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Phase-conjugate optical feedback (PCF) has been largely used as a way to stabilize and reduce the linewidth of laser emission but is also known to generate complex dynamics including self-pulsation and chaos. In contrast to the large number of theoretical works, there have been only few experiments reporting on nonlinear dynamics from PCF. Most importantly, experiments so far have not addressed the peculiarities of the PCF dynamics in comparison with dynamics observed from conventional optical feedback (COF). We report here experimentally and theoretically on two chaotic dynamics that relate to the peculiar dynamical properties of a laser diode with PCF. First, we find a chaotic dynamics that resembles the so-called low-frequency fluctuations (LFF) of a laser diode with COF, i.e. the output power shows abrupt dropouts at randomly distributed time-intervals followed by a slower recovery. Although the LFF in PCF shows similar statistical properties to those observed in the LFF in COF, they originate from a distinctively different bifurcation scenario. Increasing the PCF strength the laser diode shows successive bifurcations to time-periodic solutions at the frequency of the external cavity and multiples - also called 'external-cavity modes' (ECMs). In contrast to COF the PCF laser system shows no steady state for large enough feedback strength. Following the destabilization of several such ECMs to chaotic attractors, the dynamics shows a transition to a global attractor connecting the chaotic ECMs and that explains the sequence of power dropouts and recoveries. In addition we show how the bifurcations on these self-pulsing ECMs generate dynamics with extreme events, i.e. pulses with peak intensities well above the average value of the peaks in the output power and that show properties similar to the rogue waves in hydrodynamics. This is the first demonstration of temporal extreme events in a time-delayed optical system.
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