On the Angular Momentum of Light

The idea is now well established that light possesses angular momentum and that this comes in two distinct forms, namely spin and orbital angular momentum which are associated with circular polarisation and helical phase fronts respectively. In this thesis, we explain that this is, in fact, a mere glimpse of a much larger picture: light possesses an infinite number of distinct angular momenta, the conservation of which in the strict absence of charge reflects the myriad rotational symmetries then inherent to Maxwell's equations. We recognise, moreover, that many of these angular momenta can be identified explicitly in light-matter interactions, which leads us in particular to identify new possibilities for the use of light to probe and manipulate chiral molecules.