A quantum electrodynamical approach to nonlinear and structured light interactions with matter

This thesis employs molecular quantum electrodynamical theory to analyse the interactions between light and matter for four main processes. The first to be considered is Raman scattering, where the effect of the electrodynamic environment for the centre of spectroscopic interest is considered. This is achieved by engaging a retarded dipole-dipole interaction between the centre and a neighbouring molecule. Physically, this is explained by a virtual photon between the pair of centres. The results predict characteristic new lines on the Raman spectrum, for the species, arising from the engagement of selection rules not limited to those of a two-photon process. The second process, is hyper-Rayleigh scattering, in which a single multipolar coupling is considered in place of the more familiar electric dipole. This modification to the theory subverts the standard selection rules for a three-photon process, which can allow for second-harmonic emission to be generated by a centre of high symmetry, such as a centrosymmetric molecule. The third process offers another means of subverting the standard selection rules for second-harmonic generation, namely by incorporating six-wave mixing. First, the general mechanism is developed and pertinent results are expressed for the widely-deployed depolarisation ratio. Following this, structured light is considered and by utilising orbital angular momentum (OAM) conservation arguments, the pair of harmonic photons are found to display quantum entanglement. Moreover, the relative magnitudes of the possible emissions are found to correspond directly to that of the binomial coefficients. This thesis concludes with a family of novel structures capable of directly generating OAM light. This work exploits symmetry characteristics for a delocalised excitonic structure that can allow for a more complex multipolar emission than that of any isolated centres. The phase of the exciton is shown to display an azimuthal phase progression, a vortex feature most commonly associated with Laguerre-Gaussian light.