Edge mode bifurcations of two-dimensional topological lasers

Topological lasers are of growing interest as a way to achieve disorder-robust single-mode lasing using arrays of coupled resonators. We study lasing in a two-dimensional coupled resonator lattice exhibiting transitions between trivial and topological phases, which allows us to systematically characterize the lasing modes throughout a topological phase. We show that, unlike conventional topological robustness that requires a sufficiently large bulk band gap, bifurcations in topological edge mode lasing can occur even when the band gap is maximized. We show that linear mode bifurcations from single-mode to multi-mode lasing can occur deep within the topological phase, sensitive to both the pump shape and lattice geometry. We suggest ways to suppress these bifurcations and preserve single-edge mode lasing.