Photonic non-Bloch quadrupole topological insulators in coupled ring resonators

We investigate the second-order topological phases in a two-dimensional ring resonator array with each plaquette occupied by π gauge flux and imaginary gauge field. The real and imaginary gauge fields are induced by shifting the displacement and integrating gain or loss into the two half perimeters of the auxiliary rings. The system supports topological corner modes with their emergence being determined by the non-Bloch topological invariant …