Limits of High Harmonic Generation conversion efficiency

Abstract

High Harmonic Generation (HHG) is a fascinating phenomenon from both fundamental and technological point of view. It enables the generation of attosecond pulses and can have applications in EUV lithography and bio-microscopy. HHG can be described by the Three Step Model (TSM), due to the three stages of the process: ionization, propagation and recombination. However, HHG suffers from low efficiencies and a study, which shows the efficiency scaling with laser and material parameters is essential. For a long time experimentalists were using only 800 nm driver pulses from Ti:sapphire lasers. With the advent of new light sources like optical parametric amplifiers, different driving wavelengths became available and thus the scaling of the single atom response versus drive wavelength has attracted a lot of attention. A detailed analysis shows that the efficiency scales with w50 at the cutoff and w60 at the plateau region for a fixed EUV frequency, where w0 is the carrier frequency of the driver pulse. To understand the limitations of such a light source, we have developed a semi-analytic model for the computation of the conversion efficiency into a single harmonic for the plateau and cutoff regions. This model is one-dimensional, uses the TSM for the calculation of the single atom response and takes laser, material parameters and macroscopic effects into account. Closed form expressions for the plateau and cutoff regions are derived and used to calculate efficiencies for 400 and 800 nm driver pulses. The results are compared with experimental ones showing very good agreement. In order to investigate long-wavelength driven HHG efficiency, the 1-D model is extended to three dimensions taking into account spatiotemporal propagation effects, such as plasma defocusing and losses due to electron-neutral inverse bremsstrahlung. These phenomena change the phase matching along propagation, resulting in non-coherent harmonic generation and consequently poor efficiencies. We further study ways to mitigate the effect of plasma defocusing like the use of Supergaussian pulses and the use of Gaussian pulses with larger beam waists. The work presented can help us develop tools for an optimization study of HHG efficiency, in order to make useful EUV sources.