  Extended Drude model formalism has been successfully utilized for analyzing
optical spectra of strongly correlated electron systems including heavy-fermion
systems and high-$T_c$ superconducting iron pnictides and cuprates.
Furthermore, generalized Allen's formulas has been developed and applied to
extract the electron-boson spectral density function from measured optical data
of high temperature superconductors including cuprates in various material
phases. Here we used a reverse process to obtain various optical quantities
starting from two typical electron-boson spectral density model functions for
three intriguing (normal, pseudogap, and $d$-wave superconducting) material
phases in cuprates. We also assigned the calculated optical results to
designated regions in the phase diagram of hole-doped cuprates and compared
them with the corresponding measured optical spectra of
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). This comparison suggested that
this way of optical data analysis can be a convincing method to study
correlated electrons in the copper oxide superconductors and other
superconducting systems as well.
