Based on the expansion of the fundamental mode LP01 in single mode fiber in terms of Laguerre-Gaussian free space modes, the feedback coupling losses for two different types of cavity mirror, i.e., a curvature mirror and a combing mirror of a lens and a plane mirror, are numerically calculated for the first time. The results show that, for the curvature mirror, the lowest coupling loss is obtained when its curvature radius matches the wavefront curvature. In particular, if a plane mirror is used as the cavity mirror, it has to be placed close to the fiber end to obtain the low coupling loss. For the combing mirror, the lowest coupling loss can be obtained when the plane mirror is placed at the back focal plane of the lens, and the variation of the coupling loss is insensitive to the mirror positions for the lens with longer focal length. Finally, the plane mirror and the combing mirror of a lens and a plane mirror are suggested to be the cavity mirror in the practical construction of the high power fiber lasers.