Geometric representation lays the basis for understanding and flexible tuning of topological transitions in many physical systems. One example is the Poincaré sphere (PS), which facilitates the creation of various topological entities in light through continuous tuning spin or orbital angular momentum (OAM) states. Concurrently, how this approach can be utilized in condensed matter remains largely unexplored. In this work, we apply this geometric framework to a ferroelectric system through light-matter interaction and achieve a robust control on ferroelectric topologies. We show that: (1) PS engineering enables creation of dynamic polar antiskyrmions that are rarely found in ferroelectrics; (2) PS engineering acts as a tunable “knob”, allowing continuous control over transitions between topologically distinct skyrmion and antiskymion states; and (3) PS engineering can deterministically control the helicity of dynamical polar skyrmions and switch the chirality of polar vortices in an ultrafast manner. Our study thus opens new pathways for versatile manipulation of matter topologies through engineering structures of light.

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• Light-matter interaction
• Structured light
• Topological defects
• Ferroelectrics
• First-principles calculations