  We constructed an anti-parity-time-symmetric photonic lattice by using
perturbations. The results show the topological state will appear when the
waveguide coupling constants $\kappa_1<\kappa_2$; Interestingly, a state with
undefined winding numbers occurs when $\kappa_1=\kappa_2$, in which the light
distributes only in the wide waveguides with equal magnitude distribution.
Further studies show that the edge state will be strengthened by introducing
defect for the topologically non-trivial case, while it will not affect the
equal intensity transmission for the topologically undefined state. Our work
provides a new way to realize the topological state and equally divided light
transmission and might be applicable in optical circuits and optical
interconnect.
