Extreme events and single-pulse spatial patterns observed in a self-pulsing all-solid-state laser.

The passively Q-switched, self-pulsing all-solid-state laser is a device of widespread use in many applications. Depending on the condition of saturation of the absorber, which is easy to adjust, different dynamical regimes are observed: continuous-wave emission, stable oscillations, period doubling bifurcations, chaos, and, within some chaotic regimes, extreme events (EEs) in the form of pulses of extraordinary intensity. These pulses are sometimes called "dissipative optical rogue waves." The mechanism of their formation in this laser is unknown. Previous observations suggest they are caused by the interaction of a few transverse modes. Here we report a direct observation of the pulse-to-pulse evolution of the transverse pattern. In the periodical regimes, sequences of intensities are correlated with sequences of patterns. In the chaotic ones, a few different patterns alternate, and the EEs are related with even fewer ones. In addition, the series of patterns and the pulse intensities before and after an EE are markedly repetitive. These observations demonstrate that EEs follow a deterministic evolution, and that they can appear even in a system with few interacting modes. This information plays a crucial role for the development of a mathematical description of EEs in this laser. This would allow managing the formation of EE through control of chaos, which is of both academic and practical interest (laser rangefinder).