Plane waves individual photons

The photon can sometimes be considered as a plane wave, but some experiments also indicate that it can behave like a bullet. In investigations on interference patterns created by individual photons on a screen [21], the impinging photons produce dot-like marks on the latter, such as those made by needle-shaped objects. 

At this point it is appropriate to return to the general wave and particle concepts of light. To be more specific, we can ask whether an individual photon can be treated both as a plane wave and as a particle, and whether a broad light beam can be considered both as a stream of individual photon particles and as a plane wave. For a closer examination of these questions it becomes necessary to investigate every particular case with respect to the following points ... 

In many cases the photon can be represented by the two alternative models of a plane wave and a particle-like wavepacket. This should also apply to interference phenomena with individual photons [21]. For a given point at the screen of an experiment with two apertures, the resulting interference pattern obtained from individual photon impacts could thus be interpreted in two alternative ways ... 

These questions appear to be understandable in terms of both photon models. The wavepacket axisymmetric model has, however, an advantage of being more reconcilable with the dot-shaped marks finally formed by an individual photon impact on the screen of an interference experiment. If the photon would have been a plane wave just before the impact, it would then have to convert itself during the flight into a wavepacket of small radial dimensions, and this becomes a less understandable behavior from a simple physical point of view. Then it is also difficult to conceive how a single photon with angular momentum (spin) could be a plane wave, without spin and with the energy hv spread over an infinite volume. Moreover, with the plane-wave concept, each individual photon would be expected to create a continuous but weak interference pattern that is spread all over the screen, and not a pattern of dot-shaped impacts. 

An individual axisymmetric photon wavepacket that propagates in vacuo and meets a mirror surface, should be reflected in the same way as a plane wave, on account of the matching of the electromagnetic field components at the surface. Inside a material with a refraction index greater than that in vacuo, the transmission of the wavepacket is affected by interaction with atoms and molecules, in a way that is outside the scope of the discussion here. 

The condition 0 plane wave, because the basic equations do not permit axisymmetric individual photon wavepacket solutions to exist in such a case. 

The initial conditions of the source can contribute to the character of the emitted electromagnetic radiation. Thus emission from excited atoms occurs in the form of individual photon wavepackets and can give rise to particle-like photon beams under appropriate conditions. Electromagnetic radiation that is excited by the current system of a macroscopic antenna is, on the other hand, expected to produce nearly plane waves at large distances from the source. 

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