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 P_z increases as the square of the electric field strength whereas the transverse momentum p_t rises only linearly. The longitudinal momentum is always in the forward direction (P_Z > 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

© 1989 Optical Society of America