Topology-optimized catenary-like metasurface for wide-angle and high-efficiency deflection: from a discrete to continuous geometric phase.

We investigate the topology optimization of geometric phase metasurfaces for wide-angle and high-efficiency deflection, where adjoint-based multi-object optimization approach is adopted to improve the absolute efficiency while maintaining the polarization conversion characteristic of geometric phase metasurfaces. We show that, for the initially discrete geometric phase metasurfaces with different materials and working wavelengths, the topology shapes gradually evolve from discrete structures to quasi-continuous arrangements with the increment of optimization iteration operations. More importantly, the finally optimized metasurfaces manifest as catenary-like structure, providing significant improvements of absolute efficiency. Furthermore, for the initial structure with catenary distribution, the corresponding optimized metasurface also has a catenary-like topology shape. Our results on the topology-optimized geometric phase metasurfaces reveal that, from the perspective of numerical optimization, the continuous catenary metasurfaces is superior to the discrete geometric phase metasurfaces.