Diffraction at a time grating in above-threshold ionization: The influence of the Coulomb potential

Abstract

We analyze the photoelectron emission spectrum in atomic above-threshold ionization by a linearly polarized short-laser pulse. Direct electrons can be characterized by both intracycle and intercycle interferences. The former results from the coherent superposition of two different electron trajectories released in the same optical cycle, whereas the latter is the consequence of the superposition of multiple trajectories released in different cycles. In the present article, a semiclassical analytical expression for the complete (both intracycle and intercycle) interference pattern is derived. We show that the recently proposed semiclassical description in terms of a diffraction process at a time grating remains qualitatively unchanged in the presence of the long-range Coulomb potential. The latter causes only a phase shift of the intracycle interference pattern. We verify the predictions of the semiclassical model by comparison with full three-dimensional (3D) time-dependent Schrödinger equation (TDSE) solutions.One key finding is that the subcycle interference structures originating from trajectories launched within a time interval of less than 1 femtosecond should be experimentally observable also in low-resolution spectra for longer multicycle pulses.

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.…”

“…Atomic ionization processes are mainly produced by tunneling near the maximum amplitude of the electric field and, it was observed that each of these maxima behaves as a slit, through which one electron can be emitted [20]. In analogy to the Young's experiment, we can regard the photoelectron spectrum as the result of the interference of electron trajectories, giving rise to intracycle and intercycle interferences [3]. The intercycle interference stems from the contribution from trajectories in different optical cycles and it is observed as an equally spaced set of maxima in the photoelectron energy distribution.…”

Two-Dimensional Attosecond Electron Wave-Packet Interferometry

“…Previous experiments show that the treatment of Coulomb influence is important but not trivial [11,12,20,21]. Besides, because of the mixture of different kind interferences, the fringe positions of one kind interference will be modified by the other kinds which will thus affect the precision of the phase reconstruction [15]. Another important effect is the influence from the complex low-energy structures (LES) [22][23][24][25].…”

“…In general, the released EWPs carry electron or nuclear dynamics and the orbital structure information of the system. Therefore, the EWPs interference can be used to retrieve the information of the molecular orbital type is inter-cycle interference (ICI) with EWPs released from different laser optical cycles which leads to ATI(above-threshold ionization)-like structure in momentum distribution [13,15]. The second type is subcycle interference (SCI) with EWPs from different half cycle within one optical cycle [12,[16][17][18].…”