[Paper Review] Manufacturable blazed metasurface gratings designed by 3D topology optimization model

Simon Ans, Frédéric Zamkotsian+1 more|arXiv (Cornell University)|Mar 14, 2026

Metamaterials and Metasurfaces Applications0 citations

TL;DR

The paper generalizes 3D topology optimization for reflection-blazed metasurfaces in the Vis–NIR, showing mesh-based designs achieve ~62% average efficiency while pillar-based designs reach ~57% with manufacturable constraints.

ABSTRACT

We present the generalization of our FEM-based topology optimization framework to 3D blazed metasurfaces operating in reflection over the visible and near-infrared range [400-1,500]nm. The design region is described through a density-based SIMP interpolation and optimized using the adjoint method, enabling the treatment of several tens of thousands degrees of freedom. A first approach directly applies topology optimization to the 3D Finite Element mesh (mesh-based), yielding a freeform structure that achieves an average diffraction efficiency of 62% in order -1 over two octaves under the targeted incidence. However, such patterns remain difficult to manufacture. We therefore introduce a pillar-based parameterization, embedding fabrication constraints within the optimization loop. The resulting binary metasurface, compatible with e-beam lithography and Reactive Ion Etching techniques, achieves an average efficiency of 57% over the same spectral band in s-polarization, with low polarization dependence. This work demonstrates that large-scale 3D topology optimization can bridge the gap between broadband optical performance and realistic nanofabrication constraints for blazed metasurfaces.

Motivation & Objective

• Extend a FEM-based topology optimization framework to 3D blazed metasurfaces in reflection over 400–1,500 nm.
• Incorporate manufacturing constraints via pillar-based parametric design within the optimization loop.
• Evaluate performance (diffraction efficiency) and polarization behavior across a two-octave spectrum.
• Provide open-source tooling for conical and 3D mesh-based and pillar-based optimization.

Proposed method

• Use SIMP density interpolation to define relative permittivity in the design region.
• Solve the scattered-field Maxwell’s equations with FEM and adjoint sensitivity analysis for efficiency maximization.
• Compare mesh-based free-form 3D patterns against pillar-based manufacturable designs.
• Embed binarization and connectedness filters to enforce manufacturability constraints.
• Compute diffraction efficiencies from Fourier components of the scattered field for reflection orders.

Experimental results

Research questions

• RQ1 Can 3D topology optimization yield broadband, high-efficiency blazed metasurfaces in reflection for Vis/NIR?
• RQ2 What performance vs. manufacturability trade-offs arise when constraining designs to pillar-based geometries?
• RQ3 How do 3D designs compare to prior conical/2D designs in terms of polarization dependence and spectral stability?

Key findings

• Mesh-based 3D optimization achieves an average diffraction efficiency of 62% on order −1 over 400–1,500 nm.
• Pillar-based manufacturable design achieves an average efficiency of 57% over the same spectral band in s-polarization with low polarization dependence.
• 3D pillar-based pattern demonstrates good spectral steadiness (50–75% efficiency range) and improved mechanical sustainability over free-form 3D patterns.
• Pillar-based optimization reduces DoFs (to 160) enabling faster convergence (≈14 h 50 min for 100 iterations).
• The 3D approach reduces polarization sensitivity compared to conical designs, achieving closer performance between polarizations.