Topology-driven design of bianisotropic metasurfaces through knot particles

Bianisotropic metasurfaces enable advanced electromagnetic wave manipulation through magnetoelectric coupling. Here, we demonstrate how knot particles enable single-layer bianisotropic control using their inherent topology. Leveraging their geometric properties, we examine three-dimensional (3D) wire configurations characterized by the knot winding numbers (p,q), generating balanced electric and magnetic responses. Through multipole analysis, we demonstrate efficient polarization rotation with high transmission for different knot-particle topologies. We explore the knot-particle topologies required to achieve matched polarization rotation and derive simple design rules for the knot parameters without resorting to numerical optimization. The microscopic polarizability tensors and macroscopic susceptibilities reveal that the trefoil knot exhibits strong chiral bianisotropic behavior through its magnetoelectric coupling tensor. We implement knot-particle metasurfaces using advanced 3D printing, which realizes the full 3D geometry of the wires. We present simplified flat designs suitable for printed circuit board fabrication that preserve the essential symmetry enabling the bianisotropic properties.