  We investigate the effects of hydrodynamic nonlocal response in hyperbolic
metamaterials (HMMs), focusing on the experimentally realizable parameter
regime where unit cells are much smaller than an optical wavelength but much
larger than the wavelengths of the longitudinal pressure waves of the
free-electron plasma in the metal constituents. We derive the nonlocal
corrections to the effective material parameters analytically, and illustrate
the noticeable nonlocal effects on the dispersion curves numerically. As an
application, we find that the focusing characteristics of a HMM lens in the
local-response approximation and in the hydrodynamic Drude model can differ
considerably. Interestingly, sometimes the nonlocal theory predicts
significantly better focusing. Thus, to detect whether nonlocal response is at
work in a hyperbolic metamaterial, we propose to measure the near-field
distribution of a hyperbolic metamaterial lens.
