Anti-parity-time topologically undefined state

Abstract

Abstract Researches on the topological edge state in the photonic lattice are attracting considerable attention. Here, we report the studies on a particular state for which the topological invariant is undefined. We constructed an anti-parity-time-symmetric photonic lattice by using the perturbation method. Light distributes only in the wide waveguides with equal magnitude for the state with undefined winding numbers. Further studies show that the equal intensity transmission is unaffected except for the defect site. Our work provides a new way to study the topological state and the equally divided light transmission and might be applicable in optical circuits and optical interconnect.