Enhancement cavities where a beam of large size (several millimeters) can resonate have several applications, in particular in atomic physics. However, reaching large beam waists in a compact geometry (less than a meter long) typically brings the resonator close to the degeneracy limit. Here we experimentally study a degenerate optical cavity, 44-cm long and consisting of two flat mirrors placed in the focal planes of a lens, in a regime of intermediate finesse ($sim 150$). We study the impact of the longitudinal misalignement on the optical gain, for different input beam waists up to 5.6~mm, and find data consistent with the prediction of a model based on ABCD propagation of Gaussian beams. We reach an optical gain of 26 for a waist of 1.4~mm, which can have an impact on several applications, in particular atom interferometry. We numerically investigate the optical gain reduction for large beam waists using the angular spectrum method to consider the effects of optical aberrations, which play an important role in such a degenerate cavity. Our calculations quantitatively reproduce the experimental data and will provide a key tool for designing enhancement cavities close to the degeneracy limit. As an illustration, we discuss the application of this resonator geometry to the enhancement of laser beams with top-hat intensity profiles.
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