Misc,
Chiral Balls: Knotted Structures with Both Chirality and Three-dimensional Rotational Symmetry
(2019)cite arxiv:1904.05750.
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.
