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