Snell's Law and Refraction of Electron World Lines by Intense Laser Fields

Abstract

The dynamics of an electron driven by arbitrary plane wave laser radiation is formulated as a relativistically and mathematically exact refraction process based on an exact index of refraction. This reformulation leads to that index as an indicator of the energy transfer between the electron and the radiation. It also leads to the dynamics of the electron as being governed (i) by the Lorentzian version of what in Euclidean space is Snell's law, (ii) by an eikonal equation with the corresponding index of refraction, (iii) by geodesics on a spacetime manifold with in-general non-zero curvature ("geometrization of the laser radiation"), (iv) by the spacetime version of Fermat's principle of least time, (v) by a Lorentzian stability criterion for the circumstance which in Euclidean space corresponds to the propagation of rays passing through a periodic wave guide of lenses which all have the same focal length. That criterion demands that the laser intensity satisfy $I_{aver}<.56 x (10,000 $angstrom / lambda$)^2 x 10^{18}$watts/cm^2$.