Observed photonic phase evolutions in Brillouin random fiber laser comb

Abstract

We report the experimental demonstration of photonic phase transitions in a Brillouin random fiber laser comb (BRFLC) through a spin-glass theoretical framework in photonic systems. By systematically analyzing the statistical distribution of the Parisi overlap parameter q across different Stokes/anti-Stokes orders and pump powers, we identify three distinct photonic phases. The paramagnetic phase, characterized by a P(q) distribution peaked near zero, reflects uncorrelated intensity fluctuations and corresponds to the selective amplification of a single resonant mode in the cavity. In contrast, the spin-glass phase, marked by q-values concentrated at ±1, signifies strongly correlated or anti-correlated dynamics, arising from the interaction of dual resonant modes. Crucially, the transition between these phases is governed by the number and lifetimes of interacting optical resonance modes. Bimodal resonance triggers replica symmetry breaking (RSB), driving the system to evolve from the paramagnetic to the spin-glass phase. Beyond this, multimode oscillations induce a non-equilibrium regime which mirrors the frustration-induced multi-step RSB process observed in disordered spin systems. It corresponds to a broadened P(q) distribution that defies conventional phase classification and reveals a complex photonic state with hierarchical correlations. As the number of modes continues to increase and the mode lifetimes become anomalously short, the dominant resonant mode in the cavity eventually disappears. This transition causes the statistical distribution of the corresponding overlap parameter q to converge to a Gaussian-like profile, indicating that the system has once again returned to a disordered paramagnetic phase. Our work establishes BRFLC as a controllable platform to emulate spin-glass physics in photonics, enabling direct access to phase dynamics through tunable disorder and mode competition. The discovery of the photonic phase evolutions helps to reveal the underlying physical mechanism accounting for the BRFLC operation and contributes to the understanding of complex synergistic nonlinear physical processes in random fiber lasers.