Quantum-orbit analysis of laser-matter interactions in intense orthogonally polarised fields

A quantum-orbit analysis of laser-matter interactions allows us to understand, in terms of electron trajectories, the influence of intense orthogonally polarised fields on strong field phenomena. In doing so it allows us to understand the electron dynamics in the continuum and disentangle the influence of the field from the imprints left by the target molecule in the photoelectron and high-order harmonic spectra of strong field phenomena. This is the main topic of this thesis which focuses on temporal and spatial quantum interference in high harmonic generation (HHG) from molecules and above-threshold ionisation (ATI) from atoms. These are investigated semi-analytically at the single- molecule response and single-active orbital level, using the strong field approximation and the steepest descent method. In the case of HHG, a further investigation is performed at the macroscopic harmonic response level to model experimental HHG spectra by using Maxwell’s wave equations. HHG from molecules in orthogonally polarised fields is the most extensive topic of this work. At the single-molecule response level, we first investigate the influence of employing an orthogonally polarised field on the structural interference minima in high-order harmonic spectra from aligned diatomic molecules such as H2 and Ar2 in bichromatic orthogonally polarised fields and elliptical fields. We derive a generalised two-centre interference condition, which accounts for s-p mixing and the orbital symmetry, within the strong field and the single-active electron approximation. We show that the orthogonally polarised fields introduce an effective dynamic shift in the angle for which the two-centre interference maxima and minima occur, with regard to the existing condition for linearly polarised fields. This shift depends on the ratio between the field-dressed momentum components of the returning electron parallel and perpendicular to the major polarisation axis along each possible orbit, and therefore incorporates the electron’s angle of return. Because of this dependence, we find that there will be a blurring in the two-centre interference minima, and that increasing ellipticity leads to splitting in such patterns. We modelled the macroscopic harmonic response level, to investigate whether the features were washed out or survive high harmonic propagation to the far-field. We propose the optimal conditions for observing these shifted minima, using phase matching and polarisation gating, so they can be measured experimentally, with the possibility of extracting the electrons angle of return. In our analysis of the imprint of nodal planes in high-order harmonic spectra from aligned diatomic molecules in orthogonal polarised fields, we show that the typical suppression in the spectra associated to nodal planes is distorted. This distortion can also be employed to map the electron’s angle of return to its parent ion. We show that the velocity form of the dipole operator is superior to the length form in providing information about this distortion. However, both forms introduce artefacts that are absent in the actual momentum-space wavefunction. Furthermore, elliptically polarised fields lead to larger distortions in comparison to two-colour orthogonally polarised fields. These features are investigated in detail for O2, whose highest occupied molecular orbital provides two orthogonal nodal planes. Lastly we investigate temporal interference in direct ATI momentum distribution maps, employing linear and orthogonally polarised fields. We identify a type of intra-cycle interference that is often overlooked in other studies and using an orthogonally polarised field we show that the momentum distributions for individual trajectories separate. This reduces the overlap between the two distributions leading to the reduction of intra-cycle interference.