  We study high-order harmonic generation (HHG) resulting from the illumination
of plasmonic nanostructures with a short laser pulse. We show that both the
inhomogeneities of the local electric field and the confinement of the electron
motion play an important role in the HHG process and lead to a significant
increase of the harmonic cutoff. In order to understand and characterize this
feature, we combine the numerical solution of the time dependent Schroedinger
equation (TDSE) with the electric fields obtained from 3D finite element
simulations. We employ time-frequency analysis to extract more detailed
information from the TDSE results and to explain the extended harmonic spectra.
Our findings have the potential to boost up the utilization of HHG as coherent
extreme ultraviolet (XUV) sources.
