Nonlinear spectroscopy with twisted beams

The propensity of conventional optical beams to convey angular momentum is very well known. As a spin-1 elementary particle any photon can assume a polarisation state with a well defined 'spin' angular momentum of plus or minus 1 in the direction of propagation, corresponding to a circular polarisation of either left or right helicity. The mechanical effects of photonic angular momentum are manifest in a variety of phenomena operating at both the atomic and macroscopic scale. Photon angular momentum also exercises a key role in atomic spectroscopy and a host of other fundamental optical phenomena. The aim of this work is to study the interaction between matter and Laguerre-Gaussian beams, and others of related structure in which a helical wavefront confers an endowment with 'orbital' angular momentum. Although the principles and methods of production of these twisted beams are already quite well understood, the detailed study of the interactions is a novel subject. We explore changes in selection rules transfer of linear and angular momentum in the context of nonlinear processes, especially harmonic and sum-frequency generation.