Abstract Dynamically encircling an exceptional point (EP) in parity-time ( PT ) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti- PT ) symmetric systems and utilizing their unique topological structure, which is very different from that of PT -symmetric systems. We find that the dynamical encircling of an EP in anti- PT -symmetric systems with the starting point in the PT -broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti- PT -symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities.