Vignetting effects of wiggler bores on empty modes in free-electron laser resonators.

Through the use of the Fox-Li method with the quasi-fast Hankel transform, vignetting effects of wiggler bores on empty modes in free-electron laser resonators are numerically investigated. Two typical symmetric optical cavity configurations are considered, one being near confocal (g = -0.2) and the other being near concentric (g = -0.94). Different wiggler-bore dimensions and different optical wavelengths for which vignetting is important are investigated. The vignetted field patterns, power losses, and phase shifts are computed for the two lowest-order empty modes (TEM(00) and TEM(01)). Near-field patterns in the near-confocal case are illustrated. It is found that the mode field distributions are strongly modulated at the mirror apertures in the Fresnel diffraction regime but are not modulated at the wigglerbore ends. It is shown that vignetting with an appropriate amount of misalignment is even good for improving the mode control. Finally, the calculations are applied to the Darmstadt free-electron laser.