  Dynamical parametric encirclement around an Exceptional Point (EP) and
corresponding asymmetric state transfer phenomenon have attracted considerable
attention recently. In this context, beyond the reported time-asymmetric state
dynamics around a second-order EP (EP2) in a two-level system, the
investigation of similar state dynamics around a third-order EP (EP3) in a
multi-state system, having comparably complex topology with rich physics, is
lacking. Here, we report a fabrication-feasible few-mode planar optical
waveguide with a customized gain-loss profile and investigate the effect of
dynamical parametric encirclement around an EP3 in the presence of multiple
EP2s. The cube-root branch point behavior is established in terms of successive
switching between the propagation constants of the coupled modes following an
adiabatic encirclement process. Now, while considering the dynamical
encirclement process, the breakdown in system adiabaticity around an EP3 leads
to a unique light dynamics, where we have shown the breakdown of chirality of
the device.
