  Inspired by a dipole asymmetric template for the CMB temperature map in the
primordial scalar fluctuations observed by Planck at a large scale, we examine
the contribution of a similar template for power asymmetry in modifying the
linear polarization pattern of CMB. Replacing un-modulated temperature
fluctuation with dipolar modulated one in time evolution equations somehow
breaks linear perturbation in the various components of the CMB map. This
non-linearity allows deflecting CMB polarization in patterns that contain
divergence-free components. The explicit expressions for the angular power
spectra of the electric and magnetic-type parities of linear polarization are
derived in the form of the line of sight integral solutions. Our results
demonstrate that the electric-type polarization is modified and the
magnetic-type polarization would be produced. Such imprints depend on the
linear and square of the asymmetric amplitude for $E$- and $B$-modes power
spectra, respectively. For the observed dipole template, the value of $B$
polarization spectrum at the large scale ($\ell\lesssim 10$) is almost
equivalent to the power spectrum obtained from Compton scattering in the
presence of tensor perturbation with tensor to scalar ratio about
$r\simeq0.005$.
