Abstract

Kuramoto transition [1], epitomized by co-flashing fireflies and coupled array of Josephson junctions, is a generic phenomenon in nonlinear dynamics that refers to self-synchronization (or self-organization) of a large set of mutually coupled oscillators. Mode-locked fibre lasers, as a widely-used nonlinear optical system, can host various self-organized patterns consisting of multiple particle-like optical solitons [2], while Kuramoto transitions that involve large number of solitons have not been reported in mode-locked lasers, due to the irregular interactions between the solitons when their number increased significantly. In this work we report the observation of the self-organization of a harmonically mode-locked fibre laser based on enhanced optoacoustic interactions in photonic crystal fibre (PCF) (See Fig.1(a)) [3] and analyse this process using Kuramoto model. The establishment of high-harmonic mode-locking (HHML) that involved hundreds of laser solitons with self-stabilized regular spacings in this cavity can be interpreted as a Kuramoto transition, in which the solitons interacts with each other through sinusoidal acoustic fields generated by impulsive electrostriction in the PCF (See Fig.1(a))[3]. We employed a 34-m-length unidirectional Er-doped ring-fibre laser optoacoustically mode-locked by a 1.5-m-length PCF with acoustic core resonance at 1.9 GHz, leading to 310 solitons co-existing in the cavity. We initiated the laser by manipulating the gain depletion in the EDF and then recorded the self-organization of this HHML fibre laser. We observed that a large number of solitons quickly emerged in random positions (~ 1 ms after initiation), and then spontaneous ordering started over a period of ~ 100 ms before they formed regular spacing in accordance with the acoustic cycles (see Fig.1(b)).

© 2023 IEEE