On-demand engineering of polarization oscillation in caustic beams

Polarization oscillating beams (POB), characterized by variable local polarization states during propagation that are independent of birefringence or nonlinear effects, present a unique platform for light-matter interactions. However, previous studies have been constrained by a beam superposition framework that identifies scalar beams as orthogonal polarization bases, restricting their extension to accelerating beams. Here, we propose a new framework for constructing POB, where the phase, amplitude, and polarization correspondences between the state-space representation and the real-space dynamics are explored. According to unified rules, concurrent and arbitrary controls of the trajectory, intensity, and polarization state along the optical path of caustic beams are realized. This will expand the theoretical and practical value of POB in classical entanglement, nontrivial optical forces, chirality detection, and other related domains, while potentially offering insights into the multidimensional manipulation of vector fields.