Index of content:
Volume 1, Issue 4, December 2011
- SPECIAL TOPIC: SELECTED ARTICLES FROM PHONONICS 2011: THE FIRST INTERNATIONAL CONFERENCE ON PHONONIC CRYSTALS, METAMATERIALS AND OPTOMECHANICS, 29 MAY-2 JUNE 2011, SANTA FE, NEW MEXICO, USA
- Phononic Crystals
1(2011); http://dx.doi.org/10.1063/1.3675797View Description Hide Description
A wide range of mesoscopic phononic materials can exhibit frequency bands where transmission is forbidden, i.e. band gaps. Three different mechanisms for their origin can be distinguished, namely Bragg, hybridization and weak elastic coupling effects. Characteristicproperties of gaps of different origins are investigated and compared, for a 3D crystal of tungsten carbide beads in water, a 2D crystal of nylon rods in water, and a 3D opal-like structure of weakly sinteredaluminum beads. For the second type of crystal, it is shown that Bragg and hybridization gaps can be overlapped, allowing the study of the interaction between these two mechanisms. Atypical dispersion characteristics are demonstrated near the resonance frequency.
1(2011); http://dx.doi.org/10.1063/1.3675828View Description Hide Description
We investigate modal conversion at the boundary between a homogeneous incident medium and a phononic crystal, with consideration of the impact of symmetry on the excitation of Bloch waves. We give a quantitative criterion for the appearance of deaf Bloch waves, which are antisymmetric with respect to a symmetry axis of the phononic crystal, in the frame of generalized Fresnel formulas for reflection and transmission at the phononic crystal boundary. This criterion is used to index Bloch waves in the complex band structure of the phononic crystal, for directions of incidence along a symmetry axis. We argue that within deaf frequency ranges transmission is multi-exponential, as it is within frequency band gaps.
Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique1(2011); http://dx.doi.org/10.1063/1.3675918View Description Hide Description
Recent work has demonstrated that nanostructuring of a semiconductor material to form a phononic crystal (PnC) can significantly reduce its thermal conductivity. In this paper, we present a classical method that combines atomic-level information with the application of Bloch theory at the continuum level for the prediction of the thermal conductivity of finite-thickness PnCs with unit cells sized in the micron scale. Lattice dynamics calculations are done at the bulk material level, and the plane-wave expansion method is implemented at the macrosale PnC unit cell level. The combination of the lattice dynamics-based and continuum mechanics-based dispersion information is then used in the Callaway-Holland model to calculate the thermal transport properties of the PnC. We demonstrate that this hybrid approach provides both accurate and efficient predictions of the thermal conductivity.
In-plane confinement and waveguiding of surface acoustic waves through line defects in pillars-based phononic crystal1(2011); http://dx.doi.org/10.1063/1.3675923View Description Hide Description
We present a theoretical analysis of an in-plane confinement and a waveguiding of surface acoustic waves in pillars-based phononic crystal. The artificial crystal is made up of cylindrical pillars placed on a semi-infinite medium and arranged in a square array. With a well-chosen of the geometrical parameters, this pillars-based system can display two kinds of complete band gaps for guided waves propagating near the surface, a low frequency gap based on locally resonant mode of pillars as well as a higher frequency gap appearing at Bragg scattering regime. In addition, we demonstrate a waveguiding of surface acoustic wave inside an extended linear defect created by removing rows of pillars in the perfect crystal. We discuss the transmission and the polarization of such confined mode appearing in the higher frequency band gap. We highlight the strong similarity of such defect mode and the Rayleigh wave of free surface medium. An efficient finite element analysis is used to simulate the propagation of guided waves through silicon pillars on a silicon substrate.
Negative refraction of elastic waves in 2D phononic crystals: Contribution of resonant transmissions to the construction of the image of a point source1(2011); http://dx.doi.org/10.1063/1.3676177View Description Hide Description
Negative refraction properties of a two-dimensional phononic crystal (PC), made of a triangular lattice of steel rods embedded in epoxy are investigated both experimentally and numerically. First, experiments have been carried out on a prism shaped PC immersed in water. Then, for focusing purposes, a flat lens is considered and the construction of the image of a point source is analyzed in details, when indices are matched between the PC and the surrounding fluid medium, whereas acoustic impedances are mismatched. Optimal conditions for focusing longitudinal elastic waves by such PC flat lens are then discussed.
- Phononic Metamaterials
Resonant excitation of coupled Rayleigh waves in a short and narrow fluid channel clad between two identical metal plates1(2011); http://dx.doi.org/10.1063/1.3675800View Description Hide Description
Transmission of ultrasonic waves through a slit between two water immersed brass plates is studied for sub-wavelength plate thicknesses and slit apertures. Extraordinary high absorption is observed at discrete frequencies corresponding to resonant excitation of Rayleigh waves on the both sides of the channel. The coupling of the Rayleigh waves occurs through the fluid and the corresponding contribution to the dispersion has been theoretically derived and also experimentally confirmed. Symmetric and anti-symmetric modes are predicted but only the symmetric mode resonances have been observed. It follows from the dispersion equation that the coupled Rayleigh waves cannot be excited in a channel with apertures less than the critical one. The calculated critical aperture is in a good agreement with the measured acoustic spectra. These findings could be applied to design a broadband absorptive metamaterial.
