Spatial and spectral mode-selection effects in topological lasers with frequency-dependent gain

We develop a semiclassical theory of laser oscillation into a chiral edge state of a topological photonic system endowed with a frequency-dependent gain. As an archetypal model of this physics, we consider a Harper-Hofstadter lattice embedding population-inverted, two-level atoms as a gain material. We show that a suitable design of the spatial distribution of gain and its spectral shape provides flexible mode-selection mechanisms that can stabilize single-mode lasing into an edge state. Implications of our results for recent experiments are outlined.