Arbitrary Diffraction Engineering with Multilayered Multielement Metagratings

We theoretically formulate and experimentally demonstrate an analytical formalism for designing printed circuit board (PCB) metagratings (MGs), exercising individual control over amplitude and phase of numerous diffracted modes, in both reflection and transmission. These sparse periodic arrangements of subwavelength polarizable particles (meta-atoms) are typically designed based on full-wave optimization of the meta-atoms, with scarce analytical schemes restricted to single-layer reflecting structures, controlling only power distribution. Herein, we present an analytical model addressing a general multilayered multielement MG, featuring an arbitrary number of meta-atoms distributed across an arbitrary dielectric stack. For a desired diffraction pattern, we formulate suitable constraints, identify the required degrees of freedom, and set them to yield a fabrication-ready layout implementing the prescribed functionality; no full-wave optimization is involved. To verify and demonstrate the versatility of this approach, multilayer PCB MGs for perfect anomalous refraction and nonlocal focusing are synthesized and experimentally characterized, matching the theoretical predictions. This semianalytical methodology enables on-demand synthesis of MGs and extends their range of applicability.