Polaron contribution to the infrared optical response of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4+\mathrm{\delta }}$ and ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{NiO}}_{4+\mathrm{\delta }}$

The anomalous midinfrared absorption band in the optical conductivity of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4+\mathrm{\delta }}$ and ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{NiO}}_{4+\mathrm{\delta }}$ is interpreted in terms of photon-assisted hopping of small polarons. An analysis of the normal-state single crystal a-b plane data indicates that polarons in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{NiO}}_{4+\mathrm{\delta }}$ are small, whereas in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4+\mathrm{\delta }}$ the polarons are larger. The absence of bulk superconductivity in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{NiO}}_{4+\mathrm{\delta }}$ may be linked with smaller polaron size.