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Multifunctional metamaterials (MMM) bear promise as next-generation materialplatforms supporting miniaturization and customization. Despite manyproof-of-concept demonstrations and the proliferation of deep learning assisteddesign, grand challenges of inverse design for MMM, especially those involvingheterogeneous fields possibly subject to either mutual meta-atom coupling orlong-range interactions, remain largely under-explored. To this end, we presenta data-driven design framework, which streamlines the inverse design of MMMsinvolving heterogeneous fields. A core enabler is implicit Fourier neuraloperator (IFNO), which predicts heterogeneous fields distributed across ametamaterial array, thus in general at odds with homogenization assumptions, ina parameter-/sample-efficient fashion. Additionally, we propose a standardformulation of inverse problem covering a broad class of MMMs, andgradient-based multitask concurrent optimization identifying a set ofPareto-optimal architecture-stimulus (A-S) pairs. Fourier multiclass blendingis proposed to synthesize inter-class meta-atoms anchored on a set of geometricmotifs, while enjoying training-free dimension reduction and built-itreconstruction. Interlocking the three pillars, the framework is validated forlight-bylight programmable plasmonic nanoantenna, whose design involves vastspace jointly spanned by quasi-freeform supercells, maneuverable incident phasedistributions, and conflicting figure-of-merits involving on-demandlocalization patterns. Accommodating all the challenges without a-priorisimplifications, our framework could propel future advancements of MMM.

Deep Neural Operator Enabled Concurrent Multitask Design for Multifunctional Metamaterials under Heterogeneous Fields