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.
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