Bloch wave deafness and modal conversion at a phononic crystal boundary

In this study the acoustic scattering is determined from a finite phononic crystal through an implementation of the Helmholtz-Kirchhoff integral theorem. The approach employs the Bloch theorem applied to a semi-infinite phononic crystal (PC) half-space. The internal pressure field of the half-space, subject to an incident acoustic monochromatic plane wave, is formulated as an expansion of the Bloch wave modes. Modal coefficients of reflected (diffracted) plane waves are arrived at via boundary condition considerations on the PC interface. Next, the PC inter-facial pressure, as determined by the Bloch wave expansion (BWE), is employed along with the Helmholtz-Kirchhoff integral equation to compute the scattered pressure from a large finite PC. Under a short wavelength limit approximation (wavelength much smaller than finite PC dimensions), the integral approach is employed to calculate the scattered pressure field for a large PC subject to an incident wave with two distinct incident angles. In two dimensions we demonstrate good agreement of scattered pressure results of large finite PC when compared against detailed finite element calculations. The work here demonstrates an efficient and accurate uniform computational framework for modeling the scattered and internal pressure fields of a large finite phononic crystal.

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Broadband and wide-angle negative reflection at a phononic crystal boundary

Applied Physics Letters ◽

10.1063/1.4863691 ◽

2014 ◽

Vol 104 (4) ◽

pp. 043503 ◽

Cited By ~ 18

Author(s):

Degang Zhao ◽

Yangtao Ye ◽

Shengjun Xu ◽

Xuefeng Zhu ◽

Lin Yi

Keyword(s):

Phononic Crystal ◽

Wide Angle ◽

Crystal Boundary

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Electron-Channelling Patterns: Principles and Techniques

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100091986 ◽

1976 ◽

Vol 34 ◽

pp. 400-401

Author(s):

David C. Joy

Keyword(s):

Crystal Structure ◽

Electron Flux ◽

Lattice Structure ◽

Incident Beam ◽

Bloch Wave ◽

Crystalline Solid ◽

Angle Of Incidence ◽

Electron Channelling ◽

Regular Arrangement ◽

Backscattered Signals

In a crystalline solid the regular arrangement of the lattice structure influences the interaction of the incident beam with the specimen, leading to changes in both the transmitted and backscattered signals when the angle of incidence of the beam to the specimen is changed. For the simplest case the electron flux inside the specimen can be visualized as the sum of two, standing wave distributions of electrons (Fig. 1). Bloch wave 1 is concentrated mainly between the atom rows and so only interacts weakly with them. It is therefore transmitted well and backscattered weakly. Bloch wave 2 is concentrated on the line of atom centers and is therefore transmitted poorly and backscattered strongly. The ratio of the excitation of wave 1 to wave 2 varies with the angle between the incident beam and the crystal structure.

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Convergent-beam electron diffraction at high spatial resolution

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130390 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1152-1153 ◽

Cited By ~ 1

Author(s):

J W Steeds

Keyword(s):

Electron Diffraction ◽

High Temperature Superconductors ◽

Bloch Wave ◽

Convergent Beam Electron Diffraction ◽

Beam Electron ◽

Energy Filtering ◽

Small Probe ◽

Transmission Electron ◽

Electron Microscopes ◽

Convergent Beam

That the techniques of convergent beam electron diffraction (CBED) are now widely practised is evident, both from the way in which they feature in the sale of new transmission electron microscopes (TEMs) and from the frequency with which the results appear in the literature: new phases of high temperature superconductors is a case in point. The arrival of a new generation of TEMs operating with coherent sources at 200-300kV opens up a number of new possibilities.First, there is the possibility of quantitative work of very high accuracy. The small probe will essentially eliminate thickness or orientation averaging and this, together with efficient energy filtering by a doubly-dispersive electron energy loss spectrometer, will yield results of unsurpassed quality. The Bloch wave formulation of electron diffraction has proved itself an effective and efficient method of interpreting the data. The treatment of absorption in these calculations has recently been improved with the result that <100> HOLZ polarity determinations can now be performed on III-V and II-VI semiconductors.

