Localized Resonance Research Articles

Time-Domain-Filtered Terahertz Nanoscopy of Intrinsic Light-Matter Interactions.

Terahertz (THz) technology holds great potential across diverse applications, including biosensing and information communications, but conventional far-field techniques are limited by diffraction. Near-field optical microscopy overcomes this barrier through a sharp tip that concentrates incident THz waves into nanometric volumes, detecting scattered near-field to reveal nanoscale optical properties. However, owing to the large THz wavelengths, resonant surface waves arising on the tip and cantilever obscure the intrinsic response. Here we combine near-field microscopy with THz time-domain spectroscopy and implement time-domain filtering with an elongated cantilever to eliminate this artifact, achieving intrinsic nanospectroscopy and nanoimaging. By applying this technique, we distinguish and characterize historical pigments of an ancient sculpture, such as vermilion and red lead, on the nanoscale. We also unravel deep-subwavelength localized resonance modes in THz optical antennas, demonstrating capabilities for THz nanophotonics. Our work advances THz nanoimaging and nanospectroscopy techniques to probe intrinsic nanoscale THz light-matter interactions.

Subwavelength topological interface modes in a multilayered vibroacoustic metamaterial

We present a systematic and rigorous analytical approach, based on the transfer matrix methodology, to study the existence, evolution, and robustness of subwavelength topological interface states in practical multilayered vibroacoustic phononic lattices. These lattices, composed of membrane-air cavity unit cells, exhibit complex band structures with various bandgaps, including Bragg, band-splitting induced, local resonance, and plasma bandgaps. Focusing on the challenging low-frequency range and assuming axisymmetric modes, we show that topological interface states are confined to Bragg-like band-splitting induced bandgaps. Unlike the Su-Schrieffer-Heeger model, the vibroacoustic lattice exhibits diverse topological phase transitions across infinite bands, enabling broadband, multi-frequency vibroacoustics in the subwavelength regime. We establish three criteria for the existence of these states: the Zak phase, surface impedance, and a new reflection coefficient concept, all derived from transfer matrix components. Notably, we provide an explicit expression for the exact location of topological interface states within the band structure, offering insight for their predictive implementation. We confirm the robustness of these states against structural variations and identify delocalization as bandgaps narrow. Our work provides a complete and exact analytical characterization of topological interface states, demonstrating the effectiveness of the transfer matrix method. Beyond its analytical depth, our approach provides a useful framework and design tool for topological phononic lattices, advancing applications such as efficient sound filters, waveguides, noise control, and acoustic sensors in the subwavelength regime. Its versatility extends beyond the vibroacoustic systems, encompassing a broader range of phononic and photonic crystals with repetitive inversion-symmetric unit cells.

Attenuation of bulk waves using locally resonant soil-coupled metabarriers

Abstract Low frequency ground-borne vibrations generated by transport infrastructure are one of the most serious causes of disturbance to the general population. One possibility to reduce this problem is to use the wave filtering properties of elastic metamaterials. However, their integration in the soil complicates the prediction of their response, and the influence of soil-structure interaction needs to be correctly evaluated for an efficient design. The aim of this work is to experimentally evaluate the efficiency of metamaterial trench barriers set in soil in attenuating vibrations, using low-frequency local resonance mechanisms. A lab scale model is proposed comprising different resonating structures and a cylindrical encasement is adopted to couple the structure to the soil. The influence of various parameters is evaluated, such as metamaterial structure, geometrical characteristics of the resonator, and constituent materials. Finite Element simulations are used to develop a suitable design, analysing mode shapes and resonance frequencies of structures with and without the surrounding encasement. Experimental modal analysis is then performed on the corresponding fabricated samples, providing both model validation and out-of-soil mechanical characterization. Finally, vibration transmission loss measurements are performed in a setup in which different resonant metamaterial barriers are embedded into the soil sample, allowing the evaluation of barrier performance. Results indicate that the metamaterial structures provide good attenuation of vibrations in selected intervals in the low to high frequency range (1–5 kHz), demonstrating the feasibility of the approach in a scaled sample. Preliminary data regarding the structures providing preferable design characteristics is also obtained. These results can be useful for the design of trench barriers scaled to large dimensions in more realistic applicative settings.

