Dynamical Systems of Oscillating Ultrashort Pulse Pairs

We propose a theoretical method to model the complex phenomenon of oscillating ultrashort pulse pair molecules. Using a phenomenological viewpoint, we construct effective dynamical systems, whose degrees of freedom are the inter-pulse timing and overall phase. The effective dynamical system is characterized by a limit cycle attractor that is fit to the experimentally measured soliton oscillation using data-driven methods. Good agreement is achieved between the dynamical system orbits and experimental observations made in a mode-locked fiber laser.