  We study the gravitational lensing effect on the Cosmic Microwave Background
(CMB) anisotropies performing a ray-tracing of the primordial CMB photons
through intervening large-scale structures (LSS) distribution predicted by
N-Body numerical simulations with a particular focus on the precise recovery of
the lens-induced polarized counterpart of the source plane. We apply both a
multiple plane ray-tracing and an effective deflection approach based on the
Born approximation to deflect the CMB photons trajectories through the
simulated lightcone. We discuss the results obtained with both these methods
together with the impact of LSS non-linear evolution on the CMB temperature and
polarization power spectra. We compare our results with semi-analytical
approximations implemented in Boltzmann codes like, e.g., CAMB. We show that,
with our current N-body setup, the predicted lensing power is recovered with
good accuracy in a wide range of multipoles while excess power with respect to
semi-analytic prescriptions is observed in the lensing potential on scales
$\ell \gtrsim 3000$. We quantify the impact of the numerical effects connected
to the resolution in the N-Body simulation together with the resolution and
band-limit chosen to synthesise the CMB source plane. We found these quantities
to be particularly important for the simulation of B-mode polarization power
spectrum.
