  Semiconductor ring lasers are miniaturized devices that operate on clockwise
and counterclockwise modes. These modes are not coupled in the absence of
intracavity reflectors, which prevents the formation of a standing wave in the
cavity and, consequently, of a population inversion grating. This should
inhibit the onset of multimode emission driven by spatial hole burning. Here we
show that, despite this notion, ring quantum cascade lasers inherently operate
in phase-locked multimode states, that switch on and off as the pumping level
is progressively increased. By rewriting the master equation of lasers with
fast gain media in the form of the complex Ginzburg-Landau equation, we show
that ring frequency combs stem from a phase instability---a phenomenon also
known in superconductors and Bose-Einstein condensates. The instability is due
to coupling of the amplitude and phase modulation of the optical field in a
semiconductor laser, which plays the role of a Kerr nonlinearity, highlighting
a connection between laser and microresonator frequency combs.
