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.