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Our conventional understanding of optical responses in metals has been basedon the Drude theory. In recent years, however, it has become possible toprepare ultrapure metallic samples where the electron-electron scatteringbecomes the most dominant process governing transport and thus the Drudetheory, where momentum-relaxing scatterings such as electron-impurityscattering are assumed to be dominant, is no longer valid. This regime iscalled the hydrodynamic regime and described by an emergent hydrodynamictheory. Here, we develop a basic framework of optical responses in thehydrodynamic regime. Based on the hydrodynamic equation, we reveal theexistence of a ``hydrodynamic mode'' resulting from the viscosity effect andcompute the reflectance and the transmittance in three-dimensional electronfluids. Our theory also describes how to probe the hydrodynamic effects andmeasure the viscosity through simple optical techniques.

Nonlocal optical responses of ultrapure metals in the hydrodynamic regime