Wavepackets individual photons

Such a wavepacket configuration could provide a model for the individual photon [19]. 

The needle-shaped wavepacket solutions of the individual photon model, which agree at least sometimes with the dot-shaped marks on a screen in interference experiments... 

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. 

A light beam is now being considered that consists of a stream of individual axisymmetric photon wavepackets of narrow linewidth and where the macroscopic breadth of the beam is much larger than the individual photon radius r of Eq. (173). The volume density of the wavepackets is assumed to be uniform in space. Then the mean distance between the centra of the wavepackets becomes... 

The case of transverse field overlapping is far more complicated than that of longitudinal overlapping. According to the previous analysis, the field energy is limited mainly within a well-defined radius r. As long as the ratio 0 exceeds the critical value 0 c, the photon wavepackets of the beam will not overlap and will have hardly any mutual interaction. The beam then behaves as a stream of individual photon particles, that is, when representing each photon as an axisymmetric wavepacket. 

If the individual wavepacket solutions of the present theory could be superimposed, this would imply that the field vectors become multivalued at every point inside the photon beam. The individual photon fields would then have to cancel each other. This implies that the axisymmetric small-scale wavepacket solution of Section VII does not apply and cannot satisfy the basic Eqs. (l)-(8) in the case of a nearly plane (one-dimensional) and broad photon-dense beam configuration. 

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. 

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. 

In analogy with Eq. (191) there is also a ratio of the mean longitudinal separation distance between two photon wavepackets situated on a common axis and the individual wavepacket length 2zo, as given by... 

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