  We have identifies the otical phonon modes of the superconducting
infinite-layer compounds Sr$_{0.9}Ln_{0.1}$CuO$_2$ ($Ln$ = La, Gd, Sm; $T_c$ =
43 K for all) from their infrared reflectivity spectra obtained with a
Fourier-transform infrared spectrometer on high-quality high-purity samples
synthesized under high pressure. The La- and the Gd-doped compounds exhibited
only four (2$A_{\rm 2u}$+2$E_{\rm u}$) out of the five (2$A_{\rm 2u}$+3$E_{\rm
u}$) infrared-active phonon modes predicted by a group theoretical analysis
whereas the Sm-doped compound exhibited all five modes. We propose the atomic
displacement pattern for each phonon mode based on reported lattice dynamics
calculations and through comparison with the phonon modes of other single-layer
high-$T_{\rm c}$ cuprate superconductors.
