Catenary metasurface-based perfect reflector design via topology optimization

Metasurfaces has significantly expanded our capability to manipulate light waves, consequently establishing them as a prominent research focus in photonics. By systematically varying the geometric parameters of their constituent unit cells, precise control over the reflection phase of electromagnetic waves can be achieved. The implementation of metasurfaces with gradient geometric designs has enabled anomalous reflection at optical frequencies with efficiencies approaching 80%. Furthermore, multilayer films have been integrated into metasurface architectures to enhance in-plane energy flow within the metamaterial system, facilitating the synergistic control of both amplitude and phase. Conventional metasurface anomalous reflectors suffer from restricted angular coverage and phase control limitations in broadband visible-light applications. These designs typically optimize efficiency only at discrete reflection angles and rely on geometrically constrained unit cells. Catenary metasurfaces provide continuous phase modulation capabilities, yet traditional approaches using predetermined elliptical or parabolic structures cannot achieve high-performance arbitrary-angle beam control. To address these limitations, we develop an adaptive topology optimization framework integrating computational design with catenary physics. Here, we propose a parallelized electromagnetic solver combining finite-difference time-domain and rigorous coupled-wave analysis algorithms. Gradient-driven topology updates dynamically balance phase continuity and efficiency targets through multilayer titanium dioxide-silicon dioxide architectures. Bragg reflector stacks ensure 99% background reflectivity across the visible spectrum. Fabrication-aware binarization incorporates gaussian spatial filtering to maintain 100nm minimum feature sizes. Simulation results demonstrate deflection efficiencies exceeding 95% for arbitrary angles spanning 30 to 85 degrees. The framework accelerates design cycles by two orders of magnitude, reducing development time from weeks to hours.