  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,
which is easy to adjust, different dynamical phenomena are observed: continuous
wave emission, stable oscillations, period doubling bifurcations, chaos and, in
some chaotic regimes, extreme events in the form of pulses of extraordinary
intensity. These pulses are also sometimes called "dissipative optical rogue
waves". The mechanism of their formation is still unknown. Here, we report the
direct observation of the pulse-to-pulse evolution of the transverse pattern
with an ultrafast camera (up to 60,000 frames per second). A specific pattern
is correlated with the pulse intensity in the periodical regimes. In the
chaotic regimes, the extreme events are correlated with some patterns. The
series of patterns before and after an extreme event are often the same. These
observations demonstrate that extreme events in this system are the consequence
of the deterministic nonlinear interaction of few modes. This information plays
a crucial role in the development of a theoretical model able to describe the
mechanism giving raise to extreme events. The model is expected to lead to the
control of their formation at will, what is of practical interest.
