Surface and interface acoustic waves in solid-fluid superlattices: Green’s function approach

Hassouani, Y. El; Boudouti, El Houssaine El; Djafari‐Rouhani, Bahram; Aynaou, H.; Dobrzyński, L.

doi:10.1103/physrevb.74.144306

Cited by 19 publications

(15 citation statements)

References 71 publications

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“…The admissible number of SAWs can be established via introducing the real symmetric matriceŝ B P = iV PV t P (9) equal to the product of matricesV P (B8) and analyzing the dispersion equation on the electrically closed or open surface written in the form…”

Section: A Mechanically Free Electrically Closed and Electrically Open Surfacementioning

confidence: 99%

“…In particular, much attention has been paid to the wave propagation in one-dimensional (1D) phononic crystals, otherwise termed superlattices, which represent periodic sequences of multilayers [4]. Reflection of bulk waves was investigated in piezoelectric [5][6][7] and solid-fluid superlattices [8][9][10], as well as in solid-solid and solid-fluid Fibonacci structures [11][12][13][14]. Much effort has been devoted to studying the surface acoustic waves (SAWs) in 1D elastic and piezoelectric phononic crystals.…”

Section: Introductionmentioning

confidence: 99%

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Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

Darinskii

Shuvalov

2019

Phys. Rev. B

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The paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions.

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Section: A Mechanically Free Electrically Closed and Electrically Open Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

Darinskii

Shuvalov

2019

Phys. Rev. B

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“…Before addressing the problem of the fluid-solid SL, it is helpful to know the surface elements of its elementary constituents, namely, the Green's function of an ideal fluid of thickness d f , sound speed v f , and mass density f ; and an elastic isotropic solid characterized by its thickness d s , longitudinal speed v ᐉ , transverse speed v t , and mass density s . Let us first notice that the Green's functions associated with sagittal waves in an elastic solid is a 4 ϫ 4 matrix as these waves exhibit two directions of vibrations 40,43 in the sagittal plane ͑x 1 , x 3 ͒. However, the ideal fluid layer is characterized by only one degree of vibration, and its 4 ϫ 4 Green's function matrix has only x 3 x 3 nonzero elements.…”

Section: B Inverse Surface Green's Functions Of the Elementary Constituentsmentioning

confidence: 99%

“…39 All the above works have mainly dealt with pure longitudinal ͑compressional͒ and shear horizontal absorbing waves propagating perpendicular or parallel to the layers. [33][34][35][36][37][38] In a recent paper, 40 we have investigated the propagation and localization of acoustic waves polarized in the sagittal plane, defined by the normal to the surface and the wave vector k ʈ ͑parallel to the surface͒, in SLs made of elastic solid and ideal fluid layers. In particular, we have shown the possibility of existence of surface acoustic waves in semiinfinite solid-fluid SL or its interface with a semi-infinite fluid.…”

Section: Introductionmentioning

confidence: 99%

Sagittal acoustic waves in finite solid-fluid superlattices: Band-gap structure, surface and confined modes, and omnidirectional reflection and selective transmission

et al. 2008

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Using a Green's function method, we present a comprehensive theoretical analysis of the propagation of sagittal acoustic waves in superlattices ͑SLs͒ made of alternating elastic solid and ideal fluid layers. This structure may exhibit very narrow pass bands separated by large stop bands. In comparison with solid-solid SLs, we show that the band gaps originate both from the periodicity of the system ͑Bragg-type gaps͒ and the transmission zeros induced by the presence of the solid layers immersed in the fluid. The width of the band gaps strongly depends on the thickness and the contrast between the elastic parameters of the two constituting layers. In addition to the usual crossing of subsequent bands, solid-fluid SLs may present a closing of the bands, giving rise to large gaps separated by flat bands for which the group velocity vanishes. Also, we give an analytical expression that relates the density of states and the transmission and reflection group delay times in finite-size systems embedded between two fluids. In particular, we show that the transmission zeros may give rise to a phase drop of in the transmission phase, and therefore, a negative delta peak in the delay time when the absorption is taken into account in the system. A rule on the confined and surface modes in a finite SL made of N cells with free surfaces is demonstrated, namely, there are always N-1 modes in the allowed bands, whereas there is one and only one mode corresponding to each band gap. Finally, we present a theoretical analysis of the occurrence of omnidirectional reflection in a layered media made of alternating solid and fluid layers. We discuss the conditions for such a structure to exhibit total reflection of acoustic incident waves in a given frequency range for all incident angles. Also, we show how this structure can be used as an acoustic filter that may transmit selectively certain frequencies within the omnidirectional gaps. In particular, we show the possibility of filtering assisted either by cavity modes ͑in particular sharp Fano resonances͒ or by interface resonances.

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“…The sagittally polarized twopartial and the fully coupled three-partial SAWs were also widely investigated [46][47][48][49][50][51][52][53][54]. The spectra of SAWs along with the bulk-wave reflection and transmission coefficients were studied as well for periodic solid-fluid structures [55,56] and for solid-solid and solid-fluid Fibonacci superlattices [57][58][59][60]. Results of the numerical modeling of SAW propagation in two-dimensional piezoelectric phononic crystals may be found in [61][62][63].…”

Section: Introductionmentioning

confidence: 99%

Existence of surface acoustic waves in one-dimensional piezoelectric phononic crystals of general anisotropy

Darinskii¹,

Shuvalov²

2019

Phys. Rev. B

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The paper is concerned with the surface acoustic waves propagating in half-infinite one-dimensional piezoelectric phononic crystals of general anisotropy. The phononic crystal is formed of periodically repeated perfectly bonded layers, and its exterior boundary is one of the layer boundaries. The surface waves occurring in the so-called full stop bands are considered. It appears that the number of surface waves existing within a full stop band for a given layered structure is interrelated with their number in the same stop band for the phononic crystal different from the given one only due to the reversed ordering of layers within a period. A series of statements is proved on the maximum possible number of surface waves per full stop band for both these structures in total, i.e., embracing surface-wave occurrences in either one or the other structure. The analysis is performed for the electrically closed, electrically open, and electrically free types of boundary conditions on the mechanically free crystal surface, in which cases it admits a correspondingly different number of surface waves. A subsidiary instance of mechanically clamped surface is addressed as well. It is observed that the piezoelectric coupling can create new surface waves which disappear when piezoelectric coefficients turn to zero. Besides the general case of arbitrary anisotropy, we also consider two specific situations where the crystallographic symmetry allows the existence of sagittally polarized piezoactive surface waves and of shear horizontally polarized piezoactive surface waves. Numerical examples of surface-wave branches under various boundary conditions are provided.

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Surface and interface acoustic waves in solid-fluid superlattices: Green’s function approach

Cited by 19 publications

References 71 publications

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

Sagittal acoustic waves in finite solid-fluid superlattices: Band-gap structure, surface and confined modes, and omnidirectional reflection and selective transmission

Existence of surface acoustic waves in one-dimensional piezoelectric phononic crystals of general anisotropy

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