Tunable two-dimensional laser arrays with zero-phase locking

Two-dimensional (2D) laser arrays are shown to be achievable at a large scale\nby exploiting the interplay of higher-order topological insulator (HOTI)\nphysics and the so-called non-Hermitian skin effect (NHSE). The higher-order\ntopology allows for the amplification and hence lasing of a single-mode\nprotected by a band gap; whereas the NHSE, widely known to accumulate\npopulation in a biased direction in non-Hermitian systems, is introduced to\ncompete with the topological localization of corner modes. By tuning the system\nparameters appropriately and pumping at one site only, a single topologically\nprotected lasing mode delocalized across over two dimensions emerges, with its\npower widely tunable by adjusting the pump strength. Computational studies\nclearly indicate that the lasing mode thus engineered is stable, and the phase\ndifference between nearest lasing sites is locked at zero, even after the\ndisorder is accounted for. The total power of the lasing mode forming a 2D\ntopological laser array is proportional to the area of the 2D lattice\naccommodating a HOTI phase. Based on existing experiments, we further propose\nto use coupled optical ring resonators as a promising platform to realize\nlarge-scale 2D laser arrays.\n