LAUSR

In this Letter, we propose collective topological corner modes in all-dielectric photonic crystal (PhC) supercell arrays, where each supercell is a second-order topological insulator. We show that coupled multipole corner modes are embedded in surrounding bulk modes at the Γ point even without the band gap, and individual or superposed dipole corner modes are selectively excited with collective behaviors by incident plane waves. These collective modes possess high-quality factors with an optimized thickness of the slab, and multipole decomposition reveals they are dominated by toroidal dipole and magnetic quadrupoles. Finally, we shrink the nontrivial region in each supercell to one unit-cell limit, where we show that collective corner modes still exist. Potential large-area topological applications are also discussed.