  Vacuum magnetic birefringence (VMB) is a nonlinear electromagnetic effect
predicted by QED. In addition to the effect from QED, the effect also has a
possibility to probe the dark sector. The effect predicted by QED is parity
conservative, but the effect from the dark sector can induce parity violation.
To pursue this possibility, we calculated the effect from the dark sector with
the generalized Heisenberg-Euler effective Lagrangian that is applicable to
parity-violating theories. Various dark sector models exist, among which the
contribution of the dark sector neutrinos to the VMB experiment is examined.
The contribution comes from the mixing of photon with the dark sector Z boson
and violates parity, thus inducing a parity-violating electromagnetic
interaction. If the polarization vector is denoted by ${\epsilon}(\theta_i)$
when its direction is rotated by an angle $\theta_i$ from the direction of the
applied magnetic field, the change of the polarization from
${\epsilon}(45^\circ)$ to ${\epsilon}(-45^\circ)$ and vice versa are examined.
The contribution from the dark sector modifies the magnitude of the
polarization change, so it can be detected by measuring the magnitude
precisely. In addition to the change in the magnitude, the dark sector also
induces parity-violating effects. We also propose a new scheme to measure the
effect of parity violation directly. By measuring the change of polarization
from ${\epsilon}(0^{\circ})$ to ${\epsilon}(90^\circ)$, and vice versa, with a
ring Fabry-P\'erot resonator, one can search for the effect directly. The
signal that appears in this scheme is evidence of parity violation from beyond
standard model theories.
