We present the first wide-band (5–400 cm −1) measurements of the dynamical conductivity and the dielectric permittivity spectra of La 2− x Sr x CuO 4 ( x ≈ 0.16). A narrow Drude-like band is observed in the spectra, which is consistent with a d-wave pairing state. We determine the plasma frequency, scattering rate, and mean free path of the unpaired charge carriers responsible for this band. For the first time, “coherence peak”-like behavior is observed in the temperature dependence of the submillimeter conductivity of La 2− x Sr x CuO 4, associated with the temperature evolution of the band in the superconducting state.