Efficient numerical approaches for <i>ab-initio</i> linear and nonlinear optics

The validity of the approximations involved and the limitations of the approach are also discussed.<br><br>The nonlinear optical regime is typically addressed with non-perturbative methods based on explicit time propagation, which makes them computationally costly. We tackle this issue by proposing a reformulation of the so-called real-time approach [Phys. Rev.

B 88, 235113, (2013)] based on Floquet theory, which leads to a self-consistent time-independent eigenvalue problem. The method presented here applies to periodically-driven quantum systems with weak electric fields and remains valid for extended systems as it uses the dynamical Berry-phase polarisation.<br><br>The implementation of this Floquet scheme at the independent particle level reproduces the results of the real-time approach for 2nd and 3rd order susceptibilities of a number of bulk and two-dimensional materials, while reducing the associated computational cost by one or two orders of magnitude.

The inclusion of local fields and many-body effects introduced instabilities in the Floquet self-consistent cycle that could not be yet mitigated, leading to only a handful of converged results at the time-dependent Hartree level. These divergencies are linked to high population inversions, according to insights gained following the development of a Floquet analysis tool capable of extracting Floquet states from a time-dependent solution produced by, e.g., the real-time approach.<br><br>After critically evaluating the contributions of this thesis to the field of computational materials science, it was concluded that the methods proposed and developed here have the potential to accelerate the <i>ab-initio</i> calculation of linear and nonlinear optical properties.

Avenues for future exploration on these topics are also identified in light of the findings reported in this work.<br>