Phononic Materials Research Articles

Near-zero-index materials for photonics

The discovery, design and development of materials are critically linked to advances in many areas of research, and optics is no exception. Recently, the spectral region in which the index of refraction of a material approaches zero has become a topic of interest owing to fascinating phenomena, such as static light, enhanced nonlinearities, light tunnelling and emission tailoring. As a result, such near-zero-index (NZI) materials bridge materials development and optical research. Here, we review recent advances in various classes of NZI platforms, with particular focus on homogeneous materials, including metals, semi-metals, doped semiconductors, phononic and interband materials, discussing the novel optical phenomena that they can produce. We also overview the developments in a key area for NZI materials, nonlinear optics, and survey some of the future goals in the field, such as the development of tailorable NZI materials in the visible range and the improvement of the theoretical description of the nonlinear enhancements in these materials. Materials with a near-zero optical refractive index have stimulated much interest, as they can be used to investigate fundamental light–matter interactions. This Review surveys the wide range of near-zero-index homogeneous materials that have been explored and highlights the key experimental advancements they have enabled.

Irradiation of Transition Metal Dichalcogenides Using a Focused Ion Beam: Controlled Single‐Atom Defect Creation

AbstractManipulation and structural modifications of 2D materials for nanoelectronic and nanofluidic applications remain obstacles to their industrial‐scale implementation. Here, it is demonstrated that a 30 kV focused ion beam can be utilized to engineer defects and tailor the atomic, optoelectronic, and structural properties of monolayer transition metal dichalcogenides (TMDs). Aberration‐corrected scanning transmission electron microscopy is used to reveal the presence of defects with sizes from the single atom to 50 nm in molybdenum (MoS2) and tungsten disulfide (WS2) caused by irradiation doses from 1013 to 1016 ions cm−2. Irradiated regions across millimeter‐length scales of multiple devices are sampled and analyzed at the atomic scale in order to obtain a quantitative picture of defect sizes and densities. Precise dose value calculations are also presented, which accurately capture the spatial distribution of defects in irradiated 2D materials. Changes in phononic and optoelectronic material properties are probed via Raman and photoluminescence spectroscopy. The dependence of defect properties on sample parameters such as underlying substrate and TMD material is also investigated. The results shown here lend the way to the fabrication and processing of TMD nanodevices.

Surface phonon polaritonics made simple: great as plasmonics but lower losses

Phonon-polaritons offer an exciting avenue in nanophotonics. We comment on the novel nanofabrication approach presented by Bo Qiang et al. in this issue of Advanced Photonics. Their approach to phononic material allows better radiation manipulation, and high Q-factors.

Anomalous wave polarization through a 3D periodic auxetic lattice

Solid media supports both longitudinal and shear wave polarizations, providing a rich platform for designing phononic materials with prescribed wave filtering, engineered mode conversions, negative refraction, and other unique properties. While longitudinal waves almost always propagate at a faster velocity than shear waves in natural materials, tailoring the polarization of the faster wave velocity could enable unique control over wave propagation properties. Here, we present a three-dimensional periodic “bowtie” lattice that exhibits a shift in the faster wave polarization from the quasi-longitudinal to quasi-transverse wave in an anisotropic plane. We observe that this shift, termed “anomalous wave polarization”, is possible when the lattice behaves auxetically. Using the finite element method, we show that the wave polarizations in the bowtie lattice depend on certain geometric parameters and the wave propagation direction. We use wave velocity information to evaluate the lattice effective properties using the Bloch-wave homogenization approach and confirm the required elastic condition for the polarization anomaly in an anisotropic plane. We also emphasize the importance of identifying the wave polarization along with the wave velocity classification for lattice effective property evaluation. This lattice behavior will be useful for designing mode-converting metamaterials that have potential application in non-destructive testing and bio-medical ultrasounds.Solid media supports both longitudinal and shear wave polarizations, providing a rich platform for designing phononic materials with prescribed wave filtering, engineered mode conversions, negative refraction, and other unique properties. While longitudinal waves almost always propagate at a faster velocity than shear waves in natural materials, tailoring the polarization of the faster wave velocity could enable unique control over wave propagation properties. Here, we present a three-dimensional periodic “bowtie” lattice that exhibits a shift in the faster wave polarization from the quasi-longitudinal to quasi-transverse wave in an anisotropic plane. We observe that this shift, termed “anomalous wave polarization”, is possible when the lattice behaves auxetically. Using the finite element method, we show that the wave polarizations in the bowtie lattice depend on certain geometric parameters and the wave propagation direction. We use wave velocity information to evaluate the lattice effective properties ...

