Harnessing Selective State Space Models to Enhance Semianalytical Design of Fabrication-Ready Multilayered Huygens' Metasurfaces: Part II - Generative Inverse Design (MetaMamba)

Abstract

We present a generative framework for inverse design of five-layer transmissive Huygens' metasurfaces (HMSs), addressing a longstanding challenge in achieving full-phase, high-efficiency unit cell designs with minimal full-wave simulations. The key to achieving this is our reliance on the field-based semianalytical (SA) scheme developed in Part I of this paper, which allows rapid and highly effective synthesis of such multilayer composites, however with limited accuracy. To overcome the prohibitive data demands of traditional pipelines, we employ Mamba, a selective state space model well suited for long-range sequence modeling as the backbone of our learning framework. A bidirectional Mamba (Bi-Mamba) forward surrogate is first trained on SA-generated data and subsequently fine-tuned with full-wave CST samples. An ablation over a 1080-sample CST pool shows that as few as 270 full-wave calibration samples suffice to reach near-CST-level agreement at a fraction of the simulation cost. An autoregressive Mamba inverse generator is subsequently trained on surrogate-augmented data, treating unit-cell synthesis as a sequential generation task. The resulting one-to-many generative model produces diverse unit cell geometries conditioned on target scattering responses. It achieves CST-validated designs with field transmission magnitude 0.9 across the full 0-$2π$ phase range at 20 GHz. Moreover, a CST-calibrated surrogate trained to accurately predict frequency responses (18-22 GHz) enables functional post-selection of inverse generated designs. Together, the hybrid SA-generative methodology in this two-part compilation establishes a scalable and data-efficient solution for multilayer HMS synthesis, with natural extensions toward broadband, oblique-incidence, and higher-dimensional electromagnetic inverse-design problems.

Figures (12)

• Figure 1: Unit cell geometry. (a) Single layer parameterization. A JC patch is shown inside one period $P$, slab width $w$ and a variable leg length $W$. (b) Five-layer HMS unit cell formed by vertically stacking JC copper patterns, where each layer’s JC leg length $W_n$ and the collective electromagnetic interaction of the stack determines the resulting scattering parameters.
• Figure 2: MetaMamba pipeline. (i) A large synthetic dataset $\mathcal{D}_{\mathrm{SA}}$ is generated using the SA model, establishing the foundation for data-driven learning. (ii) The Bi-Mamba forward surrogate is pretrained on $\mathcal{D}_{\mathrm{SA}}$, used to generate an augmented dataset $\mathcal{D}_{\mathrm{Aug}}$, and an initial AR-Mamba inverse generator is trained on this surrogate-produced data. (iii) The pretrained inverse model generates candidate unit cell geometries; high-transmission representatives are selected and evaluated with full-wave (FW) simulations to form the calibration set $\mathcal{D}_{\mathrm{FW}}$. (iv) The forward surrogate is fine-tuned (FT) using $\mathcal{D}_{\mathrm{FW}}$ and used to synthesize an augmented high-fidelity corpus $\mathcal{D}_{\mathrm{AugFT}}$, enabling training of the final FW-calibrated AR-Mamba inverse model.
• Figure 3: Bi-Mamba forward surrogate (Fig. \ref{['fig:pipeline']}, steps (ii), (iv), pink blocks). Left-to-right and right-to-left scans are fused to capture global interlayer coupling and predict the scattering response $\hat{\mathbf{S}}$. The architecture efficiently models multilayer interactions by propagating context across all layer elements.
• Figure 4: AR-Mamba inverse generator (Fig. \ref{['fig:pipeline']}, steps (ii), (iv), green blocks). Conditioned on the target response $\mathbf{S^\star}$, the model predicts layer tokens sequentially from left to right. At each step $n$, the next token $W_n$ is generated causally from the previous tokens $\mathbf{W}_{<n}$ and the conditioning sequence $\mathbf{S^\star}$. This AR formulation resembles language models, enabling diverse sequence generation for HMS design.
• Figure 5: Candidate selection strategy. (a) The pretrained inverse model generates a large pool of high-transmission candidates, whose predicted responses $(|T|^2,\phi)$ are visualized in polar form and partitioned into fixed phase sectors. (b) Within each phase sector, candidates are clustered in the geometric parameter space $\mathbf{W}_{1:N}$ using K-means to promote diversity. (c) The highest-transmission representative from each cluster (encircled in (b)) is selected to form the compact, diverse calibration set that together with the full-wave simulation results will form $\mathcal{D}_{\mathrm{FW}}$.