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Abstract Systems with a discrete rotational symmetry $$2\pi /n$$ 2 π / n where $$n\ge 3$$ n ≥ 3 that also have electromagnetic duality symmetry exhibit zero backscattering. The impact of breaking one of the two symmetries on the emerging backscattering has not yet been systematically studied. Here, we investigate the effect that perturbatively breaking each of the two symmetries has on the backscattering off individual objects and 2D arrays. We find that the backscattering off electromagnetically-small prisms increases with the parameters that determine the symmetry breaking, and that the increase of the backscattering due to the progressive breaking of one of the symmetries can be related to the other symmetry. Further exploration of the interplay between the two symmetries reveals that, in systems lacking enough rotational symmetry, the backscattering can be almost-entirely suppressed for a given linear polarization by deliberately breaking the duality symmetry. This duality breaking can be interpreted as an effective increase of the electromagnetic degree of rotational symmetry for that linear polarization.

Abstract We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts causes the appearance of non-radiative components in each of the two parts. These non-radiative components, which cancel each other when both parts are summed, preclude the separate determination of each part by means of measurements of the radiation from the source or of its coupling to external electromagnetic waves. In other words, there is no toroidal radiation or independent toroidal electromagnetic coupling. The formal meaning of the toroidal multipoles is clear in our derivations. They are the higher order terms of an expansion of the multipolar coefficients of electric parity with respect to the electromagnetic size of the source.