Hypersonic Surface Phononic Bandgap Demonstration in a CMOS-Compatible Pillar-Based Piezoelectric Structure on Silicon

The promise of surface phononic crystals (PnCs) for $e.g.$ rf signal processing in wireless communication (like your mobile phone) has not been realized, due to the complexity of acoustic wave propagation in such structures, plus the lack of a low-loss, CMOS-compatible platform. The authors identify a wide, hypersonic surface phononic band gap in a pillar-based surface PnC. The significance of their platform lies in the reduced phononic material loss in dielectric pillars, and the use of CMOS-compatible AlN. This allows dense integration of low-loss hypersonic devices with electronics on the same die, enabling many exciting applications of surface PnCs.

Multiple flexural-wave attenuation zones of periodic slabs with cross-like holes on an arbitrary oblique lattice: Numerical and experimental investigation

The exploration for large and low frequency attenuation zones is one of the principal problems probed in phononic materials and structures. The flexural-wave attenuation zone properties of periodically perforated slabs with cross-like holes were investigated using ANSYS finite element software to obtain flexural dispersion curves conveniently and individually. The influence of geometric parameters, including hole shape and plate thickness, on attenuation zones was investigated. Unlike conventional phononic attenuation zone designs, typical cells with an arbitrary oblique lattice were examined. The dynamic responses of the finite periodic slabs using several designed cells were analysed numerically and experimentally under harmonic excitation conditions. The results showed that periodic slabs with cross-like holes on an oblique lattice can generate lower and multiple attenuation zones compared to square, circular, and diamond-shaped holes. The vibration modes at the attenuation zone edges were calculated and analysed to illustrate the zones’ generation mechanism. The attenuation ranges obtained numerically were generally consistent with those of the experiment. This research showed that attenuation zones of periodically perforated slabs may have potential applications in acoustic and vibration screens.

Three-Phase Microstructure Topology Optimization of Two-Dimensional Phononic Bandgap Materials Using Genetic Algorithms

The bandgap, an important characteristic of the periodic structure, is dispersion-related, which can be designed by tailoring the layout of materials within the periodic microstructures. A typical example of a periodic structure is phononic crystals (PnCs), which are traditionally fabricated from two-phase materials. Herein, we investigate the topologies of periodic three-phase PnCs. The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm, and three case studies are proposed to obtain the following: (1) the maximum relative bandgap width, (2) the maximum absolute bandgap width, and (3) the maximum bandgap at a specified frequency. More importantly, the three-phase material provides significant advantages compared to the typical two-phase materials, such as a low-frequency bandgap. This research is expected to contribute highly to vibration and noise isolation, elastic wave filters, and acoustic devices.

A reduced micromorphic model for multiscale materials and its applications in wave propagation

In this study, a reduced micromorphic model for multiscale materials is developed. In the context of this model, multiscale materials are modeled with deformable microstructures. The deformation energy is formed depending on microstrain and macroscopic strain residual fields. The constitutive equations according to the reduced micromorphic model only depend on eight material coefficients for linear elastic materials. These material coefficients are related to the material micro/macro-stiffnesses and the material’s microstructural features. The wave dispersions in multiscale materials are then derived according to the reduced micromorphic model. It is revealed that this model can reflect nine dispersion curves (three acoustic modes and six optics) for a two-scale material. To demonstrate the effectiveness of the proposed model, the wave propagation characteristics, the band structure, and the absolute bandgap features of phononic materials are investigated. It is demonstrated that the reduced micromorphic model can effectively reflect the increase in the bandgap width with the increase in the filling factor in a composite phononic material with square lattices.

