It was recently shown theoretically that the time-dependent heat conduction equation is form invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped onto (meta)materials with spatially inhomogeneous and anisotropic heat-conductivity tensors in the laboratory space. On this basis, we design, fabricate, and characterize a microstructured thermal cloak that molds the flow of heat around an object in a metal plate. This allows for transient protection of the object from heating while maintaining the same downstream heat flow as without object and cloak.

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Metamaterial-based cloaks make objects different from their surrounding appear just like their surrounding. To date, cloaking has been demonstrated experimentally in many fields of research, including electrodynamics at microwave frequencies, optics, static electric conduction, acoustics, fluid dynamics, thermodynamics and quasi two-dimensional solid mechanics. However, cloaking in the seemingly simple case of three-dimensional solid mechanics is more demanding. Here, inspired by invisible core-shell nanoparticles in optics, we design an approximate elasto-mechanical core-shell 'unfeelability' cloak based on pentamode metamaterials. The resulting three-dimensional polymer microstructures with macroscopic overall volume are fabricated by rapid dip-in direct laser writing optical lithography. We quasi-statically deform cloak and control samples in the linear regime and map the displacement fields by autocorrelation-based analysis of recorded movies. The measured and the calculated displacement fields show very good cloaking performance. This means that one can elastically hide objects along these lines.

In vacuum, air, and other surroundings that support ballistic light propagation according to Maxwell's equations, invisibility cloaks that are macroscopic, three-dimensional, broadband, passive, and that work for all directions and polarizations of light are not consistent with the laws of physics. We show that the situation is different for surroundings leading to multiple light scattering, according to Fick's diffusion equation. We have fabricated cylindrical and spherical invisibility cloaks made of thin shells of polydimethylsiloxane doped with melamine-resin microparticles. The shells surround a diffusively reflecting hollow core, in which arbitrary objects can be hidden. We find good cloaking performance in a water-based diffusive surrounding throughout the entire visible spectrum and for all illumination conditions and incident polarizations of light.