  The plasmon response of metallic nanostructures is anticipated to exhibit
nonlocal dynamics of the electron gas when exploring the true nanoscale. We
extend the local-response approximation (based on Ohm's law) to account for a
general short-range nonlocal response of the homogeneous electron gas. Without
specifying further details of the underlying physical mechanism we show how
this leads to a Laplacian correction term in the electromagnetic wave equation.
Within the hydrodynamic model we demonstrate this explicitly and we identify
the characteristic nonlocal range to be vF/omega where vF is the Fermi velocity
and omega is the optical angular frequency. For noble metals this gives
significant corrections when characteristic device dimensions approach ~1-10
nm, whereas at more macroscopic length scales plasmonic phenomena are well
accounted for by the local Drude response.
