On gravitational lensing by quadrupole potentials

We study gravitational lensing by quadrupole potentials within the linearized gravity approximation and the integration over the unperturbed photon trajectory. It is well known that the quadrupole potential contribution to the deviation angle is much smaller than that of the monopole one. We show, however, that quadrupole potentials can change the photon polarization vector, but there is no contribution from the monopole term to the first order. The effect is maximal when the axis of the quadrupole is tangential to the photon trajectory and it is proportional to the frequency(rate) of the quadrupole moment of the deflector. The second order correction of the monopole potential to the polarization is canceled away by the renormalization of the polarization vector.