Theory of nonlinear propagation of high harmonics generated in a gaseous medium

Abstract

In this thesis, we establish the theoretical tools to investigate high-order harmonic generation (HHG) by intense infrared lasers in a gaseous medium. The macroscopic propagation of both the fundamental and the harmonic fields is taken into account by solving Maxwell’s wave equations, while the single-atom (or single-molecule) response is obtained by quantitative rescattering theory. The initial spatial mode of the fundamental laser is assumed either a Gaussian or a truncated Bessel beam. On the examples of Ar, N[subscript]2 and CO[subscript]2, we demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N[subscript]2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO[subscript]2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continuous harmonic spectrum of Xe due to the reshaping of the fundamental laser field can be used to produce an isolated attosecond pulse by spectral and spatial filtering in the far field. For on-going application of using HHG to ionize aligned molecules, we present the photoelectron angular distribution from aligned N[subscript]2 and CO[subscript]2 in the laboratory frame, which can be compared directly with future experiments.