Floquet topological insulator laser

We introduce a class of topological lasers based on the photonic Floquet topological insulator concept. The proposed system is realized as a truncated array of lasing helical waveguides, where the pseudomagnetic field arises due to twisting of the waveguides along the propagation direction that breaks the time-reversal symmetry and opens up a topological gap. When sufficient gain is provided in the edge channels of the array, the system lases into topological edge states. Topological lasing is stable only in certain intervals of the Bloch momenta that ensure a dynamic, but stable balance between the linear amplification and nonlinear absorption leading to the formation of breathing edge states. We also illustrate topological robustness of the edge currents by simulating lattice defects and triangular arrangements of the waveguides.