Chapter 3 - Quantum features of structured light

Abstract

The development of structured light affords new opportunities to exploit the spatial degrees of freedom for beams with wave-vector components transverse to the direction of propagation. This introduces an additional dimension to the information-conveying capacity of individual photons. However, several quantum issues of optical vortex interactions with detectors demand scrutiny. For any essentially paraxial vortex beam, while the spin and orbital parts of photon angular momentum are well defined, the corresponding quantum operators do not satisfy the proper commutation structure; for non-paraxial fields they are not even separable. In the local measurement of any such property of individual photons it is also important to recognize that absolute measurement is fundamentally compromised by the preclusion of a position operator, as is true for any relativistic quantum particle. Quantum uncertainty itself obviates the precise positional registration of any particular orbital angular momentum through any angle-specific aperture. Optical modes with marginally different directions of propagation cannot be discriminated with arbitrary precision: conservation of the summed orbital angular momentum, comprising a sum of optical and material elements, can only be ascertained in terms of expectation values. The orthogonality of optical states of a given beam wavelength and direction, but with different orbital angular momentum values, certainly affords extensive opportunities for quantum communication: the enhanced encoding of information per photon in a high-dimensionality transverse structure is, however, subject to both fundamental quantum and technical constraints.