We compute optical galaxy luminosity functions (GLFs) in the B, V, R, and I rest-frame bands for one of the largest medium-to-high-redshift (0.4 < z < 0.9) cluster samples to date in order to probe the abundance of faint galaxies in clusters. We also study how the GLFs depend on cluster redshift, mass, and substructure, and compare the GLFs of clusters with those of the field. We separately investigate the GLFs of blue and red-sequence (RS) galaxies to understand the evolution of different cluster populations. We find that the shapes of our GLFs are similar for the B, V, R, and I bands with a drop at the red GLF faint end that is more pronounced at high-redshift: alpha(red) ~ -0.5 at 0.40 < z < 0.65 and alpha(red) > 0.1 at 0.65 < z < 0.90. The blue GLFs have a steeper faint end (alpha(blue) ~ -1.6) than the red GLFs, that appears to be independent of redshift. For the full cluster sample, blue and red GLFs intersect at M(V) = -20, M(R) = -20.5, and M(I) = -20.3. A study of how galaxy types evolve with redshift shows that late type galaxies appear to become early types between z ~ 0.9 and today. Finally, the faint ends of the red GLFs of more massive clusters appear to be richer than less massive clusters, which is more typical of the lower redshift behaviour. Our results indicate that our clusters form at redshifts higher than z = 0.9 from galaxy structures that already have an established red sequence. Late type galaxies then appear to evolve into early types, enriching the red-sequence between this redshift and today. This effect is consistent with the evolution of the faint end slope of the red-sequence and the galaxy type evolution that we find. Finally, faint galaxies accreted from the field environment at all redshifts might have replaced the blue late type galaxies that converted into early types, explaining the lack of evolution in the faint end slopes of the blue GLFs.
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