Optical beam bending and focusing in free-electron oscillators

As the bunched electron beam in the wiggler of an FEL oscillates from side to side, it generates a new optical field. This new field is coherent with the old field that entered the wiggler and bears a phase relationship to that field depending upon many variables. If the new field is in phase with the old, optical gain occurs. If it is 90 deg out of phase, the combined fields have a phase shift that represents retardation, that is,a real positive index of refraction. This phase shift generally does not occur uniformly over the cross section of the optical beam, but is concentrated in the center for an aligned system or to one side for a misaligned system. The former case leads to optical beam focusing, the latter to beam bending along with the focusing. An FEL oscillator can be a particularly sensitive arrangement for observing focusing and bending because of the abrupt termination of the macropulse of electrons. This termination triggers a transverse oscillation of the optical pulse that is trapped in the cavity around its equilibrium position. The amplitude of the oscillation can be large. During the Los Alamos oscillator experiment, the bending phenomenon was observed. In this paper we present the results of these observations, a discussion of different models that might be used to explain them, and comparison of the measurements with crude calculations using a final model.