Nonlinear dynamics in breathing-soliton lasers

Our recent work demonstrates that lasers operating in the breathing-soliton regime offer a powerful platform for investigating complex synchronisation and chaotic dynamics in nonlinear systems, all within a single oscillator—eliminating the need for external sources or coupled systems. In these lasers, harmonics of the breathing frequency can lock to the cavity repetition rate through competition between the system’s two intrinsic frequencies. In this paper, I will review the key findings of this research, which include higher-order Farey hierarchies and self-similar fractal dynamics (devil’s staircases), nonstandard synchronisation domains (unusual Arnold tongues), a novel modulated subharmonic regime bridging synchrony and desynchrony, and a new route to chaos via modulated subharmonics.