Realization of optimal bandgaps in solid-solid, solid-air, and hybrid solid-air-solid phononic crystal slabs

Reinke, Charles M.; Su, Mehmet F.; Olsson, Roy H.; El-Kady, Ihab F

doi:10.1063/1.3543848

Cited by 45 publications

(21 citation statements)

References 17 publications

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“…-modeled under 2D plain-strain conditons [27] or as a three-dimensional continuum with free surface boundary conditions [28] -and investigated the dependence of band-gap size upon the void radius. For combined out-of-plane and in-plane waves in 2D infinite-thickness PnCs formed from silicon and a square lattice of circular voids, it has been shown that the band-gap size normalized with respect to the mid-gap frequency cannot exceed 40% [27].…”

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confidence: 99%

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

2011

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We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit cell designs for (1) out-of-plane, (2) in-plane and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (∼10 40 possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band structure calculations. Focusing on highsymmetry plain-strain square lattices, we report unit cell designs exhibiting record values of normalized band-gap size for all three categories. For the combined polarizations case, we reveal a design with a normalized band-gap size exceeding 60%.Phononic crystals (PnCs) are periodic materials that exhibit distinct frequency characteristics such as the possibility of formation of band gaps. In general, it is most advantagous to have the frequency range of a band gap maximized while pulling its midpoint as low as possible in order to keep the unit cell size to a minimum. Selecting the topological distribution of the material phases inside the unit cell provides a a powerful means towards reaching this target, and this has been the focus of numerous research studies not only on PnCs but also photonic crystals (PtCs).The exploration for optimal unit cell designs was initiated by Cox and Dobson in 1999 [15] (in the context of PtCs). The articles by Burger et al. [16] and Jensen and Sigmund [17] provide a review of subsequent studies concerned with band-gap widening in PtCs. In the area of PnCs, the problem has been treated in a variety of settings and using several techniques. For example, unit cells have been optimized in one-dimension [18,19] and in two-dimensions (2D) [20][21][22][23][24][25], using gradient-based [21][22][23] as well as non-gradient-based [24,25] techniques. Interest in band-gap size maximation has also been treated outside the scope of the unit cell dispersion problem [21,26]. In all these optimization studies the focus has been primarily on PnCs based on an infinite thickness model and a material composition consisting of two or more solid (or solid and fluid) phases with the exception of a few investigations that considered thin-plate singlephase models [22,23]. Recognizing the practical significance of solid-and-air PnCs with relatively large crosssectional thickness, some studies considered the configuraton of a 2D solid matrix with periodic cylindrical voids * Corresponding author; mih@colorado.edu.-modeled under 2D plain-strain conditons [27] or as a three-dimensional continuum with free surface boundary conditions [28] -and investigated the dependence of band-gap size upon the void radius. For combined out-of-plane and in-plane waves in 2D infinite-thickness PnCs formed from silicon and a square lattice of circular voids, it has been shown that the band-gap size normalized with respect to the mid-gap frequency cannot exceed 40% [27]. In this letter we utlize a specialized optimization algorithm in pursuit of ...

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Ultrawide phononic band gap for combined in-plane and out-of-plane waves

2011

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“…In the case of periodic pillars on a membrane [67][68][69][70], besides the possibility of wide Bragg gaps, a low frequency gap exhibiting metamaterial type behavior can be obtained with an appropriate choice of the geometrical parameters [67,70], in particular a small thickness of the membrane. With the advancements of nanotechnologies, there is a great deal of interest on nanophononics [71,72], in particular phononic circuits with waveguides and cavities inside sub-micron phononic membranes working at a few GHz.…”

Section: Concluding Remarks and Further Developments In The Field Of mentioning

confidence: 99%

Fundamental Properties of Phononic Crystal

Pennec

Djafari‐Rouhani

2016

Phononic Crystals

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The control and manipulation of acoustic/elastic waves is a fundamental problem with many potential applications, especially in the field of information and communication technologies. For instance, confinement, guiding, and filtering phenomena at the scale of the wavelength are useful for signal processing, advanced nanoscale sensors, and acousto-optic on-chip devices; acoustic metamaterials, working in particular in the sub-wavelength regime can be used for efficient and broadband sound isolation as well as for imaging and super-resolution.Phononic crystals, which are artificial materials constituted by a periodic repetition of inclusions in a matrix, are proposed to achieve these objectives via the possibility of engineering their band structures. The elastic properties, shape, and arrangement of the scatterers modify strongly the propagation of the acoustic/elastic waves in the structure. The phononic band structure and dispersion curves can then be tailored with appropriate choices of materials, crystal lattices, and topology of inclusions.Similarly to any periodic structure, the propagation of acoustic waves in a phononic crystal is governed by the Bloch [1] or Floquet theorem from which one can derive the band structure in the corresponding Brillouin zone. The periodicity of the structures, that defines the Brillouin zone, may be in one (1D), two (2D), or three dimensions (3D). The propagation of acoustic waves in layered periodic materials or superlattices which are now being considered as 1D phononic crystals has been extensively studied [2] since the early paper of Rytov [3]. However, the

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“…They can exhibit complete band gaps, i.e., finite continuous frequency regions where energy propagation is forbidden for all possible wave directions Kushwaha (1993), or conversely where only evanescent waves are allowed Laude (2009). Band-gap locations and widths mainly depend on the materials employed in the crystal construction, the lattice geometry, and the size and shape of any inclusions Reinke (2011). In this paper, we introduce deeply corrugated one-dimensional phononic crystal grating in PDMS for the energy localization in the PDMS walls near the microchannel with respective protection of other parts of the device.…”

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confidence: 99%

A Numerical Analysis of Phononic-Assisted Control of Ultrasound Waves in Acoustofluidic Device

Moiseyenko

Bruus

2015

Physics Procedia

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The ability to precisely sort individual microparticles/cells/droplets in suspension is important for various chemical and biological applications such as cancer cell detection, drug screening etc. The past decade, label-free particle handling of particle suspensions by ultrasonic radiation forces and streaming has received much attention, since it relies solely on mechanical properties such as particle size and contrast in density and compressibility. We present a theoretical study of phononic-assisted control of ultrasound waves in acoustofluidic devices. We propose the use of phononic crystal diffractors, which can be introduced in acoustofluidic structures. These diffractors can be applied in the design of efficient resonant cavities, directional sound waves for new types of particle sorting methods, or acoustically controlled deterministic lateral displacement. The PnC-diffractor-based devices can be made configurable, by embedding the diffractors, all working at the same excitation frequency but with different resulting diffraction patterns, in exchangeable membranes on top of the device.

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Realization of optimal bandgaps in solid-solid, solid-air, and hybrid solid-air-solid phononic crystal slabs

Cited by 45 publications

References 17 publications

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

Fundamental Properties of Phononic Crystal

A Numerical Analysis of Phononic-Assisted Control of Ultrasound Waves in Acoustofluidic Device

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