Deep learning-assisted local resonance strategy for accurate internal damage imaging in composites

In this paper, we propose a deep neural network-assisted strategy to accurately and efficiently identify local defect resonance (LDR) modes and accurately image the internal damage in composites. A two-dimensional convolutional neural network (2D-CNN) model was constructed to identify LDR modes. The frequency-domain contour maps were used as input data, given that the LDR phenomenon exhibits discernible physical attributes in the frequency domain that are conducive to deep neural network assimilation. The obtained results demonstrate effective training outcomes and transferability, even with a limited number of samples. The LDR modes are efficiently extracted by the developed 2D-CNN model and used to obtain the accurate imaging of internal damages in composites.

Metaharvesting: emergent energy harvesting by piezoelectric metamaterials

Vibration energy harvesting is a technology that enables electric power generation by augmenting vibrating materials or structures with piezoelectric elements. In a recent work, we quantified the intrinsic energy-harvesting availability (EHA) of a piezoelectric phononic crystal (Piezo-PnC) by calculating its damping ratio across the Brillouin zone and subtracting off the damping ratio of the corresponding non-piezoelectric version of the phononic crystal. It was highlighted that the resulting quantity indicates the amount of useful energy available for harvesting and is independent of the finite structure size and boundary conditions and of any forcing conditions. Here, we investigate the intrinsic EHA of two other material systems chosen to be statically equivalent to a given Piezo-PnC: a piezoelectric locally resonant metamaterial (Piezo-LRM) and a piezoelectric inertially amplified metamaterial (Piezo-IAM). Upon comparing with the intrinsic EHA of the Piezo-PnC, we observe an emergence of energy-harvesting capacity, a phenomenon we refer to as metaharvesting. This is analogous to the concept of metadamping, except the quantity evaluated is associated with piezoelectric energy harvesting rather than raw dissipation. Our results show that the intrinsic EHA is enhanced by local resonances and enhanced further by inertial amplification. These findings offer a new paradigm for the design—at the fundamental level—of architectured piezoelectric materials with superior energy-harvesting capacity.

Tunable underwater sound absorption via piezoelectric materials with local resonators

In recent years, piezoelectric composite materials have been widely used in the design of underwater anechoic coatings due to their adaptability to tuning parameters. However, there are also some shortcomings, such as a single dissipation mechanism, narrow bandwidth, and poor low-frequency sound absorption. This work proposes an acoustic composite structure combining piezoelectric composite materials with local resonance units, which effectively enhances the sound absorption performance of the structure through the coupling effect of the piezoelectric energy consumption mechanism and local resonance mechanism. Compared to conventional acoustic structures, the proposed acoustic composite structure not only has a strong low-frequency sound absorption effect but also enriches the mid-high frequency sound absorption modes by connecting shunt damping circuits. On this basis, the effect of piezoelectric parameters and resonator morphological properties on structural sound absorption performance is further investigated, and the results show that the designed structure has the characteristic of sound absorption performance that is tunable. In addition, key factors affecting the sound absorption performance of the structure have been optimized to achieve better broadband sound absorption performance. This work may provide valuable ideas for the development of low-frequency broadband adjustable underwater sound-absorbing coatings.

Bandgap characteristics of four component periodic pile barriers in passive vibration isolation

Based on the local resonance theory, the vibration isolation performance of four-component periodic pile barriers consisting of a matrix, an outer pipe, an inner pipe, and a pile core was investigated using the finite element method (FEM). This configuration is contrasted with traditional three-component periodic pile barriers, which are composed of a matrix, a pipe, and a pile core. The four-component systems demonstrate significantly broader bandgaps compared to three-component systems. To validate the efficiency of the FEM, model test on pile barriers were conducted, facilitating a comparison between the FEM and experimental observations of bandgap characteristics. Additionally, the effects of the outer pipe’s density, elastic modulus, and thickness on the complete bandgap characteristics were comprehensively studied within the four-component structure. It is found that the broadest vibration isolation band gaps occur under hexagonal arrangement pattern. In square and hexagonal lattice configurations, the density, elastic modulus, and thickness of the outer pipe pile’s pile have predominantly influenced the upper bound frequency (UBF). There has been a positive correlation between the elastic modulus and the UBF, while the density and thickness have shown inverse relationships. Moreover, there exists a elastic modulus threshold, marking a transition in the displacement mode of the UBF, from the outer irreducible Brillouin zone (M or X) to the inner zone (Γ). Once the threshold is exceeded, both the vibration displacement mode and the width of bandgap remain substantially unchanged. The results obtained in the present paper are very useful for the design and application of periodic pile barriers in ambient vibration reduction.

