some time ago, I tried to find an answer to this same question in the literature, and I didn't succeed. My impression is:
There is no solution in the framework of classical electrodynamics. There are equations for beams but beams have a focus, and widen beyond this focus; there are equations for "electromagnetic missiles", which remain relatively unchanged for many wavelengths but they require a source of large extend, and consist necessarily of many photons. And more than a century ago, there were bold propositions like J.J. Thomson's donut shaped photons which unfortunately do not comply to the Maxwell equations in the accepted form.
The worst thing is: Even if someone would find a wave equation (perhaps J.J. Thomson was right, and the Maxwell equations are to be extended?), how could it be verified? Due to the quantum nature of single photons, any kind of measuring device will either get a full hit by a photon or a full miss; so, we cannot "have a look" at the periphery of a photon.
One can model the wave in the immediate surrounding of the hit successfully by a plane or a spherical wave, completely neglecting the continuation of this wave. Before this background, the opinion is understandable that we can know what happens at the source and what happens at the sink but any claims on the behavior of the photon in the intervening space are pure fiction.
But perhaps a colleague has a wave function up his/her sleeve? :-)
As long as both source and sink share the same rest frame, and gravitation can be neglected, each photon has a certain wavelength (within a very narrow band) /momentum/energy at the source, and the same at the sink; but the phase is not fixed.
Because both the longitudinal and the transversal size of the volume "occupied" by a single photon seems to be much larger than its wavelength, we are entitled to imagine it as a wave packet.