Dispersive surface-response formalism to address nonlocality in extreme plasmonic field confinement

The surface-response formalism (SRF), where quantum surface-response corrections are incorporated into the classical electromagnetic theory via the Feibelman parameters, serves to address quantum effects in the optical response of metallic nanostructures. So far, the Feibelman parameters have been typically obtained from many-body calculations performed in the long-wavelength approximation, which neglects the nonlocality of the optical response in the direction parallel to the metal-dielectric interface, thus preventing to address the optical response of systems with extreme field confinement. To improve this approach, we introduce a dispersive SRF based on a general Feibelman parameter d(?)(?, k(||)), which is a function of both the excitation frequency, ?, and the wavenumber parallel to the planar metal surface, k(||). An explicit comparison with time-dependent density functional theory (TDDFT) results shows that the dispersive SRF correctly describes the plasmonic response of planar and nonplanar systems featuring extreme field confinement. This work thus significantly extends the applicability range of the SRF, contributing to the development of computationally efficient semiclassical descriptions of light-matter interaction that capture quantum effects.