  For a globally coupled network of semiconductor lasers with delayed optical
feedback, we demonstrate the existence of chimera states. The domains of
coherence and incoherence that are typical for chimera states are found to
exist for the amplitude, phase, and inversion of the coupled lasers. These
chimera states defy several of the previously established existence criteria.
While chimera states in phase oscillators generally demand nonlocal coupling,
large system sizes, and specially prepared initial conditions, we find chimera
states that are stable for global coupling in a network of only four coupled
lasers for random initial conditions. The existence is linked to a regime of
multistability between the synchronous steady state and asynchronous periodic
solutions. We show that amplitude-phase coupling, a concept common in different
fields, is necessary for the formation of the chimera states.