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A Stationary Solution of High-Energy Electron Reflection (HEER) for An Arbitrary Surface

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100135472 ◽

1990 ◽

Vol 48 (2) ◽

pp. 374-375

Author(s):

YIQUN MA

Keyword(s):

Stationary Solution ◽

High Energy ◽

Bloch Wave ◽

Dynamical Theory ◽

High Energy Electron ◽

Bulk Materials ◽

Periodic Surface ◽

Electron Transmission ◽

Electron Reflection ◽

Long Time

For a long time, the development of dynamical theory for HEER has been stagnated for several reasons. Although the Bloch wave method is powerful for the understanding of physical insights of electron diffraction, particularly electron transmission diffraction, it is not readily available for the simulation of various surface imperfection in electron reflection diffraction since it is basically a method for bulk materials and perfect surface. When the multislice method due to Cowley & Moodie is used for electron reflection, the “edge effects” stand firmly in the way of reaching a stationary solution for HEER. The multislice method due to Maksym & Beeby is valid only for an 2-D periodic surface.Now, a method for solving stationary solution of HEER for an arbitrary surface is available, which is called the Edge Patching method in Multislice-Only mode (the EPMO method). The analytical basis for this method can be attributed to two important characters of HEER: 1) 2-D dependence of the wave fields and 2) the Picard iteractionlike character of multislice calculation due to Cowley and Moodie in the Bragg case.

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Effects of Higher-Order Laue Zone reflections on structure images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148083 ◽

1993 ◽

Vol 51 ◽

pp. 450-451

Author(s):

H. S. Kim ◽

S. S. Sheinin

Keyword(s):

Wave Vector ◽

Theoretical Calculations ◽

Reciprocal Lattice ◽

Image Plane ◽

Bloch Wave ◽

Dynamical Theory ◽

Higher Order ◽

Lattice Image ◽

Lattice Vector ◽

Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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Phononic-Crystal Acoustic Lens by Design for Energy-Transmission Devices

IEEJ Transactions on Electronics Information and Systems ◽

10.1541/ieejeiss.132.686 ◽

2012 ◽

Vol 132 (5) ◽

pp. 686-690

Author(s):

Yusuke Kanno ◽

Kenji Tsuruta ◽

Kazuhiro Fujimori ◽

Hideki Fukano ◽

Shigeji Nogi

Keyword(s):

Phononic Crystal ◽

Energy Transmission ◽

Acoustic Lens

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Flexural Wave Band Gaps in Phononic Crystal Thick Plates with Defects

10.26678/abcm.diname2019.din2019-0002 ◽

2019 ◽

Author(s):

Edson Jansen Pedrosa de Miranda Junior ◽

Jose Maria Campos dos Santos

Keyword(s):

Phononic Crystal ◽

Band Gaps ◽

Flexural Wave ◽

Wave Band ◽

Thick Plates

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Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

Scientific Reports ◽

10.1038/s41598-021-87904-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Hai-Fei Zhu ◽

Xiao-Wei Sun ◽

Ting Song ◽

Xiao-Dong Wen ◽

Xi-Xuan Liu ◽

...

Keyword(s):

Phononic Crystal ◽

Real Life ◽

Low Frequency ◽

Acoustic Vibration ◽

Crystal Plate ◽

Frequency Noise ◽

Two Dimensional ◽

The Matrix ◽

Noise Frequency ◽

Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

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A tunable phononic crystal system for elastic ultrasonic wave control

Applied Physics Letters ◽

10.1063/5.0054937 ◽

2021 ◽

Vol 118 (22) ◽

pp. 224104

Author(s):

Yihao Song ◽

Yanfeng Shen

Keyword(s):

Ultrasonic Wave ◽

Phononic Crystal ◽

Crystal System ◽

Wave Control

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