  It is predicted within the Standard Model of elementary particles that
asymmetric neutrino environments cause rotation of linear polarization of
electromagnetic wave -- the birefringence. We demonstrate that this effect is
strongly enhanced if additionally the photon is propagating through refractive
medium, which effectively increases the photon exposure to the neutrino medium.
Our estimate for infrared laser beam in $1\,\mathrm{m}$ long optical fiber
exposed to reactor anti-neutrino flux results in linear polarization rotation
by the angle $\sim4.6\times10^{-39}\,\mathrm{rad}$. We also derive the proper
dependence of the effect on the angle between the directions of photon and
neutrino propagation in the laboratory frame. For that purpose we derive the
correct form of the basis of polarization four-vectors, which differs from the
one widely used in literature. We also estimate the sub-leading optical effect
of the neutrino medium due to the neutrino dipole magnetic moment, in terms of
a variation of the refractive index and its angular dependence. A rough
monochromatic approximation points towards the existence of a resonant
enhancement of the effect.
