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We investigate the second-order topological phases in a two-dimensional ring resonator array with each plaquette occupied by \ensuremath{\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.

Exceptional points (EPs) are branch point singularities of self-intersecting Riemann sheets, and they can be observed in a non-Hermitian system with complex eigenvalues. It has been revealed recently that dynamically encircling EPs by adiabatically changing the parameters of a system composed of lossy optical waveguides could lead to asymmetric (input-output) mode transfer. However, the length of the waveguides had to be considerable to ensure adiabatic evolution. Here we demonstrate that the parameters can change adiabatically along a smaller encircling loop by utilizing moving EPs, leading to significant shortening of the structures compared to fixed EPs. Meanwhile, the mode transmittance is remarkably improved and the transfer efficiency persists at ∼90%. Moving EPs are very promising for applications such as highly integrated broadband optical switches and convertors operating at telecommunication wavelengths.