Theory of nonlinear electron relaxation in thin gold films and their signatures in optical observables

Based on the momentum-resolved Boltzmann equation, we provide self-consistent numerical calculations of the dynamics of conduction electrons in thin noble metal films after linear and nonlinear optical excitations with infrared and terahertz frequencies. Focusing exclusively on electron-phonon interaction, orientational relaxation is introduced and acts as dephasing of the optical excitation on a scale of tens of fs. In the linear regime, our numerical results agree with the field-strength-independent orientational relaxation rate and correspondingly fits of experimental data to a Drude model and predict for nonlinear excitations a field-strength-dependent increase of the orientational relaxation rate. In the THz regime, where the orientational relaxation proceeds faster than the oscillation cycle of the excitation THz field, a new high-order dissipative Kerr-type nonlinearity is predicted. This nonlinearity originates from the Pauli blocking included in the electron-phonon scattering and results in a nonlinearly increasing transmission of the film, detectable in experiments.