Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta-atom coupling or long-range interactions, remain largely under-explored. To this end, we present a data-driven design framework, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions, in a parameter-/sample-efficient fashion. Additionally, we propose a standard formulation of inverse problem covering a broad class of MMMs, and gradient-based multitask concurrent optimization identifying a set of Pareto-optimal architecture-stimulus (A-S) pairs. Fourier multiclass blending is proposed to synthesize inter-class meta-atoms anchored on a set of geometric motifs, while enjoying training-free dimension reduction and built-it reconstruction. Interlocking the three pillars, the framework is validated for light-bylight programmable plasmonic nanoantenna, whose design involves vast space jointly spanned by quasi-freeform supercells, maneuverable incident phase distributions, and conflicting figure-of-merits involving on-demand localization patterns. Accommodating all the challenges without a-priori simplifications, our framework could propel future advancements of MMM.

翻译：多功能超材料（MMM）作为下一代微型化与定制化材料平台具有广阔前景。尽管已有大量概念验证演示和深度学习辅助设计的蓬勃发展，但MMM逆向设计面临的重大挑战——特别是涉及可能受元原子间耦合或长程相互作用影响的异质场问题——仍鲜有深入探索。为此，我们提出一种数据驱动设计框架，可简化涉及异质场的MMM逆向设计流程。其核心创新在于隐式傅里叶神经算子（IFNO），该算子能以参数/样本高效的方式预测分布于超材料阵列中的异质场（通常与均匀化假设相悖）。此外，我们提出了覆盖广泛MMM类别的标准逆问题公式，以及基于梯度的多任务协同优化方法，可识别一组帕累托最优架构-激励（A-S）对。为合成锚定于几何基元集合的跨类元原子，我们提出傅里叶多类混合方法，该方法兼具无需训练的降维与内嵌重构特性。通过将上述三大支柱互锁，该框架在光控可编程等离激元纳米天线中得以验证——其设计空间由准自由形态超胞、可调控入射相位分布以及涉及按需局域化模式的冲突品质因数共同构成，且无需先验简化即可应对所有挑战。本框架有望推动MMM领域未来发展。