Phononic Slab Research Articles

Generalized coupled mode theory in phononic slab waveguides

We develop the generalized coupled mode theory for the phononic slab waveguides, including core and cladding regions. At first, the eigenfrequency analysis is performed to obtain the dispersion curves for shear (SH) and Rayleigh–Lamb (RL) modes that are the orthogonal modes of slab waveguide. Secondly, the coupled mode equations (CMEs) are introduced for SH and RL modes, separately. Then CMEs are utilized to study transferring elastic energy between two coupled waveguides. We also analytically investigate the coupling of SH modes between non-parallel waveguides through calculating the coupling coefficients for small angles between them. Finally, the coupling of non-parallel waveguides in two different situations is demonstrated, when they are getting away from each other, and vice versa.

Pseudospins and topological edge states for fundamental antisymmetric Lamb modes in snowflakelike phononic crystal slabs.

The topological transport of Lamb wave in phononic crystal slabs provides a great potential in reinforcing nondestructive testing, high sensitivity sensing, and information processing. In this paper, the authors investigate the pseudospins edge states of fundamental antisymmetric Lamb waves in a snowflakelike phononic slab. Significantly, the fourfold Dirac degeneracy for antisymmetric Lamb mode is accidentally formed at the Γ point with the critical angle of the snowflakelike holes, which does not require the folding of the lattices. Meanwhile, based on the rotating-scatterer mechanism, the mirror symmetry is broken and the topological multipole phase transitions are well induced during the gradual change of the scattering strength among the scatterers with the rotation angle. The topologically protected edge states and its unidirectional robust propagation are further demonstrated. The proposed topological phononic slabs will be a more hopeful option to apply in engineering practices.

Elastodynamic response of three-dimensional phononic crystals using laser Doppler vibrometry

The elastodynamic response of finite 3D phononic structures is analyzed by means of comparing experimental findings obtained through a laser Doppler vibrometry-based methodology and theoretical computations performed with the layer-multiple-scattering method. The recorded frequency-gap spectrum of the phononic slabs exhibited a good agreement of theory to experiment. Along these lines, a newly developed technique, based on laser Doppler vibrometry, has been proposed and validated for the dispersion efficiency in 3D phononic metamaterials.

Guiding and splitting Lamb waves in coupled-resonator elastic waveguides

We investigate experimentally Lamb wave propagation in coupled-resonator elastic waveguides (CREWs) formed by a chain of cavities in a two-dimensional phononic crystal slab with cross holes. Wide complete bandgaps, extending from 53 to 88 kHz, are first measured in a finite phononic crystal slab sample. A straight waveguide and a wave splitting circuit with 90° bends are then designed, fabricated and measured. Elastic Lamb waves are excited by a piezoelectric patch attached to one side of the phononic slab and detected using a scanning vibrometer. Strongly confined guiding and splitting at waveguide junctions are clearly observed for several guided waves. Numerical simulations are found to be in excellent agreement with experimental results and allow for the identification of the involved resonant cavity modes. The influence on the dispersion of guided waves of the slab thickness and of the hole length is also investigated. The results have implications for the design of innovative phononic devices with strong confinement and tailorable dispersion.

Broadband All-angle Negative Refraction by Optimized Phononic Crystals

All-angle negative refraction (AANR) of phononic crystals and its frequency range are dependent on mechanical properties of constituent materials and their spatial distribution. So far, it is impossible to achieve the maximum operation frequency range of AANR theoretically. In this paper, we will present a numerical approach for designing a two-dimensional phononic crystal with broadband AANR without negative index. Through analyzing the mechanism of AANR, a topology optimization problem aiming at broadband AANR is established and solved by bi-directional evolutionary structural optimization method. The optimal steel/air phononic crystal exhibits a record AANR range over 20% and its refractive properties and focusing effects are further investigated. The results demonstrate the multifunctionality of a flat phononic slab including superlensing effect near upper AANR frequencies and self-collimation at lower AANR frequencies.

Experimental evidence of high-frequency complete elastic bandgap in pillar-based phononic slabs

We present strong experimental evidence for the existence of a complete phononic bandgap, for Lamb waves, in the high frequency regime (i.e., 800 MHz) for a pillar-based phononic crystal (PnC) membrane with a triangular lattice of gold pillars on top. The membrane is composed of an aluminum nitride film stacked on thin molybdenum and silicon layers. Experimental characterization shows a large attenuation of at least 20 dB in the three major crystallographic directions of the PnC lattice in the frequency range of 760 MHz–820 MHz, which is in agreement with our finite element simulations of the PnC bandgap. The results of experiments are analyzed and the physics behind the attenuation in different spectral windows is explained methodically by assessing the type of Bloch modes and the in-plane symmetry of the displacement profile.

Experimental investigation of elastic modes localized within a defect in a phononic slab

Heterostructures with periodic variations of both their optical refractive index and their elastic properties may induce band gaps for both electromagnetic and acoustic waves. As a consequence of the expected enhancement of the acousto-optic interactions, these artificial materials, called “PhoXonic crystals”, are of primary interest for new sensing applications. In this context, we have experimentally studied the localization of elastic energy within a defect. The heterostructures consist in arrays of voids periodically drilled throughout silicon plates (graphite symmetry) and featuring a vacancy, or a line of vacancies. An all-optical experimental technique allows for both the generation and the detection of the elastic guided waves. The non-contact probing allows one to monitor the displacements field inside the defects. First, we have measured the dispersion of broad band elastic waves guided in between the free surfaces of the sample. Then narrow band elastic guided waves, whose central frequency corresponds to resonance modes of the cavity are generated. The optical probe allows for the measurement of the out-of-plane displacements associated to the elastic modes localized within the cavity or transmitted through the phononic structure. The spatial distribution of elastic energy inside the cavity is measured and compared with numerical predictions. This work is supported by the European Community through the FET-Open project “TAILPHOX” (Grant No. 233883).

1604 シリカガラス中2次元フォノニック構造における弾性波伝搬のFDTD解析(OS16-1.フォトニック・フォノニック構造の設計とシミュレーション(1),OS・一般セッション講演)

We investigate wave-propagation properties of the phononic structure made of polycarbonate embedded in silica glass. Phonon band and elastic wave propagation are calculated and simulated by the FDTD method. We discuss frequency dependence of the wave-propagation properties in the phononic slab in conjunction with the resonance mode excited in the cylindrical polycarbonate, which can be identified as flat hand character in the phonon band diagram.

Experimental measurements of the band structure of Lamb waves in phononic lattices

We have measured the band structure of Lamb waves propagating in 2D phononic crystals. Different cases were investigated. First we have studied the phononic film deposited on a homogeneous substrate. The phononic film is made of cylindrical iron scatterers embedded into a copper background; the substrate is a 700 μm silicon plate. The propagation is along the crystallographic direction [100] of Si. At low filling fraction, a frequency band gap for the antisymmetric mode arises at reduced Brillouin edge. At high filling fraction, a band gap opens also on the symmetric branch. We have also studied the case of phononic slabs with very high contrast between the scatterers and the matrix. The samples are made of 200 μm silicon plates with air holes lattices drilled throughout. Whatever the symmetry of the lattice, square of centered rectangular, broad band gaps open at first and second reduced Brillouin zone edges. Experimental data are then compared to theoretical predictions obtained using a plane wave expansion method.