Relativistic Dynamics of Photoelectrons*

Abstract

The relativistic dynamics of single electrons in plane-wave electromagnetic fields can be solved exactly, for arbitrary pulse shapes, in both classical and quantum mechanics. Sarachik and Schappert1 (S-S) provided a particularly lucid account of the classical theory, assuming that the electron is at rest before the pulse arrives, and showed that in the relativistic limit the longitudinal component of momentum Pz increases as the square of the electric field strength whereas the transverse momentum pt rises only linearly. The longitudinal momentum is always in the forward direction (PZ > 0) and it oscillates at double the laser frequency. The non-linearities in the relativistic motion lead to the production of high-order harmonics, which become focussed more strongly as the laser intensity is increased. The solution with more general initial conditions was given by Kruger and Bovyn.2