Negative effective dynamic mass-density and stiffness: Micro-architecture and phononic transport in periodic composites1(2011); http://dx.doi.org/10.1063/1.3675939View Description Hide Description
We report the results of the calculation of negative effective density and negative effective compliance for a layered composite. We show that the frequency-dependent effective properties remain positive for cases which lack the possibility of localized resonances (a 2-phase composite) whereas they may become negative for cases where there exists a possibility of local resonance below the length-scale of the wavelength (a 3-phase composite). We also show that the introduction of damping in the system considerably affects the effective properties in the frequency region close to the resonance. It is envisaged that this demonstration of doubly negative materialcharacteristics for 1-D wave propagation would pave the way for the design and synthesis of doubly negative material response for full 3-D elastic wave propagation.
1(2011); http://dx.doi.org/10.1063/1.3676169View Description Hide Description
Recent experiments on acoustic superlens and hyperlens found anisotropicmetamaterials constructed from periodic perforated solids can be used for super-resolution imaging. Here, we present a theoretical study on the operational bandwidth of these imaging devices using the emerging framework of transformation acoustics. Within the transformation approach, both the microstructural superlens and hyperlens can be discussed using the transfer matrix method on the same footing. We show that the geometrical structure of the periodic metamaterials induces that an acoustics hyperlens has a very wide operational frequency bandwidth with its subwavelength resolution limited by the ratio of image magnification while an acoustics superlens has a very deep subwavelength resolution limited only by the periodicity of the perforations but intrinsically working at a narrow frequency bandwidth. Such investigation will become useful for designing future transformation acoustical imaging devices.
1(2011); http://dx.doi.org/10.1063/1.3676173View Description Hide Description
Piezoelectricsuperlattices are investigated as examples of internally resonating metamaterials. The multi-field coupling characteristics of the considered configuration is identified as the mechanism enabling the generation of the internal resonances, and the related achievement of unusual wave properties. Numerical studies on two-dimensional piezoelectricsuperlattices illustrate the coupled behavior of this class of periodic systems. In addition, analytical studies developed on the basis of the long wavelength approximation support the interpretation of the coupling as an internally resonant mechanism, and allow the analysis of the influence of lattice topology on the frequencies of internal resonance.
- Wave Propagation in Periodic Structures
1(2011); http://dx.doi.org/10.1063/1.3675801View Description Hide Description
The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problemk(ω) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations.
1(2011); http://dx.doi.org/10.1063/1.3676167View Description Hide Description
Lattice materials possessing a spatially periodic microstructure are suitable in weight sensitive multifunctional structural applications such as sandwich panels. They not only possess high specific stiffness but also provide opportunities to tailor acoustic and thermal properties through designing their unit cell topology. This paper seeks to understand their mechanical response under static and dynamic loads from a structural mechanics perspective combining Bloch wave theory with Finite Element Method (FEM). Bringing together results from earlier works, it is shown that three eigenvalue problems, containing the frequency and wave vector as the unknowns, can be used to analyze bulk and surface wave phenomena. The application of eigenvalue problems to band-gaps (spatially extended response), edge effects of Saint Venant type (spatially localised response), and buckling of long cellular structures is shown.
- Nanoscale Phonon Transport
1(2011); http://dx.doi.org/10.1063/1.3675798View Description Hide Description
The concept of a phononic crystal can in principle be realized at the nanoscale whenever the conditions for coherent phonon transport exist. Under such conditions, the dispersion characteristics of both the constitutive material lattice (defined by a primitive cell) and the phononic crystal lattice (defined by a supercell) contribute to the value of the thermal conductivity. It is therefore necessary in this emerging class of phononic materials to treat the lattice dynamics at both periodicity levels. Here we demonstrate the utility of using supercell lattice dynamics to investigate the thermal transport behavior of three-dimensional nanoscale phononic crystals formed from silicon and cubic voids of vacuum. The periodicity of the voids follows a simple cubic arrangement with a lattice constant that is around an order of magnitude larger than that of the bulk crystalline silicon primitive cell. We consider an atomic-scale supercell which incorporates all the details of the silicon atomic locations and the void geometry. For this supercell, we compute the phonon band structure and subsequently predict the thermal conductivity following the Callaway-Holland model. Our findings dictate that for an analysis based on supercell lattice dynamics to be representative of the properties of the underlying lattice model, a minimum supercell size is needed along with a minimum wave vector sampling resolution. Below these minimum values, a thermal conductivity prediction of a bulk material based on a supercell will not adequately recover the value obtained based on a primitive cell. Furthermore, our results show that for the relatively small voids and void spacings we consider (where boundary scattering is dominant), dispersion at the phononic crystal unit cell level plays a noticeable role in determining the thermal conductivity.