Arrest behavior of local resonators connected by nonlocal interaction in elastic wave metamaterials with machine learning prediction

Arrest behavior of local resonators connected by nonlocal interaction in elastic wave metamaterials with machine learning prediction

Breakdown of thermalization in spin chains with single-ion anisotropy

The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with S≥1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S\\ge 1/2$$\\end{document} within the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_1-J_2,$$\\end{document} incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppresses thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in S=1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S=1/2$$\\end{document} chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized S≥1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S\\ge 1/2$$\\end{document} systems.

Optical spectra of silver clusters and nanoparticles from 4 to 923 atoms from the TDDFT+U method

The localized surface-plasmon resonances of coinage-metal clusters and nanoparticles enable many applications, the conception and necessary optimization of which require precise theoretical description and understanding. However, for the size range from few-atom clusters through nanoparticles of a few nanometers, where quantum effects and atomistic structure play a significant role, none of the methods employed previously has been able to provide high-quality spectra for all sizes. The main problem is the description of the filled shells of d electrons which influence the optical response decisively. We show that the DFT+U method, employed with real-time time-dependent density-functional theory calculations (RT-TDDFT), provides spectra in good agreement with experiment for silver clusters ranging from 4 to 923 atoms, the latter representing a nanoparticle of 3 nm. Both the electron-hole-type discrete spectra of the smallest clusters and the broad plasmon resonances of the larger sizes are obtained. All calculations use the value of the effective U parameter that provides good results in bulk silver. The agreement with experiment for all sizes shows that the U parameter is surprisingly transferable. Our results open the pathway for calculations of many practically relevant systems including clusters coupled to bio-molecules or to other nano-objects.

Phonon transmission and localization in disordered side branching graphene aperiodic lattice

Blocking phonon transport via localized resonance is a crucial method for controlling heat transfer and enhancing thermoelectric performance in nanostructures. However, the effects of disorder and asymmetrically distributed side branches on thermal transport and local resonant hybridization in two-dimensional materials remain insufficiently understood. In this work, we investigate the influence of symmetric and asymmetric disordered side branches on phonon transport in branching graphene superlattices. Our results demonstrate that aperiodic superlattices (ap-SL) can reduce thermal conductivity by up to 21% compared to periodic superlattices. The reduction in thermal conductivity in ap-SL is primarily due to phonon Anderson localization caused by disordered side branches. Interestingly, the localization lengths of symmetric and asymmetric ap-SLs are comparable, resulting in similar thermal conductivity in both cases. This finding suggests that the randomness in the upper and lower branches of asymmetric graphene superlattices does not significantly affect phonon transmission. Consequently, our work indicates that differences in symmetry between the upper and lower edge branches of graphene nanoribbons can be disregarded during experimental preparation without influencing their thermal conductivity.

Plasmon-enhanced two photon excited emission from edges of one-dimensional plasmonic hotspots with continuous-wave laser excitation.

One-dimensional junctions between parallelly and closely arranged multiple silver nanowires (NWs) exhibit a large electromagnetic (EM) enhancement factor (FR) owing to both localized and surface plasmon resonances. Such junctions are referred to as one-dimensional (1D) hotspots (HSs). This study found that two-photon excited emissions, such as hyper-Rayleigh, hyper-Raman, and two-photon fluorescence of dye molecules, are generated at the edge of 1D HSs of NW dimers with continuous-wave near-infrared (NIR) laser excitation and propagated through 1D HSs; however, they were not generated from the centers of 1D HSs. Numerical EM calculations showed that FR of the NIR region for the edges of 1D HSs was larger than that for the centers by ∼102 times, resulting in the observation of two-photon excited emissions only from the edge of 1D HSs. The analysis of the NW dimer gap distance dependence of FR revealed that the lowest surface plasmon (SP) mode, compressed and localized at the edges of 1D HSs, was the origin of the large FR in the NIR region. The propagation of two-photon-excited emissions was supported by the higher-order coupled SP mode.

