Tunable Topological Surface States of Three-Dimensional Acoustic Crystals

Topological design for band structures of artificial materials such as acoustic crystals provides a powerful tool to manipulate wave propagating in a robust and symmetry-protected way. In this paper, based on the band folding and breaking mechanism by building blocks with acoustic atoms, we construct a three-dimensional topological acoustic crystal with a large complete bandgap. At a mirror-symmetry domain wall, two gapped symmetry and anti-symmetry surface states can be found in the bandgap, originated from two opposite Su-Schrieffer-Heeger chains. Remarkably, by enforcing a glide symmetry on the domain wall, we can tune the original gapped surface states in a gapless fashion at the boundaries of surface Brillouin zone, acting as omnidirectional acoustic quantum spin Hall effect. Our tunable yet straightforward acoustic crystals offer promising potentials in realizing future topological acoustic devices.

Omnidirectional Photonic Bandgap in Two-dimensional Photonic Quasicrystal Made of Near-Transparent Dielectric Material

Complete bandgap for all-dielectric photonic crystals in the microwave region can be obtained only by using high-contrast materials. This requires the usage of dielectric materials with high relative permittivity coefficient. In this paper, we study, both numerically and experimentally, a two-dimensional all-dielectric photonic quasicrystal made of polyurethane foam, which is considered in all microwave applications as a transparent material. The quasicrystal structure having an omnidirectional two-dimensional bandgap is mathematically generated by the direct inscription of Bragg’s peaks of the structure in the reciprocal space. The sample of the quasicrystal was manufactured on CNC (computer numerical controlled) milling machine out of foam with very low dielectric permittivity of 1.254. The numerical simulations and the experimental study are in good agreement with the theoretical model.

2D in-plane elastic waves in curved-tapered square lattice frame structure

This work proposes a unique configuration of two-dimensional metamaterial lattice grid comprising of curved and tapered beams. The propagation of elastic waves in the structure is analyzed using the dynamic stiffness matrix (DSM) approach and the Floquet-Bloch theorem. The DSM for the unit cell is formulated under the extensional theory of curved beam considering the effects of shear and rotary inertia. The study considers two types of variable rectangular cross-sections, viz. single taper and double taper along the length of the beam. Further, the effect of curvature and taper on the wave propagation is analysed through the band diagram along the irreducible Brillouin zone. It is shown that a complete band gap, i.e. attenuation band in all the directions of wave propagation, in a homogeneous structure can be tailored with a suitable combination of curvature and taper. Generation of the complete bandgap is hinged upon the coupling of axial and transverse component of the lattice grid. This coupling emerges due to the presence of the curvature and further enhanced due to tapering. The double taper cross-section is shown to have wider attenuation characteristics than single taper cross-sections. Specifically, 83.36% and 63% normalized complete bandwidth is achieved for the double and single taper cross-section for a homogeneous metamaterial, respectively. Additional characteristics of the proposed metamaterial in time and frequency domain of the finite structure, vibration attenuation, wave localization in the equivalent finite structure are also studied.

Phononic Coupled-Resonator Waveguide Micro-Cavities

Phononic coupled-resonator waveguide cavities are formed by a finite chain of defects in a complete bandgap phononic crystal slab. The sample is machined in a fused silica plate by femtosecond printing to form an array of cross-shape holes. The collective resonance of the phononic cavities, in the Megahertz frequency range, are excited by a piezoelectric vibrator and imaged by laser Doppler vibrometry. It is found that well-defined resonant cavity modes can be efficiently excited, even though the phononic cavities are distant by a few lattice spacings and are only weakly coupled through evanescent elastic waves. The results suggest the possibility of engineering the dynamical response of a set of coupled phononic cavities by an adequate layout of defects in a phononic crystal slab.

Wave Directionality in Three-Dimensional Periodic Lattices

This work focuses on elastic wave propagation in three-dimensional (3D) low-density lattices and explores their wave directionality and energy flow characteristics. In particular, we examine the dynamic response of Kelvin foam, a simple-and framed-cubic lattice, as well as the octet lattice, spanning this way a range of average nodal connectivities and both stretching-and bending-dominated behavior. Bloch wave analysis on unit periodic cells is employed and frequency diagrams are constructed. Our results show that in the low relative-density regime analyzed here, only the framed-cubic lattice displays a complete bandgap in its frequency diagram. New representations of iso-frequency contours and group-velocity plots are introduced to further analyze dispersive behavior, wave directionality, and the presence of partial bandgaps in each lattice. Significant wave beaming is observed for the simple-cubic and octet lattices in the low frequency regime, while Kelvin foam exhibits a nearly isotropic behavior in low frequencies for the first propagating mode. Results of Bloch wave analysis are verified by explicit numerical simulations on finite size domains under a harmonic perturbation.

Pentamodal behaviors and acoustic bandgaps of asymmetric pentamode elastic metamaterials

The asymmetric pentamode metamaterial structure which is built by connecting double-cones with different cross-section shapes (regular triangle, square, pentagon and hexagon) to form diamond lattice is proposed in this paper. Then its phonon band structure is calculated by finite-element method (FEM), and its pentamodal behaviors and acoustic bandgaps are studied in detail. Results show that in the process of adjusting geometrical parameters, the asymmetric case performs similar pentamodal behaviors [ratio of bulk modulus to shear modulus [Formula: see text] and single-mode bandgap (SBG)] with the symmetric cases. And the asymmetric case not only remains the intrinsic complete bandgap (CBG) of mode 12-13 like symmetric cases, but also opens new and wide CBG of mode 10-11 and mode 14-15 for appropriate parameters. Therefore, introducing structural asymmetry should be an effective way to open CBG in pentamode elastic metamaterials.