  We present theoretical studies of high-order harmonic generation (HHG)
produced by non-homogeneous fields as resulting from the illumination of
plasmonic nanostructures with a short laser pulse. We show that both the
inhomogeneity of the local fields and the confinement of the electron movement
play an important role in the HHG process and lead to the generation of even
harmonics and a significantly increased cutoff, more pronounced for the longer
wavelengths cases studied. In order to understand and characterize the new HHG
features we employ two different approaches: the numerical solution of the time
dependent Schr\"odinger equation (TDSE) and the semiclassical approach known as
Strong Field Approximation (SFA). Both approaches predict comparable results
and show the new features, but using the semiclassical arguments behind the SFA
and time-frequency analysis tools, we are able to fully understand the reasons
of the cutoff extension.
