Decades ago, before optical orbital angular momentum (OAM) was related to Laguerre-Gaussian modes, J.A. Arnaud studied the degenerate optical cavities in theory, which are usable in active imaging, spatial scanning of lasers. However, the study in experiment is limited by the critical requirements in the alignment of a degenerate cavity in a long period. Then, in 1992, L. Allen et al found that laser lights with a Laguerre-Gaussian amplitude distribution have well-defined OAMs. Since then OAMs have been treated as a new resource besides polarizations and frequencies in optics, and attracted great attentions from researchers. Recently, a proposal on quantum simulation was proposed, in which OAMs were treated as lattice sites to simulate two-dimensional topological physics and degenerate cavities supporting many Laguerre-Gaussian modes are needed. My work is to explore the possibility to carry it out in experiment.