A new local resonance metamaterial for flat and cylindrical structures depended on elastic chiral spiral beams

A new local resonance metamaterial for flat and cylindrical structures depended on elastic chiral spiral beams

Additively Manufactured Stainless Steel Wind Tunnel Model Support Featuring Honeycomb Structures for Vibration Attenuation

Wind tunnel model support (WTMS) is an indispensable component of wind tunnel testing. However, the presence of vibrations within the model‐support system can compromise the accuracy of data and give rise to significant safety hazards. In this study, an approach for vibration attenuation by incorporating honeycomb structures into the design of the WTMS is proposed. To this end, stainless steel WTMSs with integrated honeycomb structures are fabricated by selective laser melting (SLM). Results showed that stainless steels prepared under optimized SLM processing parameters exhibit high crystallinity and consist of single‐phase Fe–Cr–Ni alloy. The stainless steels exhibited robust mechanical properties, including a tensile strength of ≈1 GPa, an elongation of ≈8%, and a compressive strength of ≈1.4 GPa. These exceptional mechanical properties can be attributed to the formation of a cellular structure and tangled dislocations. The first‐order and the third‐order resonant response of WTMS honeycomb structures can be effectively reduced. The vibration reduction mechanism can be attributed to the occurrence of local resonance when the natural frequency of the internal periodic unit of the WTMS closely matched the vibration frequency of the model. The utilization of honeycomb structures holds significant potential for achieving vibration attenuation in WTMS.

Bandgap formation mechanism in tacticity inspired elastic mechanical metastructures

Tacticity is long known as a significant contributor in changing the chemical and mechanical properties of the polymers drastically. This study explores mechanism of bandgap formation in elastic mechanical metastructures designed with a focus on tacticity. We introduce metabeams, comprising a primary slender beam embedded with short secondary beams featuring end masses at their tips. The investigation delves into the numerically simulated vibration characteristics of metabeams using finite element analysis, with a subsequent comparison to experimental results for fabricated metabeams. Employing a unit-cell design approach that manipulates spatial and physical parameters, we explore a wide range of uniform and non-uniform metabeam configurations based on the distance between secondary beams and distribution of local resonators as per tacticity. Hence, drawing inspiration from tacticity, we extend our investigation to isotactic and syndiotactic metabeams, altering physical parameters (mass) within the unit cell for both configurations. The strategic distribution of end masses on attached secondary beams introduces unique characteristics to isotactic and syndiotactic metabeams, allowing for the modulation of bandgaps without altering the natural frequencies of the resonators in symmetric and anti-symmetric metabeam designs. Our research demonstrates, incorporating tacticity in metabeam design offers a novel and unconventional approach to modulate the bandgap formation mechanism.

Understanding of topological mode and skin mode morphing in 1D and 2D non-Hermitian resonance-based meta-lattices

Recent advances have demonstrated that the non-Hermitian skin effect (NHSE), induced by system non-Hermiticity, can manipulate the localization of in-gap topological edge modes (TEMs) within mechanical topological insulators. This study introduces a straightforward analytical framework to elucidate the competition between NHSE and TEM localization in a classical mechanical meta-lattice, highlighting its impact on the dynamic behavior of TEMs within separate Bragg scattering band gaps (BSBGs). We propose a 1D non-Hermitian meta-lattice featuring a locally resonant system with active feedback control, characterized by a real-valued transfer function. This local resonance creates two separate BSBGs, each hosting a TEM defined by non-Hermitian bulk-edge correspondence. Our theoretical and numerical analyses reveal that the NHSE, with its asymmetric localization within the two BSBGs, can shift the localization of TEMs in distinct ways. This leads to an asymmetric phase transition, wherein one TEM can be delocalized and relocalized by tuning the transfer function, while the other maintains its initial localization. Moreover, we extend the mechanism of 1D asymmetric TEM delocalization to the non-Hermitian morphing of TEMs, showcasing notable examples such as temporal and spatial topological wave pumping with space- and time-dependent transfer functions in 1D time-varying and 2D stacked meta-lattices. This research bridges a gap between non-Hermitian mechanical constructs and their potential applications in classical mechanics, reinterpreting known topological wave control in 1D and uncovering new mechanisms in 2D.

