  The ab-plane optical conductivity of eleven single crystals, belonging to the
families Sr2-xCuO2Cl2, Y1-xCaxBa2Cu3O6, Bi2Sr2-xLaxCuO6, and Bi2Sr2CaCu2O8 has
been measured with hole concentrations p between 0 and 0.18, and for 6 K < T <
500 K to obtain an infrared picture of the p,T phase diagram of the Cu-O plane.
At extreme dilution (p = 0.005), a narrow peak is observed at 1570 cm-1 (195
meV), that we assign to a single-hole bound state. For increasing doping, that
peak broadens into a far-infrared (FIR) band whose low-energy edge sets the
insulating gap. The insulator-to-metal transition (IMT) occurs when the
softening of the FIR band closes the gap thus evolving into a Drude term. In
the metallic phase, a multi-band analysis identifies a mid-infrared band which
weakly depends on temperature and softens for increasing p, while the
extended-Drude analysis leads to an optical scattering rate larger than the
frequency, as found in other cuprates. The infrared spectral weight W(T) is
consistent with a Fermi liquid renormalized by strong correlations, provided
that the T^4 term of the Sommerfeld expansion is included above 300 K. In the
superconducting phase, the optical response of single-layer Bi2Sr2-xLaxCuO6 at
optimum doping is similar to that of the corresponding optimally-doped bilayer
Bi2Sr2CaCu2O8.

Superconductivity;Strongly Correlated Electrons