  The pressure-induced color change in the nitrogen-doped lutetium hydride has
triggered extensive discussions about the underlying physics. Here, we study
the optical response of LuH$_{2 \pm x}$N$_{y}$ in a broad frequency range at
ambient pressure and its evolution with pressure in the visible spectral range.
The broad-band optical spectra at ambient pressure reveal a Drude component
associated with intra-band electronic transitions and two Lorentz components
(L1 and L2) arising from inter-band electronic transitions. The application of
pressure causes a spectral weight transfer from L1 to the Drude component,
leading to a blue shift of the plasma edge in the reflectivity spectrum
alongside a reduction of the high-frequency reflectivity. Our results suggest
that the pressure-induced color change in LuH$_{2 \pm x}$N$_{y}$ is closely
related to the transformation between intra- and inter-band electronic
transitions, providing new insights into the mechanism of the pressure-induced
color change in LuH$_{2 \pm x}$N$_{y}$.
