Tailoring topological corner states in photonic crystals by near- and far-field coupling effects

We explore the behaviors of optically coupled topological corner states in supercell arrays composed of photonic crystal rods, where each supercell is a second-order topological insulator. Our findings indicate that the coupled corner states possess nondegenerate eigenfrequencies at the Gamma point, with coupled dipole corner states excited resonantly by incident plane waves and displaying a polarization-independent characteristic. The resonance properties of coupled dipole corner states can be effectively modulated via evanescently near-field coupling, while multipole decomposition shows that they are primarily dominated by electric quadrupole moment and magnetic dipole moment. Furthermore, we demonstrate that these coupled corner states can form surface lattice resonances driven by diffractively far-field coupling, leading to a dramatic increase in the quality factor. This work introduces more optical approaches to tailoring photonic topological states, and holds potential applications in mid-infrared topological micro-nano devices.