Harper-Hofstadter Topological Laser with Frequency-Dependent Gain

Topological lasers are a new promising class of devices that exploit the protected edge modes of topological insulators for coherent light emission. One of the first experimental realizations of such a device used a Harper-Hofstadter lattice of ring cavities in which the edge mode was selected by using a pump spatially localized on the border [1]. The inter-ring coupling constant J in the experimental setup was much more smaller than the width of the gain, thus making the latter effectively broadband; however, this is not always the case and it may vary in different experimental platforms. Going beyond the standard theory of broadband gain [2, 3], here we numerically show that, if the gain width is comparable with the inter-ring coupling constant, it is possible to promote the lasing of a topologically protected edge mode even without using a spatially selective pumping. Experimental evidence of such a behavior was reported in the pioneering work [4] and is still awaiting theoretical interpretation.