Spiral-Based Phononic Plates: From Wave Beaming to Topological Insulators.

Phononic crystals and metamaterials can sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms are mostly Bragg scattering, local resonances, and inertial amplification, derived from adhoc, often problem-specific geometries of the materials' building blocks. Here, we present a platform that ultilizes a lattice of spiraling unit cells to create phononic materials encompassing Bragg scattering, local resonances, and inertial amplification. We present two examples of phononic materials that can control waves with wavelengths much larger than the lattice's periodicity. (1)A wave beaming plate, which can beam waves at arbitrary angles, independent of the lattice vectors. We show that the beaming trajectory can be continuously tuned, by varying the driving frequency or the spirals' orientation. (2)A topological insulator plate, which derives its properties from a resonance-based Dirac cone below the Bragg limit of the structured lattice of spirals.

Battling Retardation and Nonlocality: The Hunt for the Ultimate Plasmonic Cascade Nanolens

The plasmonic nanolens was proposed as a deterministic method to achieve high field enhancements and, hence, enable single molecule photonic devices, but experimental results have failed to live up to these expectations, and recent theoretical works have brought its long-assumed advantages into doubt. To explore the limits of cascade field enhancements, we consider possible quantum solutions (“going small”) and use phononic materials at longer wavelengths (“going large”). We find that entering the quantum plasmonic limit to enhance the size ratio between constituent nanoparticles is not a fruitful strategy, as the increased electron-surface scattering decreases the field enhancement by over an order of magnitude. Using larger nanoparticles is limited in metals by retardation, but using localized surface phonon polaritons, which can be excited in polar dielectrics, is an effective strategy due to the lower energy phonon frequency and high quality factor. We compare the nanolens against the more usual dimer...

Near-field radiative transfer in spectrally tunable double-layer phonon-polaritonic metamaterials

Understanding of near-field radiative transfer is crucial for many advanced applications such as nanoscale energy harvesting, nano-manufacturing, thermal imaging, and radiative cooling. Near-field radiative transfer has been shown to be dependent on the material and morphological characteristics of systems, the gap distances between structures, and their temperatures. Surface interactions of phononic materials in close proximity of each other has led to promising results for novel near-field radiative transfer applications. For systems involving thin films and small structures, as the dimension(s) through which the heat transfer takes place is/are on the order of sub-micrometers, it is important to identify the impacts of size-related parameters on the results. In this work, we investigated the impact of geometric design and characteristics in a double-layer metamaterial system made up of GaN, SiC, h-BN; all of which have potential importance in micro-and nano-technological systems. The numerical study is performed using the NF-RT-FDTD algorithm, which is a versatile method to study near-field thermal radiation performances of advanced configurations of materials, even with arbitrary shapes. We have systematically investigated the thin film thickness, the substrate material, and the nanostructured surfaces effects, and reported on the best combination of scenarios among the studied cases to obtain maximum enhancement of radiative heat transfer rate. The findings of this work may be used in design and fabrication of new corrugated surfaces for energy harvesting purposes.

Non-reciprocal elastic wave propagation in 2D phononic membranes with spatiotemporally varying material properties

One-dimensional phononic materials with material fields traveling simultaneously in space and time have been shown to break elastodynamic reciprocity resulting in unique wave propagation features. In the present work, a comprehensive mathematical analysis is presented to characterize and fully predict the non-reciprocal wave dispersion in two-dimensional space. The analytical dispersion relations, in the presence of the spatiotemporal material variations, are validated numerically using finite 2D membranes with a prescribed number of cells. Using omnidirectional excitations at the membrane's center, wave propagations are shown to exhibit directional asymmetry that increases drastically in the direction of the material travel and vanishes in the direction perpendicular to it. The topological nature of the predicted dispersion in different propagation directions are evaluated using the computed Chern numbers. Finally, the degree of the 2D non-reciprocity is quantified using a non-reciprocity index (NRI) which confirms the theoretical dispersion predictions as well as the finite simulations. The presented framework can be extended to plate-type structures as well as 3D spatiotemporally modulated phononic crystals.