Simplified site response analysis for regional seismic risk assessments

Seismic risk assessment on a regional scale requires an estimation of ground motion intensity and its spatial variation over large geographical areas. This task is particularly challenging in the presence of very soft soil deposits where significant amplification occurs at specific frequencies that are often referred to as local resonances. It is often not feasible to conduct a nonlinear site response analysis at thousands of sites of interest across a region such as an urban area due to the computational effort involved and the required detailed information on soil profiles at each site. Thus, in regional seismic risk analyses the hazard is typically represented by a field of response spectral ordinates estimated by ground motion models. This study proposes a simplified site response analysis procedure to improve the characterization of spectral ordinates to be used in regional seismic risk assessments. In the proposed procedure, reduced-order models are used to conduct site response analysis using very few parameters to transform response spectra at rock outcrop into response spectra at the surface of each of the sites. A particular emphasis is given to soft-soil sites characterized by low shear-wave velocities overlaid on rock or firm soils. A non-uniform continuous shear beam model with a parabolic variation of shear modulus along the depth and modal damping is used in combination with Random Vibration Theory. It is shown that the proposed approach provides better estimates than those of ground motion models or physics-based ground motion simulation models which often cannot capture the local resonances. Site-specific validation of the shear beam model and overall simplified site response analysis is performed at four soft-soil sites in San Francisco, California. Despite its simplicity, it is shown that the proposed procedure adequately captures the amplitudes and spectral shapes of the motions. It is also shown that in conjunction with ground motion models or physics-based models, the proposed simplified site response analysis procedure can be used to efficiently simulate the seismic hazard on a regional scale through an example of a regional seismic hazard analysis of 160 softer soil sites in Downtown San Francisco during the Loma Prieta earthquake.

The acoustic Galton board

Phononic crystals are a class of materials with periodic structures that influence the propagation characteristics of acoustic waves through periodically arranged structural units. Here, we have developed the acoustic Galton board (AGB), a groundbreaking apparatus that serves as a cost-effective and user-friendly tool for demonstrating phononic crystal properties such as band gaps, Bragg scattering, and local resonance. The device comprises an elastic wave signal generator, an enhanced Galton board featuring a sophisticated pillar-nail array, and a signal receiver. The experimental results we have obtained demonstrate the significant impact of the AGB on elastic wave dispersion, effectively creating bandgaps that impede wave transmission within specific frequency ranges while allowing unhindered propagation in others. Furthermore, the AGB can simulate phononic crystals using both the Bragg scattering mechanism, achieved through the design of periodic rigid pillar-nail arrays, and the locally resonant mechanism, facilitated by the design of pillar-nail arrays with composite material structures. Additionally, the AGB can extend its applications to serve as a simulation tool for elastic metamaterials.

Ultra-broadband underwater meta-absorber with gradient impedance-matched composite material

Abstract We have developed an underwater acoustic meta-absorber that exhibits ultra-broadband absorption, with most of absorption coefficients exceeding 0.9 across the frequency range of 1 kHz−20 kHz. This performance is achieved through the localized trapping of acoustic waves and efficient energy dissipation, facilitated by local resonances within meticulously designed, impedance-matched composite materials. The designed gradient structure of the absorber allows for a reduced width of 84 mm (0.05λ at 1 kHz) and a customizable length, determined by the number of unit cells, each with a length of 15 mm (0.01λ at 1 kHz). This different design approach yields an ultra-broadband meta-absorber of compact dimensions, offering a promising alternative for the development of underwater absorption metamaterials and their practical applications.

Observation of high frequency Alfvén eigenmodes excited by RF-accelerated minority hydrogen ions in the EAST tokamak

Abstract The paper presents the original observation of high frequency Alfvén eigenmode excited by fast minority hydrogen ions accelerated by ion cyclotron range of frequency waves in EAST. The frequency of high frequency Alfvén eigenmodes is around 0.75~8*Ω H, where Ω H is the cyclotron frequency of hydrogen ions evaluated at the low-field side plasma edge. It tracks the on-axis magnetic field B t and the edge plasma electron density n e via the Alfvenic relation ω~ B t *n e -1/2. The high frequency Alfvén eigenmodes are always accompanied by sub-cyclotron modes in several experiments at EAST, consistent with the high frequency Alfvén eigenmode detected on other conventional tokamaks, namely ASDEX Upgrade and DIII-D. Based on the previous study, these sub-cyclotron modes are consistent with the spectrum splitting produced by toroidal mode numbers[Nuclear Fusion 43, 228 (2003)]. We also found that the location of eigenmode excitation of high frequency Alfvén eigenmode driven by RF-accelerated minority hydrogen ions remains unchanged even though the cyclotron resonance location of hydrogen ions varies with B t.