Transmission of<b><i>L</i></b>-mode phonons from a superlattice into a liquid by effective acoustic impedance matching

Kato, Hatsuyoshi

doi:10.1103/physrevb.59.11136

Cited by 16 publications

(13 citation statements)

References 7 publications

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“…Let us mention that the interface between a finite-size SL and a homogeneous liquid can be used to enhance the resonant transmission of acoustic waves from a SL into a liquid. 55 Now we assume that the mercury medium is of finite size ͑with a thickness d 0 ͒ instead of being semi-infinite in extent. Figures 11͑a͒ and 11͑b͒ give the dispersion of localized and resonant modes ͑open circles͒ induced by a cap layer of width d 0 = 0.5D and 1.5D, respectively.…”

Section: B Semi-infinite Superlattice In Contact With a Fluidmentioning

confidence: 99%

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

et al. 2006

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We study the propagation of acoustic waves associated with the surface of a semi-infinite superlattice ͑SL͒ consisting of alternating elastic solid and ideal fluid layers or its interface with a semi-infinite fluid. We present closed-form expressions for localized surface and interface waves depending on whether the SL is terminated with a fluid layer or a solid layer. We also calculate the corresponding Green's function and densities of states. These general results are illustrated by a few applications to periodic Plexiglas-water and Al-water SLs. In the case of a fluid layer termination, we generalize a rule obtained previously about the existence and behavior of surface waves in the case of pure transverse or longitudinal waves in solid-solid SLs, namely ͑i͒ the creation from the infinite SL of a free surface gives rise to ␦ peaks of weight ͑−1/4͒ in the density of states, at the edges of the SL bulk bands, ͑ii͒ by considering together the two complementary semi-infinite SLs obtained by the cleavage of an infinite SL along a plane lying within the fluid layer and parallel to the interfaces, one always has as many localized surface modes as minigaps, for any value of the wave vector k ʈ ͑parallel to the interfaces͒. However, this rule is not fulfilled when the cleavage is carried out inside the solid layer. Indeed, in this case, the dispersion curves may present zero, one, or two modes inside each gap of the two complementary SLs depending on the position of the plane where the cleavage is produced. Finally, we investigate the localized and resonant modes associated with the presence of a fluid cap layer made of mercury, with finite or semi-infinite extent, on top of the above-mentioned SLs. Different guided modes induced by the adsorbed fluid layer are obtained and their properties are investigated.

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Section: B Semi-infinite Superlattice In Contact With a Fluidmentioning

confidence: 99%

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

et al. 2006

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“…The possibility of the enhanced transmission from a semi-infinite solid to a semiinfinite fluid, in spite of a large mismatch of their acoustic impedances, has been shown theoretically and experimentally [68][69][70]. The transmission occurs through the surface resonances induced by a 1D solid-solid-layered structure inserted between these two media.…”

Section: Transmission Enhancement Assisted By Surface Resonancementioning

confidence: 97%

“…Among these applications, one can mention (1) omnidirectional band gaps [55][56][57][58], (2) the possibility to engineer small-size sonic crystals with locally resonant band gaps in the audible frequency range [59], (3) hypersonic crystals [60-63] with high-frequency band gaps to enhance acousto-optical [49][50][51] or optomechanical [64,65] interaction and to realize stimulated emission of acoustic phonons [66], and (4) the possibility to enhance selective transmission through guided modes of a cavity layer inserted in the periodic structure [6,67] or by interface resonance modes induced by the superlattice/substrate interface [68][69][70]. The advantage of 1D systems lies in the fact that their design is more feasible and they require only relatively simple analytical and numerical calculations.…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Phononic Crystals

Boudouti¹,

Djafari‐Rouhani²

2012

Springer Series in Solid-State Sciences

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In this chapter, we discuss the vibrational properties of one-dimensional (1D) phononic crystals of both discrete and continuous media. These properties include the dispersion curves of infinite crystals as well as the confined modes and localized (surface, cavity) modes of finite and semi-infinite crystals. A general rule about the existence of localized surface modes in finite and semi-infinite superlattices with free surfaces is presented. We also present the calculations of reflection and transmission coefficients, particularly in view of selective filtering through localized modes. Most of the results presented in this chapter deal with waves propagating along the axis of the superlattice. However, in the last part of the chapter, we also discuss wave propagation out of the normal incidence and, more particularly, we demonstrate the possibility of omnidirectional transmission gap and selective filtering for any incidence angle. A comparison of the theoretical results with experimental data available in the literature is also presented and the reliability of the theoretical predictions is indicated. IntroductionThe one-dimensional (1D) phononic crystals called superlattices (SLs) are of great importance in material science. These structures are, in general, composed of two or several layers repeated periodically along the direction of growth. The layers constituting each cell of the SL can be made of a combination of solid-solid or solid-fluid-layered media. These materials enter now in the category of so-called phononic crystals (see the first chapter of this book and references therein) [1][2][3] constituted by inclusions (spheres, cylinders, etc.) arranged in a host matrix along two-dimensional (2D) and three-dimensional (3D) of the space. After the proposal of SLs by Esaki [4], the study of elementary excitations in multilayered systems has been very active. Among these excitations, acoustic phonons have received increased attention after the first observation by Colvard et al.[5] of a doublet associated to folded longitudinal acoustic phonons by means of Raman scattering. The essential property of these structures is the existence of forbidden frequency bands induced by the difference in acoustic properties of the constituents and the periodicity of these systems leading to unusual physical phenomena in these heterostructures in comparison with bulk materials [6][7][8].With regard to acoustic waves in solid-solid SLs, a number of theoretical and experimental works have been devoted to the study of the band gap structures of periodic SLs [6-10] composed of crystalline, amorphous semi-conductors, or metallic multilayers at the nanometric scale. The theoretical models used are essentially the transfer matrix [7,[11][12][13] and the Green's function methods [6,[14][15][16], whereas the experimental techniques include Raman scattering [5,17,18], ultrasonics [19][20][21][22][23][24][25][26][27][28][29], and time-resolved X-ray diffraction [30]. Besides the existence of the band-gap structures in perfe...

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“…The possibility of the enhanced transmission from a semiinfinite solid to a semi-infinite fluid, in spite of a large mismatch of their acoustic impedances, has been shown theoretically and experimentally. 28 The transmission occurs through the surface resonances induced by a 1D solid-solid layered structure inserted between these two media. These reso- nances are attributed to the SL/fluid interface 28 and coincide with the surface modes of the semi-infinite SL terminated with the layer having the lower acoustic impedance.…”

Section: B Transmission Enhancement Assisted By Surface Resonancementioning

confidence: 99%

“…20,21 Among these phenomena, one can mention ͑i͒ omnidirectional band gaps, 22,23 ͑ii͒ the possibility to engineer small-size sonic crystals with locally resonant band gaps in the audible frequency range, 24 ͑iii͒ hypersonic crystals with high-frequency band gaps to enhance acoustooptical interaction 25 and to realize stimulated emission of acoustic phonons, 26 and ͑iv͒ the possibility to enhance selective transmission through guided modes of a cavity layer inserted in the periodic structure 27 or by interface resonance modes induced by the superlattice ͑SL͒/substrate interface. 28 The advantage of one-dimensional ͑1D͒ systems lies in the fact that their design is more feasible and they require only relatively simple analytical and numerical calculations. The analytical calculations enable us to understand deeply different physical properties related to the band gaps in such systems.…”

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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Transmission ofL-mode phonons from a superlattice into a liquid by effective acoustic impedance matching

Cited by 16 publications

References 7 publications

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

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

One-Dimensional Phononic Crystals

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

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