Abdelkrim Khelif

Guiding and bending of acoustic waves in highly confined phononic crystal waveguides

We demonstrate experimentally the guiding and the bending of acoustic waves in highly confined waveguides formed by removing rods from a periodic two-dimensional lattice of steel cylinders immersed in water. Full transmission is observed for a one-period-wide straight waveguide within the full band gap of the perfect phononic crystal. However, when the waveguide width is doubled, destructive interference causes the transmission to vanish in the center of the passband. Waveguiding over a wide frequency range is obtained for a one-period-wide waveguide with two sharp 90° bends. Finite-difference time-domain computations are found to be in good agreement with the measurements.

Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates

We show the evidence of the existence of large complete phononic band gaps (CPBGs) in two-dimensional phononic crystals (PCs) formed by embedding cylindrical air holes in a solid plate (slab). The PC structure is made by etching a hexagonal array of air holes through a freestanding plate of silicon. A fabrication process compatible with metal-oxide-semiconductor technology is used on silicon-on-insulator substrate to realize the PC devices. Measuring the transmission of elastic waves through eight layers of the hexagonal lattice PC in the ΓK direction, more than 30dB attenuation is observed at a high frequency; i.e., 134MHz, with a band gap to midgap ratio of 23%. We show that this frequency region matches very well with the expected CPBG found through theoretical calculations.

Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency

We study theoretically the propagation of elastic waves in two-dimensional composite media composed of a square array of hollow steel cylinders embedded in water using the finite-difference time-domain method. These composite media constitute a class of acoustic band gap materials with narrow pass bands in their transmission stop bands. The frequency at which the pass band occurs is tunable by controlling the inner radius of the tubular steel inclusions. The effect of the tube inner radius on the transmission spectrum is semiquantitatively separable from the effect of the composite periodicity. A linear defect formed of a row of hollow cylinders in an array of filled cylinders produces an elastic waveguide that transmits at the narrow pass band frequency. We show that two of these tunable waveguides with different inner radii can be employed to filter and separate two specific frequencies from a broad band input signal.

Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs

We demonstrate planar structures that can provide simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical (or phoxonic) crystal slabs. Different phoxonic crystal (PxC) structures, composed of square, hexagonal (honeycomb), or triangular arrays of void cylindrical holes embedded in silicon (Si) slabs with a finite thickness, are investigated. Photonic band gap (PtBG) maps and the complete phononic band gap (PnBG) maps of PxC slabs with different radii of the holes and thicknesses of the slabs are calculated using a three-dimensional plane wave expansion code. Simultaneous phononic and photonic band gaps with band gap to midgap ratios of more than 10% are shown to be readily obtainable with practical geometries in both square and hexagonal lattices, but not for the triangular lattice.

Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals

Phononic crystals with triangular and honeycomb lattices are investigated experimentally and theoretically. They are composed of arrays of steel cylinders immersed in water. The measured transmission spectra reveal the existence of complete band gaps but also of deaf bands. Band gaps and deaf bands are identified by comparing band structure computations, obtained by a periodic-boundary finite element method, with transmission simulations, obtained using the finite difference time domain method. The appearance of flat bands and the polarization of the associated eigenmodes is also discussed. Triangular and honeycomb phononic crystals with equal cylinder diameter and smallest spacing are compared. As previously obtained with air-solid phononic crystals, it is found that the first complete band gap opens for the honeycomb lattice but not for the triangular lattice, thanks to symmetry reduction.

Acoustic channel drop tunneling in a phononic crystal

We study both theoretically and experimentally the possibility of resonant tunneling of acoustic waves between two parallel guides created in a phononic crystal composed of steel cylinders in water. In the absolute band gap of the phononic crystal, ranging from 250to325kHz, a full transmission band exists for propagation inside a straight waveguide. We show that the transfer of a particular wavelength can occur between two parallel waveguides coupled together through an appropriate coupling structure. The latter is composed of isolated cavities interacting with stubs located at the sides of the waveguides.

Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry

Surface acoustic wave propagation within a two-dimensional phononic band gap structure has been studied using a heterodyne laser interferometer. Acoustic waves are launched by interdigital transducers towards a square lattice of holes etched in a piezoelectric medium. Interferometer measurements performed at frequencies lying below, within, and above the expected band gap frequency range provide direct information of the wave interaction with the phononic crystal, revealing anisotropic scattering into higher diffraction orders depending on the apparent grating pitch at the boundary between the phononic crystal and free surface. Furthermore, the measurements also confirm the existence of an elastic band gap, in accordance with previous electrical measurements and theoretical predictions.

Surface acoustic wave trapping in a periodic array of mechanical resonators

The existence of two families of surface acoustic modes trapped by steep ridges on a piezoelectric substrate, shear horizontal and vertically polarized surface modes, is demonstrated experimentally using high aspect ratio interdigital transducers fabricated on lithium niobate. The experimental variation of the resonance frequencies of the various surface modes is obtained experimentally, and up to an order of magnitude slowing of surface waves is observed, with the phase velocity dropping from 4000 down to 450m∕s. It is argued that the observed resonances are surface modes trapped by the ridge electrodes.

Highly selective electroplated nickel mask for lithium niobate dry etching

A sulfur hexafluoride based reactive ion etching process allowing to etch several micron deep holes with diameters of the order of a few microns in lithium niobate is reported. Etching of deep structures with aspect ratios up to 1.5 was made possible through the use of an electroplated nickel mask exhibiting a selectivity as high as 20 with respect to lithium niobate. Several crystallograpic orientations were investigated, although particular interest was paid to Y-axis oriented substrates. Photoresist as well as metal masks were also tested and their selectivity was compared. The influence of process parameters such as applied rf power or operating pressure on the sidewall slope angle of the etched patterns was investigated. The technique has been successfully applied to the fabrication of phononic crystals consisting of periodical arrays of 9 μm diameter, 10 μm deep holes, with a 10 μm period, and presenting sidewall angles as high as 73° etched in Y-axis oriented lithium niobate.

Energy storage and dispersion of surface acoustic waves trapped in a periodic array of mechanical resonators

It has been shown previously that surface acoustic waves can be efficiently trapped and slowed by steep ridges on a piezoelectric substrate, giving rise to two families of shear-horizontal and vertically polarized surface waves. The mechanisms of energy storage and dispersion are explored by using the finite element method to model surface acoustic waves generated by high aspect ratio electrodes. A periodic model is proposed including a perfectly matched layer to simulate radiation conditions away from the sources, from which the modal distributions are found. The ratio of the mechanical energy confined to the electrode as compared to the total mechanical energy is calculated and is found to be increasing for increasing aspect ratio and to tend to a definite limit for the two families of surface waves. This observation is in support of the interpretation that high aspect ratio electrodes act as resonators storing mechanical energy. These resonators are evanescently coupled by the surface. The dispersion d...