Chiral balls: Knotted structures with high order symmetry and their unique electromagnetic properties

Abstract

In physics, geometrical symmetry is a fundamental property of importance since it is associated with physical conservation. Here, we reveal an exceptional form of symmetry for a family of knots that are both chiral and three-dimensional (3D) rotationally symmetric about every axis of a standard Cartesian coordinate system. We call these unique knotted structures chiral balls. Moreover, chirality can bring about polarization transformation in electromagnetic waves. As a consequence of their 3D rotational symmetry, we further expect the polarization transformation performance of chiral balls to exhibit ultra-wide angle-independent behavior. Such a remarkable property has not been previously reported on in the literature. As a case study, we investigate the intrinsic electromagnetic scattering properties of a representative conductive chiral ball using characteristic mode analysis and then further verify them by measuring its radiation performance. The result shows that the chiral ball can exhibit an unprecedented extraordinary omnidirectional circularly polarized electromagnetic scattering property. Because of their unique properties, chiral balls are expected to not only have a profound impact on the fields of electromagnetics and optics but also potentially far beyond.