  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}$watts/cm^2$.
