  In this Letter, we present a rigorous method to study the stability of
periodic lasing systems. In a linear model, the presence of a continuum of
modes (with arbitrarily close lasing thresholds) gives the impression that
stable single-mode lasing cannot be maintained in the limit of an infinite
system. However, we show that nonlinear effects of the Maxwell-Bloch equations
can lead to stable systems near threshold given a simple stability condition on
the sign of the laser detuning compared to the band curvature. We examine
band-edge (1d) and bound-in-continuum (2d) lasing modes and validate our
stability results against time-domain simulations.
