  It was proved that the joint operation of electromagnetic reciprocity and
$n$-fold ($n\geq3$) rotational symmetry would secure arbitrary
polarization-independent backscattering efficiency [Phys. Rev. B \textbf{103},
045422 (2021)]. Here we remove the restriction of reciprocity and study the
backscatterings of plane waves by rotationally symmetric magneto-optical
structures, with collinear incident wavevector, rotational axis and externally
applied magnetic field. It is revealed that though nonreciprocity removes the
degeneracy of backscattering efficiencies for circularly-polarized incident
waves of opposite handedness, the remaining rotational symmetry is sufficient
to guarantee that the efficiency is related to the polarization ellipticity
only, having nothing to do with the orientations of the polarization ellipses.
Moreover, the backscattering efficiency reaches its extremes (maximum or
minimum values) always for circularly-polarized incident waves, and for other
polarizations the efficiency is their ellipticity-weighted arithmetic average.
The principles we have revealed are dictated by rotational symmetries only,
which are irrelevant to specific geometric or optical parameters and are
intrinsically robust against any rotational-symmetry preserving perturbations.
The correlations we have discovered could be further exploited for fundamental
explorations in nonreciprocal photonics and practical applications including
polarimetry and ellipsometry.
