Is single-mode lasing possible in an infinite periodic system?

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.