Asymmetric Switching of Edge Modes by Dynamically Encircling Multiple Exceptional Points

Dynamically encircling exceptional points (EPs) in the parameter space of a non-Hermitian system has drawn widespread attention for realizing asymmetric mode switching and related applications. While previous works have been restricted to two-level systems, the switching between edge states in a multistate system that contains more complex dynamics remains to be explored. Herein, asymmetric switching of edge modes in multistate systems is demonstrated by encircling multiple EPs. A multistate non-Hermitian system containing multiple EPs is constructed based on a one-dimensional lattice, which can support four edge-localized modes. Dynamically encircling the EPs in parameter space leads to a specific edge mode surviving to the end, determined by the encircling direction. Correspondingly, optical waveguide arrays are designed to investigate mode evolution through refractive index modulation. Simulated results show that clockwise (counterclockwise) encirclement leads to an output mode localized at the left (right) side of the waveguide array with a phase difference of 0 (\ensuremath{\pi}), regardless of the input modes; this excellently illustrates the asymmetric switching of edge modes in a multistate system. Moreover, such an effect can be extended to the multistate system with an arbitrary number of EPs. This work enables investigation of interesting effects in non-Hermitian physics by engineering the EPs and topological properties, especially for complex multistate systems, which will be useful for developing functional nanophotonic devices.