Konrad Altmann
LAS-CAD GmbH, Germany
Title: Embedding the photon with its relativistic mass as a particle into the electromagnetic wave explains the Gouy phase shift as an energetic effect
Biography
Biography: Konrad Altmann
Abstract
A new aspect concerning the relationship between a photon and electromagnetic wave has been developed by considering the question why the energy and the mass density of an electromagnetic wave described by m=E/c² are propagating in the same direction. For instance, in optical resonators, the energy density usually propagates along curved lines. However, according to Newton's first law the mass density should propagate along a straight line if no force is exerted it. In order to solve this problem, which represents a contradiction between fundamental physical laws, the assumption has been made that a transverse force is exerted on the mass density and in consequence on the mass of the photons forcing them to follow the propagating energy density. This force has been computed by considering the infi nitesimal change of the normalized Poynting vector with respect to an infi nitesimal propagation step. Integration of the negative value of this force along the curvature of the phase front shows that the photon is moving within a transverse potential. Th is potential allows describing the transverse quantum mechanical motion of the photon by the use of a Schrodinger equation which is identical with the Schrodinger equation describing the motion of the electron, except that the mass of the electron is replaced by the relativistic mass of the photon. In this way, it could for the first time be shown that the Schrödinger equation is also describing the motion of a particle which has no rest mass. The eigensolutions χnm(x,y,z) of this Schrodinger equation allow to compute the probability density |χnm(x,y,z)|² of the photons propagating with an electromagnetic wave. Th e obtained results have been verifi ed for the case of the plane, the spherical and the Gaussian wave. In case of a Gaussian wave it could be shown that the probability density |χnm(x,y,z)|² )|² of the photon computed in this way is in full agreement with the normalized local intensity provided by paraxial wave optics for a Gaussian mode of order n,m. Also, the Guoy phase shift could be computed by the use of this particle picture in full agreement with the result obtained by the use of wave optics. Moreover, this particle picture allows explaining the Guoy phase shift , which so far has only been considered as a phase shift without any further physical meaning, as an energetic eff ect. It could be shown that due to the Gouy eff ect the axial energy of the photon is reduced with the consequence that the total energy of the photon turns out to be the sum of this reduced axial energy and the energy of the transverse quantum mechanical motion of the photon as obtained as energy eigen solution of the Schrodinger equation.