Can Knots Exhibit Both Chirality and Rotational Symmetry?

Knots have been put forward to explain various physical phenomena due to their topological stability. Nevertheless, very few published works have reported on their unique combination of strong chirality and rotational symmetry. While conventional optically active materials are composed of chiral molecules, which usually lack symmetry, a meta-molecule that is intrinsically isotropic and simultaneously exhibits strong optical activity has not yet been reported. Here, we introduce a knotted meta-molecule that possesses both rotational symmetry and strong chirality. The chirality of the meta-molecule exhibits optical activity corresponding to a 90° polarization rotation of the incident waves. More importantly, arising from the continuous multi-fold rotational symmetry of the chiral torus knot structure, the observed polarization rotation behavior is found to be independent of the incident wave's polarization state. Knots that possess such a unique and fundamentally important property have the potential for a wide range of applications in optical physics, chemistry, material science, and engineering.