  The optical conductivity (OC) of cuprates is studied theoretically in the low
density limit of the t-t'-J-Holstein model. By developing a limited phonon
basis exact diagonalization (LPBED) method capable of treating the lattice of
largest size 4x4 ever considered, we are able to discern fine features of the
mid-infrared (MIR) part of the OC revealing three-peak structure. The two
lowest peaks are observed in experiments and the highest one is tacitly
resolved in moderately doped cuprates. Comparison of OC with the results of
semianalytic approaches and detailed analysis of the calculated isotope effect
indicate that the middle-energy MIR peak is of mostly magnetic origin while the
lowest MIR band originates from the scattering of holes by phonons.