A review of computational phononics: the bulk, interfaces, and surfaces

Broad-based interest in microscale heat transport in novel materials, engineered phononic materials, metamaterials, and their relevant systems has created significant demand for computational approaches to aid in investigation and design of materials that support phonons. This review describes the significant improvements that have been made and new needs that have emerged for capabilities associated with the computability of phonons. The technical scope encompasses issues, especially relevant to bulk, interface, and surface effects. Traditional approaches such as molecular dynamics, lattice dynamics, and Boltzmann transport equation continue to advance the field but are frequently extended to the limits of their physical or numerical validity. New materials beyond traditional group-IV, III–V, and II–VI semiconductors, phenomena that critically depend on scattering, such as in low-dimensional nanostructures, materials with interior surfaces and defects, and in high-temperature environments, continue to push these limits. The basis for the traditional calculation methods shares their origins with the earliest theories for thermal transport, acoustic waves in solids, spectroscopy and dynamical crystal lattices. These will remain in wide use in the future. But computing methods and the accompanying advances in microprocessor technologies have enabled growth of phonon computing models and methods in sophistication, accuracy, fidelity and complexity that will lead to fundamental impacts beyond the classic types of problems for which they were developed. With their increasingly integrated use for design and research, the myriad developments that presently exist must be understood for their suitability for certain applications and their ability to aid in the pursuit of new technologies.

Self-controlled wave propagation in hyperelastic media

We demonstrate theoretically that an ultrasonic wave propagating in a hyperelastic medium can self-control its phase velocities. This phenomenon occurs because the propagation of the ultrasonic wave generates acoustic radiation stresses in the medium, which can induce large deformation of the medium with significant stiffening effect. In turn, such deformation reshapes the wave propagation while the deformation stiffening changes significantly the phase velocities of the wave till the acoustic radiation stresses are balanced by elastic stresses in the current configuration of the hyperelastic medium. As a result of deformation stiffening, an initially isotropic medium becomes anisotropic, thus enabling self-control or self-bending of the wave propagation. We further reveal that, due to snap-through instability of acoustomechanical deformation in the hyperelastic medium, the ultrasonic wave can discontinuously switch its phase velocities from one state to another by jumping over a large unstable regime. This self-control and switchable mechanism of ultrasonic wave propagation in homogenous hyperelastic media offers innovative design opportunities for phononic, thermal and acoustic materials and devices.

Single phase 3D phononic band gap material

Phononic band gap materials are capable of prohibiting the propagation of mechanical waves in certain frequency ranges. Band gaps are produced by combining different phases with different properties within one material. In this paper, we present a novel cellular material consisting of only one phase with a phononic band gap. Different phases are modelled by lattice structure design based on eigenmode analysis. Test samples are built from a titanium alloy using selective electron beam melting. For the first time, the predicted phononic band gaps via FEM simulation are experimentally verified. In addition, it is shown how the position and extension of the band gaps can be tuned by utilizing knowledge-based design.

Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia

In this paper the relaxed micromorphic continuum model with weighted free and gradient micro-inertia is used to describe the dynamical behavior of a real two-dimensional phononic crystal for a wide range of wavelengths. In particular, a periodic structure with specific micro-structural topology and mechanical properties, capable of opening a phononic band-gap, is chosen with the criterion of showing a low degree of anisotropy (the band-gap is almost independent of the direction of propagation of the traveling wave). A Bloch wave analysis is performed to obtain the dispersion curves and the corresponding vibrational modes of the periodic structure. A linear-elastic, isotropic, relaxed micromorphic model including both a free micro-inertia (related to free vibrations of the microstructures) and a gradient micro-inertia (related to the motions of the microstructure which are coupled to the macro-deformation of the unit cell) is introduced and particularized to the case of plane wave propagation. The parameters of the relaxed model, which are independent of frequency, are then calibrated on the dispersion curves of the phononic crystal showing an excellent agreement in terms of both dispersion curves and vibrational modes. Almost all the homogenized elastic parameters of the relaxed micromorphic model result to be determined. This opens the way to the design of morphologically complex meta-structures which make use of the chosen phononic material as the basic building block and which preserve its ability of “stopping” elastic wave propagation at the scale of the structure.

