Controlling Topology and Polarization State of Lasing Photonic Bound States in Continuum

Recently, optical bound states in continuum (BICs) incorporated with optical gain have been reported to exhibit lasing. Here, it is shown that each of the four BICs supported by C4v$_{4v}$ symmetric photonic crystal slab can be made to lase, allowing the control over the topological charge of the resulting laser beam. The type of each BIC and their topological charges are identified by imaging the far-field polarization vortices of the lasing signal. Results are compared with experimentally obtained dispersions, finite element method simulations, and multipole decomposition method based on the microscopic polarization currents in the photonic crystal plane. A demonstration of multimode lasing of two non-degenerate BICs with opposite topological charges is presented. The momentum space overlap of the BICs results in a unique polarization pattern. The study provides a generalizable example for engineering the topological properties of coherent light.