We experimentally report on asymmetric dwell-time statistics of polarization chaos dynamics generated from free-running vertical-cavity surface-emitting lasers (VCSELs). Theoretically, we explain this behavior by introducing a misalignment between the phase and amplitude anisotropy within the spin-flip model for VCSELs. It induces an asymmetry in the VCSEL polarization behavior which is then responsible for significant changes in the statistics of the chaotic mode-hopping with an increase in the average residence time and an inversion of the dominant mode.

Extreme intensity pulses sharing statistical properties similar to rogue waves have been recently observed in a laser diode with phase-conjugate feedback [A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 38, 703 (2013)], but remain unexplained. We demonstrate here that a rate equation model of a laser diode that includes an instantaneous phase-conjugate feedback field reproduces qualitatively well the statistical features of these extreme events as identified in the experiment, i.e., the deviation of the intensity statistics to a Gaussian-shape statistics and the statistics of the time separating extreme events. The numerical simulations confirm the importance of the feedback strength in increasing the number of such extreme events and allow us to explain how extreme events emerge from a sequence of bifurcations on self-pulsating solutions, the so-called external cavity modes.