Parity-time-symmetry-induced Janus bound states in the continuum and rings of lasing threshold modes

The far-field polarization of a photonic crystal (PhC) slab is inherently linked to its spatial symmetries. We demonstrate that introducing a parity-time ($\mathcal{PT}$)-symmetric perturbation---while breaking up-down mirror symmetry---leads to the emergence of a Janus bound state in the continuum (BIC) and a momentum-space ring of lasing threshold modes. Starting from a PhC slab that hosts both symmetry-protected BIC and accidental BICs, we investigate the effects of $\mathcal{PT}$-symmetric perturbations on these states. The perturbation transforms accidental BICs into pairs of circularly polarized states ($C$ points) and induces a ring of lasing threshold modes in momentum space, while leaving the symmetry-protected BIC unaffected. As the perturbation strength increases, four $C$ points on one side merge with the symmetry-protected BIC, whereas those on the opposite side remain separate, giving rise to a Janus BIC characterized by asymmetric topological charges in the upward and downward radiation. Meanwhile, the ring of lasing threshold modes expands, enhancing the quality ($Q$) factor of nearby resonant modes due to the diverging $Q$ at the lasing threshold. As a result, $C$ points with ultra-high-$Q$ factors emerge, offering new opportunities for advanced chiral light-matter interactions and vortex beam generation.