Farey tree and devil's staircase of frequency-locked breathers in ultrafast lasers

Abstract

Nonlinear systems with two competing frequencies show locking or resonances. In lasers, the two interacting frequencies can be the cavity repetition rate and a frequency externally applied to the system. Conversely, the excitation of breather oscillations in lasers naturally triggers a second characteristic frequency in the system, therefore showing competition between the cavity repetition rate and the breathing frequency. Yet, the link between breathing solitons and frequency locking is missing. Here we demonstrate frequency locking at Farey fractions of a breather laser. The winding numbers show the hierarchy of the Farey tree and the structure of a devil's staircase. Numerical simulations of a discrete laser model confirm the experimental findings. The breather laser may therefore serve as a simple model system to explore universal synchronization dynamics of nonlinear systems. The locked breathing frequencies feature high signal-to-noise ratio and can give rise to dense radio-frequency combs, which are attractive for applications.

References in corpus (3)

• Instabilities, breathers and rogue waves in optics
• Devil's staircase transition of the electronic structures in CeSb
• Pulsating dissipative solitons in a Mamyshev oscillator

Cited by in corpus (6)

• Deep learning for dynamic modeling and coded information storage of vector-soliton pulsations in mode-locked fiber lasers
• Farey tree locking of terahertz semiconductor laser frequency combs
• Exploring nonlinear dynamics in periodically driven time crystal: from synchronized to chaotic motion
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Resonant Kushi-comb-like multi-frequency radiation of oscillating two-color soliton molecules
• Theory of Optomechanical Locking in Driven-Dissipative Coupled Polariton Condensates