Warm cavity modes of free-electron laser resonators with on-axis holes

The optical mode structure and gain of a free-electron laser (FEL) resonator with holes on axis in the small optical signal regime is examined using a matrix formulation. A gain matrix, describing optical mode mixing and amplitude gain in the wiggler, is derived from the FEL evolution equations. A loss matrix, describing the effect on the transverse optical mode structure of the resonator end mirrors, is derived using the method of A.G. Fox and T. Li (1960). The laser matrix is the product of the gain and loss matrices. The eigenvectors and eigenvalues of the laser matrix give the transverse optical mode profile and gain of the resonator. The resonator of the Mark III infrared FEL at Duke University and a confocal resonator, for two holes sizes are examined. The results demonstrate the possibility of output coupling through the holes of the Mark III resonator, and the possibility of using the holes of the confocal resonator for gain control