Chiroptical responses modulated by competitions between structural chiralities and magnetizations

We study chiroptical scattering properties of magneto-optical structures possessing rotation symmetries, with both rotation axis and externally applied static magnetic field parallel to the incident direction. For no less than threefold rotation symmetries (with or without magnetizations), cross sections of scattering and extinction are invariant as long as the incident polarizations locate on the same latitude line of the Poincaré sphere (polarization ellipses of the same ellipticity but different orientations), while for general incident polarizations, cross sections of scattering and extinction are ellipticity-weighted arithmetic average of those for circularly polarized incident waves. We further characterize the chiroptical responses through relative distinctions between cross sections for incident waves of left-handed and right-handed circular polarizations, and reveal that the external magnetic field can both suppress and enhance the chiroptical responses, depending on its direction and strength. When the chiroptical response is fully eliminated by the magnetization, the cross sections get decoupled to the polarization ellipticities as well, becoming fully independent of arbitrary incident polarizations. Our arguments are based on global structural symmetries only, and thus all conclusions drawn are irrelevant to local geometric parameters or specific material parameters of the scatterers, as long as the rotation symmetry is preserved. The principles we have revealed can be applied in many magnetism-induced nonreciprocal structures, and are robust against any rotation-symmetry-preserving structural defects and perturbations.