Experiments on transformation thermodynamics: Molding the flow of heat

It has recently been 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 micro-structured 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.Comment: 10 pages, 4 figure

Hall-effect sign-inversion in a realizable 3D metamaterial

In 2009, Briane and Milton proved mathematically the existence of three-dimensional isotropic metamaterials with a classical Hall coefficient which is negative with respect to that of all of the metamaterial constituents. Here, we significantly simplify their blueprint towards an architecture composed of only a single constituent material in vacuum/air, which can be seen as a special type of porosity. We show that the sign of the Hall voltage is determined by a separation parameter between adjacent tori. This qualitative behavior is robust even for only a small number of metamaterial unit cells. The combination of simplification and robustness brings experimental verifications of this striking sign-inversion into reach.Comment: 9 figures, 7 page

On three-dimensional dilational elastic metamaterials

Dilational materials are stable three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and characterize crystalline metamaterials approaching this ideal. To reveal all modes, we calculate the phonon band structures. On this basis, using cubic symmetry, we can unambiguously retrieve all different non-zero elements of the rank-4 effective metamaterial elasticity tensor, from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes isotropic and approaches -1 in the limit of small internal connections. This finding is also supported by independent static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poisson's ratios as low as -0.8 in good agreement with theory. Microscopic samples are also presented.Comment: 8 figure

Phonon band structures of three-dimensional pentamode metamaterials

Three-dimensional pentamode metamaterials are artificial solids that approximately behave like liquids, which have vanishing shear modulus. Pentamodes have recently become experimental reality. Here, we calculate their phonon band structures for various parameters. Consistent with static continuum mechanics, we find that compression and shear waves exhibit phase velocities that can realistically be different by more than one order of magnitude. Interestingly, we also find frequency intervals with more than two octaves bandwidth in which pure single-mode behavior is obtained. Herein, exclusively compression waves exist due to a complete three-dimensional band gap for shear waves and, hence, no coupling to shear modes is possible. Such single-mode behavior might, e.g., be interesting for transformation-elastodynamics architectures.Comment: 5 figure

Cloaking in Heat Conduction and Light Diffusion

In free-space optics, invisibility cloaking is fundamentally limited by relativity, making passive broadband, macroscopic cloaks impossible. This thesis explores invisibility cloaking beyond ballistic optics. In the regimes of heat conduction and light diffusion, the relativity problem vanishes due to inherently slower energy transport. Macroscopic cloaks for transient heat flow and static diffusive light transport are designed, realized and experimentally characterized

Supplement 1: Transient behavior of invisibility cloaks for diffusive light propagation

Originally published in Optica on 20 February 2015 (optica-2-2-84