalPhysical Review A
Issue number1
Early online date6 Jan 2021
Publication statusPublished - 31 Jan 2021


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