  Characterization of the first ever laboratory produced metallic hydrogen
sample relies on measurements of optical spectra. Here we present
first-principles calculations of the reflectivity of hydrogen between 400 and
600 GPa in the $\mathrm{I4_1/amd}$ crystal structure, the one predicted at
these pressures, based on both time-dependent density functional and Eliashberg
theories, thus, covering the optical properties from the infrared to the
ultraviolet regimes. Our results show that atomic hydrogen displays an
interband plasmon at around 6 eV that abruptly suppresses the reflectivity,
while the large superconducting gap energy yields a sharp decrease of the
reflectivity in the infrared region approximately at 120 meV. The
experimentally estimated electronic scattering rates in the 0.7-3 eV range are
in agreement with our theoretical estimations, which show that the huge
electron-phonon interaction of the system dominates the electronic scattering
in this energy range. The remarkable features in the optical spectra predicted
here encourage to extend the existing optical measurements to the infrared and
ultraviolet regions.
