Coherence in macroscopic high harmonic generation for different spatial focal phase distributions

To best take advantage of ultrafast laser sources from high harmonic generation (HHG) one needs to control properties of the spectrum such as the extent of the highest harmonics, the strength of the harmonic lines, and the cleanliness of the harmonics. To this end we study the impact of phase matching on the macroscopic HHG signal for the Gouy and Gaussian phase distributions as a function of the gas jet position [1]. The microscopic yields are obtained by interpolating results of the time-dependent Schrödinger equation and an individual-emitter approach is used to generate the approximate macroscopic signals [2]. Several measures are developed to qualitatively discuss the strengths and widths of the harmonic line and the relevance of off-harmonic radiation. For both the Gouy and Gaussian phase distributions the largest extent of the spectra is for positions of the gas jet after the focus. The relative strength of the harmonics is weaker for the Gaussian phase distribution due to the additional transverse dependence of the focal phase.