Broadband measurement of Feibelman's quantum surface response functions

Feibelman [Formula: see text]-parameter, a mesoscopic complement to the local bulk permittivity, describes quantum optical surface responses for interfaces, including nonlocality, spill-in and -out, and surface-enabled Landau damping. It has been incorporated into the macroscopic Maxwellian framework for convenient modeling and understanding of nanoscale electromagnetic phenomena, calling for the compilation of a [Formula: see text]-parameter database for interfaces of interest in nano-optics. However, accurate first-principles calculations of [Formula: see text]-parameters face computational challenges, whereas existing measurements of [Formula: see text]-parameters are scarce and restricted to narrow spectral windows. We demonstrate a general broadband ellipsometric approach to measure [Formula: see text]-parameters at a gold-air interface across the visible-ultraviolet regimes. Gold is found to spill-in and spill-out at different frequencies. We also observe gold's Bennett mode, a surface-dipole resonance associated with a pole of the [Formula: see text]-parameter, around 2.5 eV. Our measurements give rise to and are further validated by the passivity and Kramers-Kronig causality analysis of [Formula: see text]-parameters. Our work advances the understanding of quantum surface response and may enable applications like enhanced electron field emission.