Despite strong experimental and theoretical evidence supporting superresolution imaging based on microlenses, the imaging mechanisms involved are not well understood. Based on the transformation optics approach, we demonstrate that a microlens may act as a two-dimensional fish-eye or an inverted Eaton lens. An asymmetric inverted Eaton lens may exhibit considerable image magnification, which has been confirmed experimentally.

One of the most important goals of condensed matter physics is materials by design, i.e. the ability to reliably predict and design materials with a set of desired properties. A striking example is the deterministic enhancement of the superconducting properties of materials. Recent experiments have demonstrated that the metamaterial approach is capable of achieving this goal, such as tripling the critical temperature T_C in Al-Al₂O₃ epsilon near zero (ENZ) core-shell metamaterial superconductors. Here, we demonstrate that an Al/Al₂O₃ hyperbolic metamaterial geometry is capable of a similar T_C enhancement, while having superior transport and magnetic properties compared to the core-shell metamaterial superconductors.

It is well known that extraordinary photons in hyperbolic metamaterials may be described as living in an effective Minkowski spacetime, which is defined by the peculiar form of the strongly anisotropic dielectric tensor in these metamaterials. Here, we demonstrate that within the scope of this approximation, the sound waves in hyperbolic metamaterials look similar to gravitational waves, and therefore the quantized sound waves (phonons) look similar to gravitons. Such an analogue model of quantum gravity looks especially interesting near the phase transitions in hyperbolic metamaterials where it becomes possible to switch quantum gravity effects on and off as a function of metamaterial temperature. We also predict strong enhancement of sonoluminescence in ferrofluid-based hyperbolic metamaterials, which looks analogous to particle creation in strong gravitational fields.