Abstract
The coherent reflectivity of a dense, relativistic, ultra-thin electron layer is derived analytically for an obliquely incident probe beam. Results are obtained by two-fold Lorentz transformation. For the analytical treatment, a plane uniform electron layer is considered. All electrons move with uniform velocity under an angle to the normal direction of the plane; such electron motion corresponds to laser acceleration by direct action of the laser fields, as it is described in a companion paper [Eur. Phys. J. D 55, 433 (2009)]. Electron density is chosen high enough to ensure that many electrons reside in a volume λR 3, where λR is the wavelength of the reflected light in the rest frame of the layer. Under these conditions, the probe light is back-scattered coherently and is directed close to the layer normal rather than the direction of electron velocity. An important consequence is that the Doppler shift is governed by γx=(1-(Vx/c)2)-1/2 derived from the electron velocity component Vx in normal direction rather than the full γ-factor of the layer electrons.
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Wu, HC., Meyer-ter-Vehn, J. The reflectivity of relativistic ultra-thin electron layers. Eur. Phys. J. D 55, 443–449 (2009). https://doi.org/10.1140/epjd/e2009-00082-0
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DOI: https://doi.org/10.1140/epjd/e2009-00082-0