Nonconstant ponderomotive energy in above-threshold ionization by intense short laser pulses

We analyze the contribution of the quiver kinetic energy acquired by an electron in an oscillating electric field of a short laser pulse to the energy balance in atomic ionization processes. Due to the time dependence of this additional kinetic energy, a temporal average is assumed to preserve a stationary energy conservation rule, which is used to predict the position of the energy peaks observed in the photoelectron (PE) spectra. For a plane wave and a flattop pulse, the mean value of the quiver energy over the whole pulse leads to the concept of ponderomotive energy Up. However, for a short pulse with a fast changing intensity, the stationary approximation loses its validity. We check these concepts by studying first the PE spectrum within the semiclassical model (SCM) for multiple-step pulses. The SCM offers the possibility to establish a connection between emission times and the PE spectrum in the energy domain. We show that PE substructures stem from ionization at different times mapping the pulse envelope. We also analyze the PE spectrum for a realistic sine-squared envelope within the Coulomb-Volkov and ab initio calculations solving the time-dependent Schrodinger equation. We found that the electron emission amplitudes produced at different times interfere with each other producing, in this way, a new additional pattern that modulates the above-threshold ionization (ATI) peaks.