Chiral Balls: Knotted Structures with Both Chirality and Three-dimensional Rotational Symmetry

Abstract

Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form of symmetry for a family of knots that are both chiral and three-dimensional (3-D) rotationally symmetric about every axis of a standard Cartesian coordinate system. We call these unique knotted structures chiral balls. To demonstrate the unprecedented physical characteristics exhibited by these unique structures, we study the electromagnetic scattering properties of a representative conductive chiral ball. In particular, a characteristic mode analysis is performed to investigate the intrinsic scattering properties of this chiral ball. With both chirality and 3-D rotational symmetry, the chiral ball is shown to exhibit an extraordinary isotropic circularly polarized scattering property, which has not been previously reported for any known electromagnetic structures. 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 far beyond.