(untitled) (Communications in Computational Physics, 2006)
The transverse construction of optical modes in the wiggler is calculated and the numerical simulations of the free-electron laser hole-coupled resonator are carried out. These 3D-simulations include optical amplitude distributions, modes evolvement of optical field and the influence of hole-radius on the distributing of modes. The numerical simulations confirm that the fraction of the even-order modes increase in the start-up stage and then decreases in the exponential gain stage. Moreover, it is found that the fundamental mode is dominant in the saturate stage. Based on this observation, we estimate the optical output coupling by using the the fundamental mode. It is found that the numerical results and the first-order estimate are in good agreement for a range of the hole size.