Exact Classical and Quantum Dynamics in Background Electromagnetic Fields

Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focusing of intense laser fields implies a need to go beyond the plane wave model. By exploiting Poincaré symmetry and superintegrability we show how to construct, and solve without approximation, new models of laser-matter interactions. We illustrate the method with a model of a radially polarized (TM) laser beam, for which we exactly determine the classical orbits and quantum wave functions. Including in this way the effects of transverse field structure should improve predictions and analyses for experiments at intense laser facilities.

Figure 1

Upper left: The transverse and longitudinal electric field profiles (16). Upper right: Density and vector field plot of the transverse fields at fixed $x^{+}$. Lower panel: Electron trajectories at $\gamma =-1/2$. A circular distribution of electrons in the transverse plane, initially at rest when the fields vanish, is drawn toward the symmetry ($z$) axis and focused to a single point as time evolves. The electrons are expelled from this point as the fields switch off.