  We perform a complete study of the gravitational lensing effect beyond the
Born approximation on the Cosmic Microwave Background (CMB) anisotropies using
a multiple-lens raytracing technique through cosmological N-body simulations of
the DEMNUni suite. The impact of second order effects accounting for the
non-linear evolution of large-scale structures is evaluated propagating for the
first time the full CMB lensing jacobian together with the light rays
trajectory. We carefully investigate the robustness of our approach against
several numerical effects in the raytracing procedure and in the N-body
simulation itself, and find no evidence of large contaminations. We discuss the
impact of beyond-Born corrections on lensed CMB observables, and compare our
results with recent analytical predictions that appeared in the literature,
finding a good agreement, and extend these results to smaller angular scales.
We measure the gravitationally-induced CMB polarization rotation that appears
at second order, and compare this result with the latest analytical
predictions. We then present the detection prospect of beyond-Born effects with
the future CMB-S4 experiment. We show that corrections to the temperature power
spectrum can be measured only if a good control of the extragalactic
foregrounds is achieved. Conversely, the beyond-Born corrections on E and
B-modes power spectra will be much more difficult to detect.
