Eur. Phys. J. D 55, 443-449 (2009)
https://doi.org/10.1140/epjd/e2009-00082-0

The reflectivity of relativistic ultra-thin electron layers

Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany

Received: 28 November 2008
Revised: 28 January 2009
Published online: 19 March 2009

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 λ_R³, where λ_R 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 γ_x=(1-(V_x/c)²)^-1/2 derived from the electron velocity component V_x in normal direction rather than the full γ-factor of the layer electrons.