Precision calculation of above-threshold multiphoton ionization in intense short-wavelength laser fields: The momentum-space approach and time-dependent generalized pseudospectral method

Abstract

We present an approach in momentum (P) space for the accurate study of multiphoton and above-threshold ionization (ATI) dynamics of atomic systems driven by intense laser fields. In this approach, the electron wave function is calculated by solving the P-space time-dependent Schrödinger equation (TDSE) in a finite P-space volume under a simple zero asymptotic boundary condition. The P-space TDSE is propagated accurately and efficiently by means of the time-dependent generalized pseudospectral method with optimal momentum grid discretization and a split-operator time propagator in the energy representation. The differential ionization probabilities are calculated directly from the continuum-state wave function obtained by projecting the total electron wave function onto the continuum-state subspace using the projection operator constructed by the continuum eigenfunctions of the unperturbed Hamiltonian. As a case study, we apply this approach to the nonperturbative study of the multiphoton and ATI dynamics of a hydrogen atom exposed to intense shortwavelength laser fields. High-resolution photoelectron energy-angular distribution and ATI spectra have been obtained. We find that with the increase of the laser intensity, the photoelectron energy-angular distribution changes from circular to dumbbell shaped and is squeezed along the laser field direction. We also explore the change of the maximum photoelectron energy with laser intensity and strong-field atomic stabilization phenomenon in detail.

Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method

“…We have estimated the accuracy of our results to be 10% throughout the spectrum using the same procedures as for figure 3. Our result qualitatively differs from figure 2 in [9], where a surprising irregularity appears near 10U p , while no such structure exists in our spectrum. Unfortunately no detailed discussion of accuracy or convergence is given in [9].…”

“…Our result qualitatively differs from figure 2 in [9], where a surprising irregularity appears near 10U p , while no such structure exists in our spectrum. Unfortunately no detailed discussion of accuracy or convergence is given in [9]. One possible source of the discrepancy is insufficient discretization.…”

“…Results obtained with 192 radial discretization points are accurate to a few per cent and never exceed 10% in the whole range shown. The pulse parameters agree with those used for figure 2 in [9]. Near 10U p there appears a striking qualitative difference between our result and [9].…”

“…In different wording, one can say that they are caused by interference between the rising and trailing edges of the pulse [20]. For comparison with the results reported in [9], we also computed the spectrum at the lower intensity of 5 × 10 13 W cm −2 and T = 10 cycles FWHM (corresponding to 20 cycles total pulse duration). Figure 5 shows our result for the total photo-ionization spectrum obtained with only 192 discretization points and 25 angular momenta.…”

Resonance-like enhancement in high-order above-threshold ionization of formic acid

“…(4) gives the TDSE in momentum space. This equation is solved via the timedependent Generalized pseudospectral scheme [27,28]. Using the calculated time-dependent wave function of the system, we simulate the ATI spectrum utilizing the scheme proposed by Dionissopoulou et al [29].…”