The title of this chapter is really a misnomer, for the word “laser” should properly be replaced by “electromagnetic plane wave” (epw); but we ask the reader's indulgence for this simple idealization, which is reasonable as long as the perpendicular dimensions of the laser beams under question, henceforth called the “width”, are much larger than the dimensions of the charged particle on which they are acting, or than the transverse distances over which the particle is to move. The latter condition, in particular, is not always satisfied, and provides a limit of applicability of the idealization, as in the first Section, below. Certainly, for the case of charged-pair production in the overlap region of volume D3 of two perpendicularly-oriented laser beams, each of width D, one expects this idealization to be reasonable as long as D > u0ƛc, where ƛc denotes the Compton wavelength of each of the produced particles, and u0 ~ 102 sets the scale for distances over which coherent absorption of the laser photons can take place.

Classical charged-particle propagation in a laser (epw) field

This problem can be and has been solved in several ways; and its solution is worth discussing here, before quantum-mechanical treatments are begun, in order to provide a simple example of the utility of OEs, and to set the stage for what may occur after a pair is torn from the vacuum in the region of intersection of two intense lasers.