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Polaronic features similar to those previously observed in the photoinducedspectra of cuprates have been detected in the reflectivity spectra ofchemically doped parent compounds of high-critical-temperature superconductors,both $n$-type and $p$-type. In Nd$_2$CuO$_{4-y}$ these features, whoseintensities depend both on doping and temperature, include local vibrationalmodes in the far infrared and a broad band centered at $\sim$ 1000 cm$^{-1}$.The latter band is produced by the overtones of two (or three) local modes andis well described in terms of a small-polaron model, with a binding energy ofabout 500 cm$^{-1}$. Most of the above infrared features are shown to survivein the metallic phase of Nd$_{2-x}$Ce$_x$Cu0$_{4-y}$, Bi$_2$Sr$_2$CuO$_6$, andYBa$_2$Cu$_3$O$_{7-y}$, where they appear as extra-Drude peaks. The occurrenceof polarons is attributed to local modes strongly coupled to carriers, as shownby a comparison with tunneling results.Comment: File latex, 31 p., submitted to Physical Review B. Figures may be  faxed upon reques

Polaronic optical absorption in electron-doped and hole-doped cuprates