Poincar\'{e} sphere engineering of dynamical ferroelectric topological solitons

Geometric representation lays the basis for understanding and flexible tuning of topological transitions in many physical systems. An example is given by the Poincar\'{e} sphere (PS) that provides an intuitive and continuous parameterization of the spin or orbital angular momentum (OAM) light states. Here, we apply this geometric construction to understand and continuously encode dynamical topologies of ferroelectric solitons driven by OAM-tunable light. We show that: (1) PS engineering enables controlled creation of dynamic polar antiskyrmions that are rarely found in ferroelectrics; (2) We link such topological transition to the tuning of the light beam as a ``knob'' from OAM (PS pole) to non-OAM (PS equator) modes; (3) Intermediate OAM-state structured light results in new ferroelectric topologies of temporally hybrid skyrmion-antiskyrmion states. Our study offers new approaches of robust control and flexible tuning of topologies of matter using structured light.