  We study theoretically a dramatic enhancement of spontaneous emission in
metamaterials with the hyperbolic dispersion modeled as a cubic lattice of
anisotropic resonant dipoles. We analyze the dependence of the Purcell factor
on the source position in the lattice unit cell and demonstrate that the
optimal emitter position to achieve large Purcell factors and Lamb shifts are
in the local field maxima. We show that the calculated Green function has a
characteristic cross-like shape, spatially modulated due to structure
discreteness. Our basic microscopic theory provides fundamental insights into
the rapidly developing field of hyperbolic metamaterials.
