Conceptualization of the photon for quanta of structured light

The development of optical modes with intrinsic structure has significantly redirected attention to the established concept and fundamental physics of the photon. In particular, to accommodate the modal structure of beams with transverse structure, two aspects of conventional representation invite special modification: the mathematical formulations, and figurative depictions. Reappraisals of the former highlight known deficiencies in simple plane wave mode expansions, at the price of associating the properties of individual quanta with macroscopic beam parameters wrought by the physical optics. Experimental proofs that such features do indeed reside in individual photons lead to conceptual problems, yet it is clear that alternative viewpoints engender still deeper difficulties. Such quandaries are also evident in the variety of diagrammatic representations used for structured radiation. Though such depictions cannot ever adequately represent the quantum physics, their incautious use can become seriously misleading, misrepresenting the underlying mathematics and supporting wrong conclusions. This analysis aims to expose and underscore some issues that invite closer attention.