Coherence in macroscopic high harmonic generation for spatial focal phase distributions of monochromatic and broadband Gaussian laser pulses.

Efficient application of ultrafast laser sources from high harmonic generation requires an understanding of how the spectrum can be controlled - the extent of the highest harmonics and the strength and cleanness of the harmonic lines. We study one important aspect in the coherent build-up of macroscopic high-order harmonic generation, namely the impact of different phase distributions in the focal area on the features of the generated radiation. Specifically, we compare the high harmonic signals for the commonly-used Gouy distribution of a monochromatic beam with those for the phase distribution of a short broadband Gaussian pulse. To this end, we apply a theoretical model in which the microscopic yields are obtained via interpolation of results of the time-dependent Schrödinger equation, which are then used in an individual-emitter approach to determine the macroscopic signals. Regions of poor and good coherent build-up as a function of the position of the gas jet are identified using measures for the strength of the harmonic lines and for the impact of off-harmonic radiation. While the largest extent of the spectra as well as the strongest contribution of off-harmonic radiation is found for positioning the gas jet after the focus for both distributions, the relative strength of the harmonics is overall weaker for the short Gaussian pulse distribution and the spectra differ for a gas jet positioned at the focus. These differences are mainly caused by the additional dependence of the focal phase in the transverse direction for the short Gaussian pulse distribution.