A quantum electrodynamics framework for the nonlinear optics of twisted beams

A theory is presented for the detailed formulation of the nonlinear optics of laser beams endowed with orbital angular momentum. Following an introductory excursion into the general principles of such twisted beams, a quantum electrodynamical formulation is developed for representing the photonics of their interaction with matter. Detailed results are given for Laguerre-Gaussian beams in the large-Rayleigh-range limit. Utilization of the theory in nonlinear optics is illustrated by application to second-harmonic generation.