Generalized Phase Tailoring of Arbitrary Orthogonal Polarizations in Meta-Structure with High-Order Geometric Symmetry.

Symmetry, a core principle of aesthetics, plays a crucial role in both physics and mathematics. Recent investigations into high-symmetry meta-structures (Cm, m ≥ 3) have revealed intriguing concepts and phenomena in optics and materials science. However, increasing symmetry introduces challenges in tailoring anisotropy, limiting the potential of highly symmetric structures for functional wavefront engineering. While nonlinear geometric Berry phase and generalized geometric phase have enabled circular polarization control in Cm (m ≥ 3) meta-structures, these approaches are inherently spin-dependent and restricted to circular polarization states. Here, shape tailoring, including modifications to unit cell dimension and Cm meta-structure parameters is presented, to effectively enhance the anisotropy and phase control capabilities of Cm (m ≥ 3) meta-structures. By further incorporating generalized geometric phase, independent phase control of arbitrary orthogonal polarization states is achieved, and validated both numerically and experimentally. This generalized framework enhances the wavefront tailoring capacity of Cm (m ≥ 3) meta-structures and has substantial potential for integrating flexible wavefront functions with high-symmetry-driven exotic phenomena. Moreover, this approach offers inspiration for further applications in fields such as condensed matter physics and materials science, i.e., integrating the symmetry of the unit cell and lattice.