Multielectron High Harmonic Generation: Simple Man on a Complex Plane

Abstract

IntroductionAttosecond science has emerged with the discovery of coherent electron-ion collisions induced by a strong laser field, usually referred to as "recollisions" [1]. This discovery was initiated by the numerical experiments of K. Schafer, J. Krause and K. Kulander (see [2]). The work [1] drew on the concepts developed by F. Brunel and colleagues [3][4][5]. It has also been predated by the concept of the "atomic antenna" [6] developed by M. Kuchiev. With the benefit of hindsight, we now see the "atomic antenna" [6] as the earliest quantum counterpart of the classical picture developed by [1,7]. 1)The classical picture of strong-field-induced ionization dynamics is summarized as follows. Once ionization removes an electron from an atom or a molecule, this electron finds itself in the strong oscillating laser field. Newton's equations of motion show that, within one or a few cycles after ionization, the oscillating electron can be driven back by the laser field to reencounter the parent ion. During this reencounter, referred to as recollision, the electron can do many things: scatter elastically (diffract), scatter inelastically (excitation or ionization of the parent ion), or radiatively recombine with the ion. It is this latter process that we will focus on here. The classical picture is usually referred to as the three-step model, or the simple man model. 2) 1) While the quantum vision of [6] has predated the classical picture, at that time it lacked the striking clarity and transparency of the classical model [1], which linked several key -and seemingly disparate -strong-field phenomena, like high harmonic generation, production of very high-energy electrons, and extreme efficiency of double ionization. The history of this discovery and of its impact on nonlinear optics and technology are rich and interesting in their own right. Some of it is recounted, from a more historical perspective, in Chapter 10. Our purpose here is different -we simply urge the reader to read the papers [3-6, 8], as well as a seemingly unrelated paper [9]. 2) As far as one of us (M.I.) can remember, the latter term has been used by K. Kulander, K. Schafer and H.-G. Muller, who have largely contributed to the development of this classical model. Attosecond and XUV Physics, First Edition. Edited by Thomas Schultz and Marc Vrakking.

Attosecond control of spin polarization in electron-ion recollision driven by intense tailored fields

“…Within the strong-field approximation (SFA), the continuum electron wave function at time t is given by [34]:…”

“…2 can be used to calculate different observables, such as photoelectron yields, induced polarization and harmonic spectra [34]. Here we are interested in analyzing the degree of spin-polarization of the electrons that are driven back to the ionic core.…”

“…Application of the saddle-point method (see e.g. [34]) to the integral eq. 5 allows us to perform the semi-classical analysis of this expression in terms of electron trajectories, getting insight into the physical origin of spin polarization during recollision.…”

Role of tunnel ionization in high harmonic generation from substituted benzenes

“…We use a form of the SFA 20 extended to high-harmonic generation in molecules by summing coherently over multiple cation states 4,16,[21][22][23] . For completeness, our model also includes laser induced dynamics in the cation between ionization and recombination 24 .…”

Multidimensional high harmonic spectroscopy

“…However, the SFA gives analytical result which allows one to build the physical intuition about the process of strong field interaction. While the SFA accuracy is only exponential, the corrections to the pre-exponential factor can be included in the result later, using different methods, numerical and analytical [157].…”