PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the Continuum

It is well known that spatial symmetry in a photonic crystal (PhC) slab is capable of creating bound states in the continuum (BICs), which can be characterized by topological charges of polarization vortices. Here, we show that when a PT-symmetric perturbation is introduced into the PhC slab, a new type of BICs (pt-BICs) will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with pt-BICs embedded in these rings. Different from ordinary BICs, the Q-factor divergence rate of a pt-BIC is reduced and anisotropic in momentum space. Also, pt-BICs can even appear at off-high symmetry lines of the Brillouin zone. The pt-BICs also carry topological charges and can be created or annihilated with the total charge conserved. A unified picture on pt-BICs and the associated lasing threshold modes is given based on the temporal coupled mode theory. Our findings reveal the new physics arising from the interplay between PT symmetry and BIC in PhC slabs.