Polarization dependence of the third-harmonic generation in multiband superconductors

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, 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 nonresonant 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.