Medium Propagation Effects in High-Order Harmonic Generation of Ar

Abstract

High-order harmonic generation (HHG) is an extreme nonlinear optical process in which an intense ultrafast infrared laser light is efficiently converted to an ultrafast coherent extreme ultraviolet (XUV) or soft X-ray light. As discussed in Chap. 1, HHG has been widely studied for its potential as a short-wavelength light source [1], or the production of ultrashort light pulses [2]. It has also been shown to extract the information of atomic structure [3] or to image the molecular structure with sub-Angstrom precision in space and sub-femtosecond precision in time [4–7]. HHG process in single-atom response level can be intuitively understood in terms of the semiclassical “three-step” model [8, 9]. However, the laser field interacts with a macroscopic medium, and high harmonics from all atoms are generated coherently, a full description of experimentally observed harmonic spectra requires the treatment of the nonlinear propagation of fundamental laser beam together with high harmonics in the medium. As discussed in Chap. 2, the most accurate way to obtain the microscopic single-atom induced dipole is to solve the time-dependent Schrodinger equation (TDSE) numerically. Since this approach is quite time consuming and the calculations have to be carried out for hundreds of laser peak intensities in order to describe the nonuniform laser distribution inside a focused laser beam, this is rarely done in existing studies including the macroscopic propagation effect of HHG [10]. Instead, much simpler strong-field approximation (SFA) [11] is often used to calculate the single-atom induced dipole. Despite this limitation, the temporal and spatial properties of HHG observed experimentally have been reasonably understood from such SFA-based calculations. On the other hand, in a few examples, macroscopic HHG spectra obtained using TDSE-calculated induced dipoles do show significant quantitative discrepancies compared to SFA-based calculations [12, 13], and such studies have been limited to a few atomic gases only.