Topological Lasers and Exceptional Points in Parity-Time Symmetric Zero-Index Metamaterials

The unique wave-manipulation capabilities of zero-index metamaterials (ZIMs) offer a new opportunity for realizing bound states in the continuum (BICs). However, the relationship between anomalous scattering and BICs remains underexplored when parity-time (PT) symmetry is introduced. In this work, we demonstrate that a BIC splits into a pair of lasing modes carrying opposite topological charges by introducing PT symmetry through gain-loss cylinders embedded in ZIM layers. Theoretical analysis and numerical simulations reveal that lasing and unidirectional transparency phenomena result from the singularities and exceptional points of the scattering matrix. Moreover, exceptional points can be tuned via propagation phase modulation in the air gap, and their coalescence produces quasi-BICs with symmetric responses. This work provides a framework for manipulating BICs and topological lasing modes in non-Hermitian systems, offering new insights for designing non-Hermitian photonic devices.