  In a superconductor the third-harmonic generation (THG) of a strong THz pulse
is enhanced below Tc by the resonant excitation of lattice-modulated charge
fluctuations (LCF), which modulate the response according to the polarization
of the field. Here we compute the THG within a multiband model for the
prototype NbN superconductor. We show that the non-resonant contribution coming
from the instantaneous electronic response and the finite width of the pulse
significantly suppress the polarization dependence of the signal, challenging
its observation in real systems.
