Chapter 2 - Structured light

Abstract

The type of structured light focused on in this chapter is the one associated with twisted light, or optical vortices. We briefly outline the standard formalism of the optical angular momentum, emphasizing the formal division into spin angular momentum (SAM) and orbital angular momentum (OAM). The discrete integer nature of the winding number ℓ, associated with the optical vortex, suggests using the OAM property as a platform for implementing a high dimensional generalization of the two-bit quantum states associated with SAM. The key point is that the higher degrees of freedom afforded by the OAM enhance the capacity for optical information transfer. We consider, in general terms, the OAM of optical vortex beams and the chirality and helicity densities of such light beams and seek to highlight the main features of the most widely discussed vortex beams, namely Bessel beams, and Laguerre-Gaussian beams. For the latter we broaden the discussion to include the non-paraxial regime, before dealing with the paraxial regime as a limit of the non-paraxial theory. We explore in detail how OAM and optical spin combine in the case of multiple beams to generate novel polarization gradients. We focus only on the two-beam cases which include co-propagating and counter-propagating configurations and couple those with different types of polarization arrangements, namely circular polarizations, the case of orthogonal linear polarizations and the case of two beams with polarization vectors inclined at angle γ. We also discuss the case of bi-chromatic beams, differing slightly in frequency and when the focal planes of the beams are shifted, thus creating novel interference patterns in the region between the focal planes.