  Our conventional understanding of optical responses in metals has been based
on the Drude theory. In recent years, however, it has become possible to
prepare ultrapure metallic samples where the electron-electron scattering
becomes the most dominant process governing transport and thus the Drude
theory, where momentum-relaxing scatterings such as electron-impurity
scattering are assumed to be dominant, is no longer valid. This regime is
called the hydrodynamic regime and described by an emergent hydrodynamic
theory. Here, we develop a basic framework of optical responses in the
hydrodynamic regime. Based on the hydrodynamic equation, we reveal the
existence of a ``hydrodynamic mode'' resulting from the viscosity effect and
compute the reflectance and the transmittance in three-dimensional electron
fluids. Our theory also describes how to probe the hydrodynamic effects and
measure the viscosity through simple optical techniques.