An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures

Owing to their ability to block propagating waves at certain frequencies, phononic materials of self-repeating cells are widely appealing for acoustic mitigation and vibration suppression applications. The stop band behavior achieved via Bragg scattering in phononic media is most commonly evaluated using wave propagation models which predict gaps in the dispersion relations of the individual unit cells for a given frequency range. These models are in many ways limited when analyzing phononic structures with dissipative constituents and need further adjustments to account for viscous damping given by complex elastic moduli and frequency-dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power flow in finite phononic structures. It is shown that the steady-state spatial propagation of vibrational power flow initiated by an external disturbance reflects the wave propagation pattern in the phononic medium and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The treatment is shown to be very effective for phononic structures with viscoelastic components and provides a clear distinction between Bragg scattering effects and wave attenuation due to material damping. Since the approach is integrated with finite element methods, the presented analysis can be extended to two-dimensional lattices with complex geometries and multiple material constituents.

Confinement of phonon propagation in laser deposited tungsten/polycarbonate multilayers

Nanoscale multilayer thin films of W and PC (Polycarbonate) show, due to the great difference of the components’ characteristics, fascinating properties for a variety of possible applications and provide an interesting research field, but are hard to fabricate with low layer thicknesses. Because of the great acoustic mismatch between the two materials, such nanoscale structures are promising candidates for new phononic materials, where phonon propagation is strongly reduced. In this article we show for the first time that W/PC-multilayers can indeed be grown with high quality by pulsed laser deposition. We analyzed the polymer properties depending on the laser fluence used for deposition, which enabled us to find best experimental conditions for the fabrication of high-acoustic-mismatch W/PC multilayers. The multilayers were analyzed by fs pump-probe spectroscopy showing that phonon dynamics on the ps time-scale can strongly be tailored by structural design. While already periodic multilayers exhibit strong phonon localization, especially aperiodic structures present outstandingly low phonon propagation properties making such 1D-layered W/PC nano-structures interesting for new phononic applications.

A Gradient-Based Optimization Method for the Design of Layered Phononic Band-Gap Materials

Phononic materials with specific band-gap characteristics at desired frequency ranges are in great demand for vibration and noise isolation, elastic wave filters, and acoustic devices. The attenuation coefficient curve depicts both the frequency range of band gap and the attenuation of elastic wave, where the frequency ranges corresponding to the none-zero attenuation coefficients are band gaps. Therefore, the band-gap characteristics can be achieved through maximizing the attenuation coefficient at the corresponding frequency or within the corresponding frequency range. Because the attenuation coefficient curve is not smooth in the frequency domain, the gradient-based optimization methods cannot be directly used in the design optimization of phononic band-gap materials to achieve the maximum attenuation within the desired frequency range. To overcome this difficulty, the objective of maximizing the attenuation coefficient is transformed into maximizing its Cosine, and in this way, the objective function is smoothed and becomes differentiable. Based on this objective function, a novel gradient-based optimization approach is proposed to open the band gap at a prescribed frequency range and to further maximize the attenuation efficiency of the elastic wave at a specific frequency or within a prescribed frequency range. Numerical results demonstrate the effectiveness of the proposed gradient-based optimization method for enhancing the wave attenuation properties.

Application of plane wave expansion and stiffness matrix methods to study transmission properties and guided mode of phononic plates

Numerical procedure based on plane wave expansion and stiffness matrix method is developed to calculate the transmission factor of a micro two-dimensional phononic plate. Calculations of the dispersion curve have been achieved by introducing particular functions which transform motion equations into an eigenvalue problem. The state vector has been generalized to a phononic material, it leads to a comparatively convenient matrix formulation. The influence of the layer number on the transmission factor is studied. In addition, our interest is focused on the observed gap and how it behaves when phononic structure undergoes a slight change. The result shows that if the central phononic layer is replaced by one or two homogeneous layers, guided modes originate inside the frequency band gaps.