Perfectly aperiodic asymmetric scalable metasurface based on the hat monotile

Abstract

Metasurfaces are conventionally designed on periodic lattices, which renders their electromagnetic response spatially uniform and leaves the spatial arrangement itself unused as an information-bearing design resource. In this study, we propose and numerically validate a metasurface built on an aperiodic monotile: the recently discovered "hat" polykite, a single tile mathematically guaranteed to tile the plane only nonperiodically. The twelve distinguishable orientations of the hat serve as a natural design basis; each carries resonant elements tuned to one of twelve absorption frequencies between 4.600 and 4.914 GHz, transcribing the provable aperiodicity and mirror asymmetry of the geometry into the electromagnetic response. Gaussian-beam scanning over a compositionally unique 6 times 6 grid yields irregular, position-dependent electromagnetic signatures whose pairwise separations reach beyond 6 dB. In particular, coherence-guided selection of multiple frequencies increases the stable rank of the position-signature matrix from 1.0 to approximately 1.6 with three frequency components, whereas the accumulation of mutually similar electromagnetic features fails to add effective dimensions, demonstrating that properly selected multifrequency characteristics enhance the spatial distinguishability embedded in the surface. A shift-correlation analysis in which the cosine similarity never exceeds 0.5 confirms that the response inherits the absence of translational order from the tiling. Compatible with standard printed-circuit fabrication, the aperiodic metasurface design establishes a deterministic route toward position-identifiable electromagnetic environments for localization, chipless identification, and integrated sensing and communication.