Gradient-index Phononic Crystal Research Articles

Gradient-index phononic crystal lens-based enhancement of elastic wave energy harvesting

We explore the enhancement of structure-borne elastic wave energy harvesting, both numerically and experimentally, by exploiting a Gradient-Index Phononic Crystal Lens (GRIN-PCL) structure. The proposed GRIN-PCL is formed by an array of blind holes with different diameters on an aluminum plate, where the blind hole distribution is tailored to obtain a hyperbolic secant gradient profile of refractive index guided by finite-element simulations of the lowest asymmetric mode Lamb wave band diagrams. Under plane wave excitation from a line source, experimentally measured wave field validates the numerical simulation of wave focusing within the GRIN-PCL domain. A piezoelectric energy harvester disk located at the first focus of the GRIN-PCL yields an order of magnitude larger power output as compared to the baseline case of energy harvesting without the GRIN-PCL on the uniform plate counterpart.

Focusing of Rayleigh waves with gradient-index phononic crystals

We report on the subwavelength focusing of Rayleigh waves using gradient-index (GRIN) phononic crystals (PCs) made of air holes scatters in a thick silicon substrate. The subwavelength focusing is demonstrated both in the inner and in the silicon substrate behind the GRIN PCs by using a non-contact experimental technique. In both situations, the focal zone was observed at the position, which is in very good agreement with our theoretical predictions, at a frequency in the sound cone free of radiation into the substrate.

Beam paths of flexural Lamb waves at high frequency in the first band within phononic crystal-based acoustic lenses

This work deals with an analytical and numerical study of the focusing of the lowest order anti-symmetric Lamb wave in gradient index phononic crystals. Computing the ray trajectories of the elastic beam allowed us to analyze the lateral dimensions and shape of the focus, either in the inner or behind the phononic crystal-based acoustic lenses, for frequencies within a broad range in the first band. We analyzed and discussed the focusing behaviors inside the acoustic lenses where the focalization at sub-wavelength scale was achieved. The focalization behind the gradient index phononic crystal is shown to be efficient as well: we report on FMHM = 0.63λ at 11MHz.

Focusing and waveguiding of Lamb waves in micro-fabricated piezoelectric phononic plates

This paper presents results on the numerical and experimental studies of focusing and waveguiding of the lowest anti-symmetric Lamb wave in micro-fabricated piezoelectric phononic plates. The phononic structure was based on an AT-cut quartz plate and consisted of a gradient-index phononic crystal (GRIN PC) lens and a linear phononic plate waveguide. The band structures of the square-latticed AT-cut quartz phononic crystal plates with different filling ratios were analyzed using the finite element method. The design of a GRIN PC plate lens which is attached with a linear phononic plate waveguide is proposed. In designing the waveguide, propagation modes in square-latticed PC plates with different waveguide widths were studied and the results were served for the experimental design. In the micro-fabrication, deep reactive ion etching (Deep-RIE) process with a laboratory-made etcher was utilized to fabricate both the GRIN PC plate lens and the linear phononic waveguide on an 80μm thick AT-cut quartz plate. Interdigital transducers were fabricated directly on the quartz plate to generate the lowest anti-symmetric Lamb waves. A vibro-meter was used to detect the wave fields and the measured results on the focusing and waveguiding of the piezoelectric GRIN PC lens and waveguide are in good accordance with the numerical predictions. The results of this study may serve as a basis for developing an active micro plate lens and related devices.

Efficient focalization of antisymmetric Lamb waves in gradient-index phononic crystal plates

The focalization of elastic waves within a two dimensional gradient-index phononic crystal (GRIN PC) is numerically and experimentally investigated. The structure is formed by a square lattice of air holes in a silicon plate with transverse variation of holes’ diameters. The geometry and efficiency of focalization are computed with a finite element method. A non-contact laser-ultrasonic technique is used both to excite flexural Lamb waves and to monitor in situ the displacements field within the GRIN PC. The efficient subwavelength focusing is achieved and analyzed; furthermore, we describe the oscillatory behavior of focusing and show the relationship between the responses of waves in GRIN PC and the source intensity.

Design of acoustic beam aperture modifier using gradient-index phononic crystals.

This article reports the design concept of a novel acoustic beam aperture modifier using butt-jointed gradient-index phononic crystals (GRIN PCs) consisting of steel cylinders embedded in a homogeneous epoxy background. By gradually tuning the period of a GRIN PC, the propagating direction of acoustic waves can be continuously bent to follow a sinusoidal trajectory in the structure. The aperture of an acoustic beam can therefore be shrunk or expanded through change of the gradient refractive index profiles of the butt-jointed GRIN PCs. Our computational results elucidate the effectiveness of the proposed acoustic beam aperture modifier. Such an acoustic device can be fabricated through a simple process and will be valuable in applications, such as biomedical imaging and surgery, nondestructive evaluation, communication, and acoustic absorbers.

Focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal plate

In this letter, we numerically demonstrate focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal (PC) silicon plate and its application as a beam-width compressor for compressing Lamb wave into a stubbed phononic tungsten/silicon plate waveguide. The results show that beam width of the lowest antisymmetric Lamb wave in the PC thin plate can be compressed efficiently and fitted into tungsten/silicon PC plate waveguide over a wide range of frequency.

Acoustic mirage in two-dimensional gradient-index phononic crystals

We report the design of a two-dimensional gradient-index phononic crystal (GRIN PC) structure, which effectively demonstrates the “acoustic mirage” effect on the wavelength scale. Using the GRIN PC, the propagating direction of acoustic waves can be continuously bent along an arc-shaped trajectory by gradually tuning the filling ratio of PCs. We investigate the acoustic mirage effect through both plane wave expansion and finite-difference time-domain methods. By controlling the incident angle or operating frequency, the arc-shaped trajectory of acoustic wave propagation can be dynamically adjusted. The GRIN PC structure is composed of steel cylinders, positioned in a square lattice, and immersed in an epoxy. It can be fabricated through a simple process and seamlessly integrated with existing acoustic devices. In addition, we establish that such an acoustic effect can be used in the design of tunable acoustic waveguides, which could find applications in acoustic switching, filtering, and biosensing.

Acoustic beamwidth compressor using gradient-index phononic crystals

We report a novel approach to effectively couple acoustic energy into a two-dimensional phononic-crystal waveguide by an acoustic beamwidth compressor using the concept of a gradient-index phononic crystal (GRIN PC). The GRIN PC-based beamwidth compressor is composed of a square array of solid scatterers embedded in epoxy. By gradually modulating the density and elastic modulus of the scatterers along the direction transverse to the phononic propagation, the beamwidth compressor can efficiently compress the wide acoustic beam to the scale of the phononic-crystal waveguide. This acoustic beamwidth compressor is investigated through a finite-difference time-domain method. A beam-size conversion ratio of 6.5 : 1 and a transmission efficiency of up to 90% is obtained over the working frequency range of the phononic-crystal waveguide. Potential applications for this device include acoustic biosensors and signal processors.

Gradient-index phononic crystals

We designed and characterized a two-dimensional, gradient-index phononic crystal (GRIN PC) to control the propagation of acoustic waves. The GRIN PC was composed of solid cylinders arranged in a square lattice and immersed in an epoxy. The refractive index along the direction transverse to the phononic propagation was designated as a hyperbolic secant gradient distribution. This distribution was modulated by means of the density and elastic moduli of the cylinders. The effective refractive indices in each row of the GRIN PC were determined from band diagrams obtained via a plane-wave expansion method. The acoustic wave propagation was numerically investigated by a finite-difference time-domain method, and the results were compared to the analytical beam trajectories derived from the hyperbolic secant profile. These results show that the GRIN PC allows acoustic focusing over a wide range of working frequencies, making it suitable for applications such as flat acoustic lenses and couplers.

Scandium: SIR W. Crookes. ( Phil. Trans. Roy. Soc., A2O9, 15.)

This paper presents results on the numerical and experimental studies of focusing and waveguiding of the lowest anti-symmetric Lamb wave in micro-fabricated piezoelectric phononic plates. The phononic structure was based on an AT-cut quartz plate and consisted of a gradient-index phononic crystal (GRIN PC) lens and a linear phononic plate waveguide. The band structures of the square-latticed AT-cut quartz phononic crystal plates with different filling ratios were analyzed using the finite element method. The design of a GRIN PC plate lens which is attached with a linear phononic plate waveguide is proposed. In designing the waveguide, propagation modes in square-latticed PC plates with different waveguide widths were studied and the results were served for the experimental design. In the micro-fabrication, deep reactive ion etching (Deep-RIE) process with a laboratory-made etcher was utilized to fabricate both the GRIN PC plate lens and the linear phononic waveguide on an 80 μm thick AT-cut quartz plate. Interdigital transducers were fabricated directly on the quartz plate to generate the lowest anti-symmetric Lamb waves. A vibro-meter was used to detect the wave fields and the measured results on the focusing and waveguiding of the piezoelectric GRIN PC lens and waveguide are in good accordance with the numerical predictions. The results of this study may serve as a basis for developing an active micro plate lens and related devices.