Ultimate resolution of indefinite metamaterial flat lenses

We propose an approach allowing a systematic optimization of lenses based on hyperbolic metamaterials. The lensing properties of these highly anisotropic materials are summed up in a complex effective index extracted from the complex dispersion relation. The analytical expression of this effective index in the homogenization regime or its direct computation from the Bloch band diagram in the resonant regime leads to hyperbolic metamaterials that outperform the state-of-art flat lenses. We show that feasible metal-dielectric multilayers provide superresolved images for visible light (around 400 nm) even when fully taking absorption into account.