Abstract: Since the presence of a out coupling hole alters the transverse structure of the intra cavity light in a FEL oscillator,the finite element method is used to the optical field equations and a good proximation is made for the out-coupling process in the mirror,and then some numerical results are given.It is shown that the features of the transverse structure of the intra-cavity field are well described and the numerical results are significantly improved.

Key words: hole-coupling, FEL oscillator, finite element method