Phase matching effects in high harmonic generation at the nanometer scale

Plasmon resonances are known to amplify the electromagnetic fields near metallic nanostructures, providing 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- 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 these limitations, as the common sources of phase mismatch -optical density and focusing geometry- are negligible for subwavelength propagation distances. We demonstrate that phase matching still plays a relevant role in HHG from nanostructures due to the non-perturbative character of HHG, that links the harmonic phase to the intensity distribution of the driving field. Our computations 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.