End-to-End Deep Learning Framework for Freeform Metasurfaces via Non-Uniform Rational B-Splines Meta-Atoms

Conventional metasurface designs face fundamental trade-offs among geometric freedom, fabrication fidelity, and optical functionality. Here, we transcend these limitations through Non-Uniform Rational B-Splines (NURBS)-enabled computational co-design, establishing a paradigm in which freeform curvature control, deep learning optimization, and nanoscale lithography act synergistically. Unlike topology-constrained meta-atoms requiring iterative electromagnetic simulations, our framework deploys a Transformer-based differentiable surrogate to harness the parametric continuity of NURBS for arbitrary wavefront sculpting. Crucially, we introduce dose curvature proximity compensated lithography, which restores symmetry between design intent and fabricated structure through geometry dependent electron beam modulation. Experimental validation demonstrates achromatic wavelength scale focusing across 405-633 nm, with refined focal plane line profile analysis yielding full-width-at-half-maximum (FWHM) values of 1.15λ ± 0.02λ and limited focal shift across the measured wavelength range. The fabricated 200 μm diameter metalens resolves approximately 2.19 μm features in resolution target imaging and enables biological cell image analysis with sensitivity to subcellular refractive index variations (Δn ≈ 0.02). This co-design platform opens avenues for implantable photonics, microscopy, and quantum manipulation requiring precise freeform architectures.