Extracting photoelectron spectra from the time-dependent wave function: Comparison of the projection onto continuum states and window-operator methods

TL;DR

This paper compares two numerical methods for extracting photoelectron spectra from the time-dependent wave function in atomic ionization studies, highlighting the importance of boundary conditions for accurate spectral features.

Contribution

It provides a systematic comparison of projection and window-operator methods, emphasizing the impact of boundary conditions on spectral accuracy in atomic ionization simulations.

Findings

Projection method's accuracy depends on boundary conditions.

Window-operator method offers an alternative extraction technique.

Correct boundary conditions are crucial for resolving interference structures.

Abstract

Over the last three decades numerous numerical methods for solving the time-dependent Schr\"{o}dinger equation within the single-active electron approximation have been developed for studying ionization of atomic targets exposed to an intense laser field. In addition, various numerical techniques for extracting the photoelectron spectra from the time-dependent wave function have emerged. In this paper we compare photoelectron spectra obtained by either projecting the time-dependent wave function at the end of the laser pulse onto the continuum state having proper incoming boundary condition or by using the window-operator method. Our results for three different atomic targets show that the boundary condition imposed onto the continuum states plays a crucial role for obtaining correct spectra accurate enough to resolve fine details of the interference structures of the photoelectron angular distribution.