In the paper “Embedding the photon with its relativistic mass as a particle into the electromagnetic wave” [Opt. Express 26, 1375 (2018). [CrossRef] [PubMed] ], it has been shown that the problem why the energy and the mass density of an electromagnetic wave are propagating in the same direction can be solved by the assumption that a transverse force is exerted on the photons. This leads to the result that the photon is moving within a transverse potential, which allows the description of the transverse quantum mechanical motion of the photon by a Schrödinger equation. These results are used to show that, in the case of a Gaussian wave, the effective axial propagation constant can be expressed as , where Eph is the total energy of the photon and Enm(z) are the energy eigenvalues of the transverse quantum mechanical motion of the photon. Since, according to this result, represents a real energy, it has also been concluded that the effective axial propagation constant represents a real propagation constant. This leads to the conclusion that represents the real local wave length of the photon at the position z. According to this conclusion, λnm(z) increases inversely proportionally to the energy difference Eph-Enm(z), which decreases with decreasing z, and therefore describes the Gouy phase shift in agreement with wave optics. This shows that the deeper physical reason for Gouy phase shift consists in the fact that the energy of the photon is increasingly converted into its transverse quantum mechanical motion when the photon approaches the focus. This explains the Gouy phase shift as an energetic effect.
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