  Recent experiments with strong THz fields in unconventional cuprates
superconductors have clearly evidenced an increase of the non-linear optical
response below the superconducting critical temperature Tc. As in the case of
conventional superconductors, a theoretical estimate of the various effects
contributing to the non-linear response is needed in order to interpret the
experimental findings. Here we report a detailed quantitative analysis of the
non-linear THz optical kernel in cuprates within a realistic model, accounting
for the band structure and disorder level appropriate for these systems. We
show that the BCS quasiparticle response is the dominant contribution for
cuprates, and its polarization dependence accounts very well for the
third-harmonic generation measurements. On the other hand, the polarization
dependence of the THz Kerr effect is only partly captured by our calculations,
suggesting the presence of additional effects when the system is probed using
light pulses with different central frequencies.
