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RELATIVISTIC BATEMAN-HILLION SOLUTIONS FOR THE ELECTROMAGNETIC 4-POTENTIAL IN HERMITE-GAUSSIAN BEAMS

By R. Ducharme

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Abstract:
The electromagnetic field equations are solved to give the 4-potential in Hermite-Gaussian beams as a function of both the 4-positions of the beam waist and each point in the field. These solutions are the sums of products of position-dependent complex 4-vectors and modified Bateman-Hillion functions. It is assumed that the time difference between the beam waist and each other point is equal to the distance between the points divided by the speed of light. This method is shown to generate solutions that preserve their forms under Lorentz transformations that also correspond to the well known paraxial solutions for the case of nearly parallel beams.

Citation:
R. Ducharme, "Relativistic Bateman-Hillion Solutions for the Electromagnetic 4-Potential in Hermite-Gaussian Beams," Progress In Electromagnetics Research M, Vol. 42, 39-47, 2015.
doi:10.2528/PIERM15030104

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