Quantum features in the orthogonality of optical modes for structured and plane-wave light

A fundamental photon creation–annihilation commutation relation underpins the familiar quantum formulation of optics. However, an internal inconsistency becomes apparent in the pursuit of structured light applications. This requires the relationship between operator commutation and mode orthogonality to be recast in a form ensuring full consistency with the precepts of quantum theory. A suitable reformulation, shown to register correctly an intrinsic quantum uncertainty in the associated interactions, has special relevance to optical vortex physics—particularly with regard to information content—through its connection to the degrees of freedom in the associated radiation modes.