Above-threshold ionization by few-cycle pulses

Abstract

The theoretical description and the experimental methods and results for above-threshold ionization (ATI) by few-cycle pulses are reviewed. A pulse is referred to as a few-cycle pulse if its detailed shape, parametrized by its carrier-envelope phase, affects its interaction with matter. Angular-resolved ATI spectra are analysed with the customary strong-field approximation (SFA) as well as the numerical solution of the time-dependent Schrödinger equation (TDSE). After a general discussion of the characteristics and the description of few-cycle pulses, the behaviour of the ATI spectrum under spatial inversion is related to the shape of the laser field. The ATI spectrum both for the direct and for the rescattered electrons in the context of the SFA is evaluated by numerical integration and by the method of steepest descent (saddle-point integration), and the results are compared. The saddle-point method is modified to avoid the singularity of the dipole transition matrix element at the steepest-descent times. With the help of the saddle-point method and its classical limit, namely the simple-man model, the various features of the ATI spectrum, their behaviour under inversion, the cut-offs and the presence or absence of ATI peaks are analysed as a function of the carrier-envelope phase of the few-cycle laser field. All features observed in the spectra can be explained in terms of a few quantum orbits and their superposition. The validity of the SFA and the concept of quantum orbits are established by comparing the ATI spectra with those obtained numerically from the ab initio solution of the TDSE.

ClassSTRONG: Classical simulations of strong field processes

“…Red (Green) circles correspond to the electron kinetic energy, in terms of U p units (U p = I/4ω 2 is the ponderomotive energy with I the laser intensity and ω its frequency), of the direct (rescattered) electron as a function of the ionization time. It includes lines indicating the values of the classical electron kinetic energies limits for both the direct, 2U p , and rescattered, 10U p , electron [7]. We can observe our classical simulations exactly fulfill these limits.…”

“…If the electron elastically rescatters, gains energy and continues its travel to the detector we talk about above-threshold ionization (ATI) (see [7]). The ATI phenomenon receives special attention due to the fact that the ATI yield is highly sensitive to the so-called carrier envelope phase, and consequently it constitutes a very robust pulse characterization tool.…”

The impact of the carrier envelope phase-dependence on system and laser parameters

“…This opens the door to a great variety of new investigations such as time-resolved measurement of electronic processes or precision control of chemical reactions see, e.g., [3,4,5,6,7,8,9]. One of the main new aspects of such few-cycle pulses is that the Carrier Envelope Phase (CEP), i.e.…”

Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments

“…Thus, many nonlinear interactions based on the strong-field ionization mechanism, such as highorder harmonic generation, above-threshold ionization, etc, are found to be dependent on the CEP [6,[17][18][19]. These CEP-dependent phenomena open up an exciting potential for applications in many fields.…”

“…One prospect is the application of the CEP as a precise coherent control tool to manipulate an electron in atoms and molecules [6,17]. In turn, the CEPdependent phenomena can also be utilized for measuring the CEP [18,19], which leads to light wave-form control. As a result, the investigations of the CEP-related laser-matter interactions have become an extremely important matter in ultrafast science.…”