Quasi-Phase Matching in High Harmonic Generation using Structured Plasmas

High harmonic generation (HHG) is an important process in attosecond science. Its efficiency is, however, limited to values below 10
^-5
of the incident power into a single harmonic. Phase matching can increase the efficiency but deals with low ionization rates. Furthermore HHG from laser-produced plasmas has shown some promising advantages in increasing the response of the conversion. These are the appearance of resonantly enhanced harmonics or the efficient generation in carbon or nanoparticle containing plasmas. On the contrary laser-produced plasmas inherently possess a high degree of ionization which hampers any phase-matching scheme with these sources. This dilemma can be circumvented by quasi-phase matching (QPM). In this case the conversion process is suppressed when the harmonics are generated out of phase leading to a quadratic growth of the harmonic intensity with interaction distance. Experimentally QPM can be achieved e.g. by applying a structured conversion medium in a focused driving beam geometry. Here, we show how such a scheme is realized with laser-produced plasmas. The idea of using a structured plasma for QPM is not new [1], but in none of these earlier studies QPM has been optimized for maximum efficiency nor controlled for different regions of the harmonic spectrum.