Polarization singularities in planar electromagnetic resonators with rotation and mirror symmetries

In this work, we apply the group representation theory to systematically study polarization singularities in the inplane components of the electric fields supported by a planar electromagnetic (EM) resonator with generic rotation and reflection symmetries. We reveal the intrinsic connections between the symmetries and the topological features, i.e., the spatial configuration of the in-plane fields and the associated polarization singularities. The connections are substantiated by a simple relation that links the topological charges of the singularities and the symmetries of the resonator. To verify, a microwave planar resonator with the D8 group symmetries is designed and numerically simulated, which demonstrates the theoretical findings well. Our discussions can be applied to generic EM resonators working in a wide EM spectrum, such as circular antenna arrays, microring resonators, and photonic quasi-crystals, and provide a unique symmetry perspective on many effects in singular optics and topological photonics. & COPY; 2023 Chinese Laser Press