Resonant third-harmonic generation driven by out-of-equilibrium electron dynamics in sodium-based near-zero index thin films

We investigate resonant third-harmonic generation in near-zero index thin films driven out-of-equilibrium by intense optical excitation. Adopting the Landau weak coupling formalism to incorporate electron-electron and electron-phonon scattering processes, we derive a novel set of hydrodynamic equations accounting for collision-driven nonlinear dynamics in sodium. By perturbatively solving hydrodynamic equations, we model third-harmonic generation by a thin sodium film, finding that such a nonlinear process is resonant at the near-zero index resonance of the third-harmonic signal. Thanks to the reduced absorption of sodium, we observe that third-harmonic resonance can be tuned by the impinging pump radiation angle, efficiently modulating the third-harmonic generation process. Furthermore, owing to the metallic sodium response at the pump optical wavelength, we find that the third-harmonic conversion efficiency is maximised at a peculiar thin film thickness where evanescent back-reflection provides increased field intensity within the thin film. Our results are relevant for the development of future ultraviolet light sources, with potential impact for innovative integrated spectroscopy schemes.