Above-threshold ionization by few-cycle pulses

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