Optical reflectivity spectra of single-crystal ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{2\mathit{n}+4+\mathit{x}}$ (n=1 and 2)

The optical reflectivity spectra of the single-crystal Bi-based cuprates, ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{x}}$ and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CuO}}_{6+\mathrm{x}}$, were measured in a wide energy range from 0.05 to 40 eV, and analyzed through the Kramers-Kronig relation. The obtained spectra are different from other superconducting cuprates, such as (La,Sr${)}_2$ ${\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathrm{x}}$, which might be ascribed to the existence of the characteristic ${\mathrm{Bi}}_2$ ${\mathrm{O}}_2$ layer. The optical excitations within ${\mathrm{Bi}}_2$ ${\mathrm{O}}_2$ layer start from 2 eV or higher energy, so it is unlikely that the electrons in the ${\mathrm{Bi}}_2$ ${\mathrm{O}}_2$ layer contribute to low-energy excitation or dc conduction in this family of high-$T_c$ superconductors.