Observation and all-optical manipulation of replica symmetry breaking dynamics in a multi-Stokes-involved Brillouin random fiber laser photonic system.

In this paper, we propose and demonstrate an all-optical control of RSB transition in a multi-wavelength Brillouin random fiber laser (MWBRFL). Multi-order Stokes light components can be subsequently generated by increasing the power of the Erbium-doped fiber amplifier (EDFA) inside the MWBRFL, providing additional disorder as well as multiple Stokes-involved interplay. It essentially allows diversified laser mode landscapes with adjustable average mode lifetime and random mode density of the 1 order Stokes, which benefits the switching between replica symmetry breaking (RSB) and replica symmetry (RS) states in an optically controlled manner. Results show that the average mode lifetime of the 1 order Stokes component gradually decreases from 250.0 ms to 1.2 ms as high orders from the 2 to the 5 of Stokes components are activated. Meanwhile, the order parameter q of the 1 order Stokes random lasing emission presents distinct statistical distributions within the selective sub-window under various EDFA optical powers. Consequently, all-optical dynamical control of the 1 Stokes random laser mode landscapes with adjustable average mode lifetime turns out to be attainable, facilitating the RSB transition under an appropriate observation time window. These findings open a new avenue for exploring the underlying physical mechanisms behind the occurrence of the RSB phenomenon in photonic complex systems.