Phase matching effects in high harmonic generation at the nanometer scale

TL;DR

This paper investigates phase matching effects in high harmonic generation at the nanometer scale, revealing their significance despite the subwavelength propagation distances, and explores control techniques applicable at this scale.

Contribution

It demonstrates that phase matching influences HHG in nanostructures due to the intensity-dependent phase, enabling control methods like quantum path selection at the nanoscale.

Findings

Phase matching affects HHG in nanostructures despite short propagation distances.

The phase of harmonics is linked to the intensity distribution of the driving field.

Control techniques such as quantum path selection are feasible at the nanoscale.

Abstract

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.