Competing couplings drive four synchronization regimes in a three-color all-fiber soliton laser

Abstract

Synchronized multicolor ultrafast fiber lasers are attractive single-source solutions for multimodal nonlinear imaging, yet the mechanisms that stabilize or destabilize their timing locking remain largely unexplored. We combine a field-level cavity model with a reduced inertial circle-map model to map the synchronization dynamics of an all-fiber three-color coupled-cavity soliton laser. The field model, based on the coupled generalized nonlinear Schrödinger equations with explicit group-velocity walk-off and a shared carbon-nanotube saturable absorber, reproduces self-starting three-color soliton formation and timing capture over a window of ±(2–3) ps, in agreement with reported experimental tolerances. Reducing the pulse timings to a circle map with two competing coupling channels—an attractive force from total-intensity bleaching of the shared absorber and a repulsive force from cross-phase-modulation-induced frequency shifts—we map the full synchronization phase diagram in the pump-ratio–cavity-mismatch plane. Four regimes are identified and classified by the largest Lyapunov exponent and the winding number: phase locking, quasi-periodic slipping, chaotic timing dynamics organized in Arnold-tongue-like windows, and free-running unlocking. Wavelet analysis of the slip velocity provides an experimentally accessible discriminator of the four regimes. The locked state exhibits femtosecond-level integrated timing jitter, and the in-phase capture range peaks at the experimentally observed optimal common-arm length of ≈6 m and collapses at a pump-ratio compensation point where the two channels cancel, rationalizing the pump-dependent synchronization ranges measured previously. The results establish coupled-cavity soliton lasers as a testbed for circle-map universality and provide design rules for robust multimodal imaging sources.