Optical Study of the ${\mathrm{Sr}}_{14-\mathit{x}}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{O}_{41}$ System: Evidence for Hole-Doped ${\mathrm{Cu}}_2{O}_3$ Ladders

The optical conductivity spectrum of ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$, composed of two-leg ${\mathrm{Cu}}_2{\mathrm{O}}_3$ ladders and edge-sharing ${\mathrm{CuO}}_2$ chains, is investigated on single crystals with various compositions. Upon isovalent Ca substitution for Sr a rapid transfer of the spectral weight takes place from the high- to low-energy region, essentially in the same manner as that observed in the doped ${\mathrm{CuO}}_2$ planes of high- $T_c$ cuprates. We identify this behavior as a consequence of charge redistribution between chains and ladders, and estimate the hole density in each structural unit from the transferred spectral weight.