Lasing from complete set of topological states in twodimensional photonic crystal structure

Recently, topologically engineered photonic structures have garnered significant attention as their eigenstates may offer a new insight on photon manipulation and an unconventional route for nanophotonic devices with unprecedented functionalities and robustness. Herein, we present lasing actions at all hierarchical eigenstates that can exist in a topologically designed single two-dimensional (2D) photonic crystal (PhC) platform: 2D bulk, one-dimensional edge, and zero-dimensional corner states. In particular, multiple topological eigenstates are generated in a hierarchical manner with no bulk multipole moment. The unit cell of the topological PhC structure is a tetramer composed of four identical air holes perforated into an InGaAsP multiple-quantum-well epilayer slab. A square area of a topologically nontrivial PhC structure is surrounded by a topologically trivial counterpart, resulting in multidimensional eigenstates of one bulk, four side edges, and four corners within and at the boundaries. Spatially resolved optical excitation spontaneously results in lasing actions at all nine hierarchical topological states. Our experimental findings may provide insight into the development of sophisticated next-generation nanophotonic devices and robust integration platforms.