We experimentally study the nonlinear dynamics of a femtosecond ytterbium doped mode-locked fiber laser. With the laser operating in the pulsed regime a route to chaos is presented, starting from stable mode-locking, period two, period four, chaos and period three regimes. Return maps and bifurcation diagrams were extracted from time series for each regime. The analysis of the time series with the laser operating in the quasi mode-locked regime presents deterministic chaos described by an unidimensional Rössler map. A positive Lyapunov exponent λ = 0.14 confirms the deterministic chaos of the system. We suggest an explanation about the observed map by relating gain saturation and intra-cavity loss.

We investigated the random lasing process and Replica Symmetry Breaking (RSB) phenomenon in neodymium ions (Nd3+) doped lead-germanate glass–ceramics (GCs) containing MgO. Glass samples were fabricated by conventional melt-quenching technique and the GCs were obtained by carefully devitrifying the parent glasses at 830 °C for different time intervals. The partial crystallization of the parent glasses was verified by X-ray diffraction. Photoluminescence (PL) enhancement of $$\approx$$ ≈ 500% relative to the parent glasses was observed for samples with a higher crystallinity degree (annealed during 5 h). Powders with grains having average size of 2 µm were prepared by griding the GCs samples. The Random Laser (RL) was excited at 808 nm, in resonance with the Nd3+ transition 4I9/2 → {4F5/2, 2H9/2}, and emitted at 1068 nm (transition 4F3/2 → 4I11/2). The RL performance was clearly enhanced for the sample with the highest crystallinity degree whose energy fluence excitation threshold (EFEth) was 0.25 mJ/mm2. The enhanced performance is attributed to the residence-time growth of photons inside the sample and the higher quantum efficiency of Nd3+ incorporated within the microcrystals, where radiative losses are reduced. Moreover, the phenomenon of Replica Symmetry Breaking (RSB), characteristic of a photonic-phase-transition, was detected by measuring the intensity fluctuations of the RL emission. The Parisi overlap parameter was determined for all samples, for excitation below and above the EFEth. This is the first time, for the best of the authors knowledge, that RL emission and RSB are reported for a glass–ceramic system.