Perturbative optical parametric amplification in the extreme ultraviolet

The response of a medium illuminated with a light field can be expanded in many orders in perturbative non-linear optics. Here we use two multiple-cycle high-intensity laser pulses at 800 and 1,400 nm to generate extreme ultraviolet radiation where the multi-photon processes can be treated as the driving force of a perturbative optical parametric amplification. When a very high-intensity pulse (>7.10(14) W cm(-2)) at 800 nm is applied in addition to a high-intensity pulse at 1,400 nm, we are able to enhance the flux of the coherent extreme ultraviolet radiation in the photon energy range around 80 eV by more than an order of magnitude compared with the generation with a single-wavelength pulse. This opens the way to extend the powerful techniques of perturbative non-linear optics to the case of a high-intensity-driving field in multiple-photon processes.