  Coupled clocks are a classic example of a synchronization system leading to
periodic collective oscillations. This phenomenon already attracted the
attention of Christian Huygens back in 1665,who described it as a kind of
"sympathy" among oscillators. In this work we describe the formation of two
types of laser frequency combs as a system of oscillators coupled through the
beating of the lasing modes. We experimentally show two completely different
types of synchronizations in a quantum dot laser { in-phase and splay states.
Both states can be generated in the same device, just by varying the damping
losses of the system. This effectively modifes the coupling among the
oscillators. The temporal output of the laser is characterized using both
linear and quadratic autocorrelation techniques. Our results show that both
pulses and frequency-modulated states can be generated on demand. These
findings allow to connect laser frequency combs produced by amplitude-modulated
and frequency-modulated lasers, and link these to pattern formation in coupled
systems such as Josephson-junction arrays.
