On Mechanical Metamaterials

Mechanical Metamaterials are artificial materials which give access to elastic properties beyond natural materials. Within this work linear elastic material properties are tailored to exploit a Poisson\u27s ratio of close to 0.5 as well as approaching -1. These material properties are computed and the density is adjusted to specific values to control e.g. the impedance. At last two different cloaking concepts are realized with these materials and elastostatic cloaking is achieved

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

On the feasibility of pentamode mechanical metamaterials

Conceptually, all conceivable three-dimensional mechanical materials can be built from pentamode materials. Pentamodes also enable to implement three-dimensional transformation acoustics - the analogue of transformation optics. However, pentamodes have not been realized experimentally to the best of our knowledge. Here, we investigate inasmuch the pentamode theoretical ideal suggested by Milton and Cherkaev in 1995 can be approximated by a metamaterial with current state-of-the-art lithography. Using numerical calculations calibrated by our fabricated three-dimensional microstructures, we find that the figure of merit, i.e., the ratio of bulk modulus to shear modulus, can realistically be made as large as about 1,000.Comment: 4 pages and 5 figure

Hybrid 2D-3D optical devices for integrated optics by direct laser writing

Integrated optical chips have already been established for application in optical communication. They also offer interesting future perspectives for integrated quantum optics on a chip. At present, however, they are mostly fabricated using essentially planar fabrication approaches like electron-beam lithography or UV optical lithography. Many further design options would arise if one had complete fabrication freedom in regard to the third dimension normal to the chip without having to give up the virtues and the know-how of existing planar fabrication technologies. As a step in this direction, we here use three-dimensional dip-in direct-laser-writing optical lithography to fabricate three-dimensional polymeric functional devices on pre-fabricated planar optical chips containing Si3N4 waveguides as well as grating couplers made by standard electron-beam lithography. The first example is a polymeric dielectric rectangular-shaped waveguide which is connected to Si3N4 waveguides and that is adiabatically twisted along its axis to achieve geometrical rotation of linear polarization on the chip. The rotator’s broadband performance at around 1550 nm wavelength is verified by polarization-dependent grating couplers. Such polarization rotation on the optical chip cannot easily be achieved by other means. The second example is a whispering-gallery-mode optical resonator connected to Si3N4 waveguides on the chip via polymeric waveguides. By mechanically connecting the latter to the disk, we can control the coupling to the resonator and, at the same time, guarantee mechanical stability of the three-dimensional architecture on the chip

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

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