Electrons that break free during photoionization acquire a phase shift induced by the many-body potential of the parent ion. This phase shift can be interpreted as a delay in the photoionization process. This delay is very brief—on the order of attoseconds—and the time-scale of the process is short enough to, until recently, have been approximated as instantaneous. Recent developments in experimental methods have enabled the generation of light pulses of attosecond duration, allowing these phenomena to be probed in experiments. The photoionization delay can be measured in short-pulse pump-probe experiments that utilizes methods like RABBIT or streaking. Originally these experimental protocols used linearly polarized light and non-angularly resolved measurements.

When the capability to use circularly polarized pulses in experiments grow, the numerical methods used to simulate such experiments must follow, and be made capable of accounting for pulses with non-linear polarization. As more experiments collect angularly resolved data it is important to develop tools to analyse these more complex results.

This thesis summarizes the work I have done to extend two numerical simulation methods to circular polarization, as well as the extension of a theoretical tool to angularly resolved delays. By decoupling the angular and radial parts through the implementation of coupled two-photon operators, I have enabled the calculation of two-photon matrix elements for any detection angle and combination of photon polarizations.

I have computed general formulas for so-called asymmetry parameters that can be used to effectively describe and analyze the angular dependence of cross sections and delays. I have further worked on extending a program suite that simulates the interaction of atoms with light in the time-dependent regime so that it can simulate light of arbitrary polarization.

Through these efforts we have found ways to either simplify experiments, or to make them directly sensitive to only the effects of the probe pulse, which is the physically interesting part of the experimental signal.

Anisotropy parameters describing the angular dependence of the photoionization delay are defined. The formalism is applied to results obtained with the relativistic random phase approximation with exchange for photoionization delay from the outermost s-orbitals in selected rare-gas atoms. Any angular dependence in the Wigner delay is induced here by relativistic effects, while the measurable atomic delay exhibits such a dependence also in the nonrelativistic limit. The contributions to the anisotropy from the different sources are disentangled and discussed. For the heavier rare gases, it is shown that measurements of the delay for electrons ejected in specific angles, relative to, e.g., those ejected along the laser polarization, are directly related here to the Wigner delay. For a considerable range of angles, the contributions from the second photon largely get canceled when the results in different angles are compared, and this angle-relative atomic delay is then close to the corresponding Wigner delay.

Advances in experimental physics, specifically light sources emitting at an attosecond time scale, has enabled the time resolution of atomic processes like photoionization. Recent developments have allowed these sources to produce light with non-linear polarization. There exists various theoretical methods that can simulate experimental set-ups that make use of these attosecond sources. The aim of this thesis project was to extend two of these methods to be able to simulate circularly polarized light in order to both better model experimental results and come up with new potentially interesting experiments. This has resulted in an extended version of the Random Phase Approximation with Exchange method capable of simulating an ionization process by light of arbitrary polarization, as well as well as an extended version of the NewStock package that is capable of time-resolved simulation of matter interactions with arbitrary light pulses.

We present calculations on the atomic delay in photoionzation obtained with different combinations of linearly and circularly polarized light, and show how a tensor operator approach can be used to readily obtain results for any combination from a single calculation of the radial integrals. We find that for certain choices of polarization and detection geometry a single time-delay measurement is enough to extract the atomic delay since the relative phase in a RABBIT type measurement will be imprinted on the photo electron anisotropy. We show further that the full angular dependence can be qualitatively understood from a plane wave analysis. The results are illustrated by many-body calculations of two-photon above threshold ionization on argon.

Photoionization cross sections and delays are calculated within the relativistic random phase approximation with exchange for xenon and radon in the energy region between the first and second ionization threshold. Resonance parameters for the first few resonances in both systems are presented and the angular dependence is discussed.