Knots, symmetry, and scattering

We investigate the physics underlying the scattering of circularly polarized plane waves from a toroidal knot and related unknot. We find that backscattering along the axis of rotational symmetry from trefoil knots is cross polarized; copolarized backscatter is in the numerical noise. In contrast, untrefoils give appreciable backscattering cross sections for both polarizations. We also study an intermediate class of structures: morphs, which provides a geometrical bridge between trefoil and untrefoil. We pursue physical insight for the depolarization associated with asymmetric objects, tracing the connection from the induced charge distribution, to the induced moments, to the polarization of the backscattered field.