  Plasmon resonances are known to amplify the electromagnetic fields near
metallic nanostructures. Therefore, they are considered to provide a promising
scheme to generate extreme-ultraviolet harmonics, using low power drivings.
During high-order harmonic generation (HHG), the driving and harmonic fields
accumulate a phase difference as they propagate through the target. In a
typical set-up -a laser focused into a gas jet or cell- the propagation
distances amount to several wavelengths, and the cumulative phase-mismatch
affects strongly the efficiency and properties of the harmonic emission. In
contrast, HHG in metallic nanostructures is considered to overcome this
limitations, as the common sources of phase mismatch -optical density and
focusing geometry- are negligible for subwavelength propagation distances.
Nevertheless, in this letter we demonstrate that phase matching still plays a
relevant role in HHG from nanostructures. Our computations attribute this to
the non-perturbative character of HHG, that links the phase of the harmonics to
the intensity distribution of the driving field. We also show that widely used
applications of phase matching control, such as quantum path selection and the
increase of contrast in attosecond pulse generation, are also feasible at the
nanoscale.
