Numerical simulations of strong-field processes in momentum space*

Abstract

The time-dependent Schrödinger equation (TDSE) is usually treated in the real space in the text book.However, it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields. Here we demonstrate that the TDSE can be efficiently solved in the momentum space. The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space, but significantly reducing the computation cost.

Comparative study of photoionization of atomic hydrogen by solving the one- and three-dimensional time-dependent Schrödinger equations*

“…To circumvent the aforementioned numerical difficulty, instead of solving the TDSE in its full dimensionality, one often solve it in reduced dimensions. [15,16] Reduced-dimensional (RD) TDSE is much more computationally tractable, but can still grasp the key physics in a lot of cases. For linearly (circularly) polarized pulses, the main dynamics happens along the polarization axis (in the polarization plane) and, therefore, the other two (one) dimensions can be approximately ignored.…”