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 pi 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 due to skin effects. The bulk modes, exhibiting second-order skin effects in both trivial and nontrivial phases, are accumulated at opposite corners depending on whether clockwise or counterclockwise modes are excited. By introducing an interface with different imaginary gauge fields, we show the bulk modes exist at the interface while the topological corner modes are localized at the physical corners. Furthermore, the skin effects are also presented in the passive ring resonators. The study may find applications in lasers and broadband light trapping.

Automated summary

Investigated second-order topological phases in a two-dimensional ring resonator array where the system supports topological corner modes determined by non-Bloch topological invariants. Bulk modes accumulate in opposite corners depending on clockwise or counterclockwise excitation, with the introduction of an interface with different imaginary gauge fields showing bulk modes at the interface and topological corner modes localized at physical corners. Skin effects also observed in passive ring resonators, with potential applications in lasers and broadband light trapping.