Intracycle and intercycle interferences in above-threshold ionization: The time grating

Abstract

Within a semiclassical description of above-threshold ionization (ATI) we identify the interplay between intracycle and intercycle interferences. The former is imprinted as a modulation envelope on the discrete multiphoton peaks formed by the latter. This allows one to unravel the complex interference pattern observed for the full solution of the time-dependent Schrödinger equation (TDSE) in terms of diffraction at a grating in the time domain. These modulations can be clearly seen in the dependence of the ATI spectra on the laser wavelength. Shifts in energy modulation result from the effect of the long Coulomb tail of the atomic potential.Tunneling ionization is a highly nonlinear quantummechanical phenomenon induced by intense laser pulses (> ∼ 10 14 W/cm 2 ). Electrons are emitted by tunneling through the potential barrier formed by the combination of the atomic potential and the external strong field. Tunneling has recently attracted increasing interest as a probe of the atomic and molecular structure [1-3]. Tunneling occurs within each optical cycle predominantly around the maxima of the absolute value of the electric field. The interference of the successive bursts of ejected electrons reaching the same final momentum gives rise to features in photoelectron energy and momentum distribution which are markedly different from typical above-threshold ionization (ATI) spectra by multicycle lasers. This temporal double-slit interference has recently been studied both experimentally [1,4] and theoretically [5]. On the other hand, the ATI peaks separated by a photon energy can be themselves viewed as an interference pattern formed by electron bursts repeated each optical cycle. Details of the interplay between these intra-and intercycle interferences have not yet been clearly identified and analyzed, to the best of our knowledge.In this Rapid Communication, we study the influence of different interference processes on ATI spectra generated by multicycle laser pulses. We clarify the underlying mechanism within a simple one-dimensional (1D) model employing classical trajectories. Within the framework of the strongfield approximation (SFA) [6] the qualitative features, the modulation of the ATI peaks akin to the modulation of Bragg peaks by the structure factor in crystal diffraction, can be unambiguously identified in the ATI spectrum determined from the full solution of the three-dimensional time-dependent Schrödinger equation (TDSE). The multicycle laser pulse thus acts as a diffraction grating in the time domain. Quantitative deviations between the SFA predictions and the full TDSE can be traced to the Coulomb tail of the atomic potential affecting this modulation. The latter opens up the opportunity to observe effects of the atomic potential in easy-to-obtain photoelectron spectra after ionization by multicycle laser pulses.Our simple semiclassical model of photoelectron spectra is based on the 1D "simple man's model (SMM)" [6][7][8]. Let us consider an atom interacting with a linearly polarized laser pulse. The...

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

“…The semiclassical model (SCM) described in previous works [3,4,6], utilizes the saddle point approximation to replace the time integration in Eq. (20) by a sum over ionization or release times t r where the oscillating phase…”

“…(8) has been widely used to describe the emitted electron immersed in the laser field. For example the Strong Field Approximation (SFA) [12,13,17,22], the Coulomb-Volkov Approximation (CVA) [5,8,11,15,23] and the semiclassical application of the Simple Man's Model (SCM) [3,4,6] employ the non-stationary Volkov state as final wavefunction. The use of length gauge for the perturbation potential, i.e.…”

Trajectory-Based Coulomb-Corrected Strong Field Approximation

“…Substituting W(t s ) into the transition amplitude (76) and factoring the same prefactor out of all terms, (76) becomes…”

“…Using (74) and (75) to reformulate the transition amplitude (73), the TCSFA transition amplitude thus reads (76) where…”

“…3(a). The interference is known as the "intra-cycle interference" [76] (more precisely, "intra-half-cycle interference"). Figure 4(a) shows a tilting φ-p z distribution.…”