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arXiv · 1705.08554

On beam models and their paraxial approximation

W. J. Waters·B. King
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Abstract

We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.

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W. J. Waters, B. King. 2017-05-23. On beam models and their paraxial approximation. https://doi.org/10.1088/1555-6611%2Faa94dc

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