Calculation of phonon dispersion in carbon nanotubes using a continuum-atomistic finite element approach1(2011); http://dx.doi.org/10.1063/1.3675917View Description Hide Description
Dispersion calculations are presented for cylindrical carbon nanotubes using a manifold-based continuum-atomistic finite element formulation combined with Bloch analysis. The formulated finite elements allow any (n,m) chiralnanotube, or mixed tubes formed by periodically-repeating heterojunctions, to be examined quickly and accurately using only three input parameters (radius, chiral angle, and unit cell length) and a trivial structured mesh, thus avoiding the tedious geometry generation and energy minimization tasks associated with ab initio and lattice dynamics-based techniques. A critical assessment of the technique is pursued to determine the validity range of the resulting dispersion calculations, and to identify any dispersion anomalies. Two small anomalies in the dispersion curves are documented, which can be easily identified and therefore rectified. They include difficulty in achieving a zero energy point for the acoustic twisting phonon, and a branch veering in nanotubes with nonzero chiral angle. The twisting mode quickly restores its correct group velocity as wavenumber increases, while the branch veering is associated with a rapid exchange of eigenvectors at the veering point, which also lessens its impact. By taking into account the two noted anomalies, accurate predictions of acoustic and low-frequency optical branches can be achieved out to the midpoint of the first Brillouin zone.
Asymmetric energy transport in defected boron nitride nanoribbons: Implications for thermal rectification1(2011); http://dx.doi.org/10.1063/1.3675924View Description Hide Description
Using molecular dynamics simulations, the thermal transport properties of boron nitride nanoribbons (BNNR) containing geometrically-asymmetric triangular nano-vacancies were investigated. By suitably interpreting the time-evolution of spatially decomposed heat-current autocorrelation function in terms of phonon propagation characteristics, we have demonstrated the possibility of observing defect induced direction-dependent thermal transport in BNNR. This was further confirmed by appropriate analysis of direction dependent thermal diffusivity estimations in BNNR.
1(2011); http://dx.doi.org/10.1063/1.3675925View Description Hide Description
We discuss computational analysis of phononic thermal conduction in the suspended membrane geometry, in the case where heat can flow out radially in two dimensions from a central source. As we are mostly interested in the low-temperature behavior where bulk scattering of phonons becomes irrelevant, we study the limit where all phononscattering takes place at the membrane surfaces. Moreover, we limit the discussion here to the case where this surface scattering is fully diffusive, the so called Casimir limit. Our analysis shows that in the two-dimensional case, no analytic results are available, in contrast to the well known 1D Casimir limit. Numerical solutions are presented for the temperature profiles in the membrane radial direction, for several different membrane thicknesses and heater diameters. Our results can be applied, for example, in the design of membrane-supported bolometric radiation detectors.
1(2011); http://dx.doi.org/10.1063/1.3676171View Description Hide Description
This work presents a derivation of phonon-mass impurity scattering rates applicable to dispersive phonon systems. This form of mass impurity scattering is compared with the previously accepted form assuming a nondispersive crystal by calculating the thermal conductivity of Si. The mass impurity scattering rate determined from this approach considering dispersion is in excellent agreement with theoretical calculations, where the scattering rates determined from the dispersionless model under predict the role of phonon-mass impurity scattering in thermal transport by over an order of magnitude.
- RF Phononics
1(2011); http://dx.doi.org/10.1063/1.3675799View Description Hide Description
We discuss theoretically the simultaneous existence of phoxonic, i.e., dual phononic and photonic,band gaps in a periodic silicon strip waveguide. The unit-cell of this one-dimensional waveguide contains a hole in the middle and two symmetric stubs on the sides. Indeed, stubs and holes are respectively favorable for creating a phononic and a photonic band gap. Appropriate geometrical parameters allow us to obtain a complete phononic gap together with a photonic gap of a given polarization and symmetry. The insertion of a cavity inside the perfect structure provides simultaneous confinement of acoustic and optical waves suitable to enhance the phonon-photon interaction.
1(2011); http://dx.doi.org/10.1063/1.3675802View Description Hide Description
The resonant modes of elastic waves in disk resonators are computationally studied with the finite difference time domain method. Different materials examined for the disk such as platinum and silicon. The effect of a glass substrate is also important especially in the case of silicon disks because of the similarity of sound velocities and mass densities between the two materials. The possibility of using those structures as sensors is also considered.
On chip complex signal processing devices using coupled phononic crystal slab resonators and waveguides1(2011); http://dx.doi.org/10.1063/1.3676168View Description Hide Description
In this paper, we report the evidence for the possibility of achieving complex signal processing functionalities such as multiplexing/demultiplexing at high frequencies using phononic crystal (PnC) slabs. It is shown that such functionalities can be obtained by appropriate cross-coupling of PnC resonators and waveguides. PnC waveguides and waveguide-based resonators are realized and cross-coupled through two different methods of mechanical coupling (i.e., direct coupling and side coupling). Waveguide-based PnC resonators are employed because of their high-Q, compactness, large spurious-free spectral ranges, and the possibility of better control over coupling to PnC waveguides. It is shown that by modifying the defects in the formation of the resonators, the frequency of the resonance can be tuned.