Conditions for breaking the extinction symmetry in electromagnetic scattering

Previous studies have shown that the extinction efficiency of reciprocal scatterers of arbitrary shape is the same under illumination with plane electromagnetic waves of opposite incident directions with the same field polarizations. It has also been shown that to break this symmetry, all related symmetries, including time-reversal, spatial inversion, and rotational symmetries, should be broken. In this paper, we further investigate the conditions for breaking the extinction symmetry. Our numerical experiments indicate that breaking the time-reversal and geometrical symmetries is not sufficient, rather the object should also be non-reciprocal. However, while non-reciprocity is necessary, it is not sufficient: a certain asymmetry with respect to the incident plane wave is also required. To break the extinction symmetry with these conditions, the polarization of the incident waves has to be linear or elliptical. For circular polarization, the extinction invariance cannot be broken with any geometry or non-reciprocity. Additionally, with characteristic modes, we study and explain the observation that for opposite illumination directions, the electromagnetic fields can be completely different while the corresponding extinction cross-sections coincide.