One-dimensional Phononic Crystal Research Articles

Improving the functionality of biosensors through the use of periodic and quasi-periodic one-dimensional phononic crystals

Abstract Resonant acoustic band gap materials have steered a new sensing technology era. This study is presented to investigate of the one-dimensional (1D) phononic crystals (PnCs), involving periodic, as well as quasi-periodic 1D layered PnCs represented as a highly sensitive biosensor to detect and monitor the quality of milk. In this regard, the numerical findings show that the examined periodic PnCs structure outperformed the quasi-periodic structure. In particular, it provides a wider phononic band gap and greater sensitivity as well. In addition, the quasi-periodic design (especially Fibonacci sequence S4) introduces multiple resonance peaks via transmission spectra, which may lead to some conflicts during the detection process. The findings reveal that the frequency of the resonant peak can effectively change with varied milk solution concentrations and temperatures. The optimized sensor is capable of differentiating between concentrations ranging between 0 and 50 % with a 10 % step, and it can also differentiate between temperatures, which range between 5 °C and 50 °C. This makes it ideal for precise detection of other liquids and solutions. The sensor performs efficiently for all milk solution concentrations. Here, the findings demonstrated that the examined defective PnC structure exhibited the most favorable sensitivity of the value of 94.34 MHz, so it showed the highest sensitivity when varying milk concentrations. In addition, the configurated sensor provided high QF and FOM values of 3,853.645161 and 157.42, respectively. On the other hand, the sensor performs very well for all temperatures of the milk solution. As such, the S 4 quasi-periodic structure is characterized as the optimal sensor structure when varying temperatures, introducing a sensitivity of 4.78 MHz/°C, QF of 4,278.521, and FOM of 7.48 °C−1.

Enhanced Performance of Fluidic Phononic Crystal Sensors Using Different Quasi-Periodic Crystals

In this paper, we introduce a comprehensive theoretical study to obtain an optimal highly sensitive fluidic sensor based on the one-dimensional phononic crystal (PnC). The mainstay of this study strongly depends on the high impedance mismatching due to the irregularity of the considered quasi-periodic structure, which in turn can provide better performance compared to the periodic PnC designs. In this regard, we performed the detection and monitoring of the different concentrations of lead nitrate (Pb(NO3)2) and identified it as being a dangerous aqueous solution. Here, a defect layer was introduced through the designed structure to be filled with the Pb(NO3)2 solution. Therefore, a resonant mode was formed within the transmittance spectrum of the considered structure, which in turn shifted due to the changes in the concentration of the detected analyte. The numerical findings demonstrate the role of the different sequences such as Fibonacci, Octonacci, Thue–Morse, and double period on the performance of the designed PhC detector. Meanwhile, the findings of this study show that the double-period quasi-periodic sequence provides the best performance with a sensitivity of 502.6 Hz/ppm, a damping rate of 5.9×10−5, a maximum quality factor of 8463.5, and a detection limit of 2.45.

Dynamic control of Lamb modes in phononic crystals

This study explores the possibilities of temporal control of one-dimensional phononic crystal consisting of a homogeneous piezoelectric plate on which metallic electrodes are structured. Previous works [1] have shown that Lamb-type guided modes in these periodically structured piezoelectric ceramic plates exhibit a tunable frequency dispersion that can be controlled by external electric circuits connected to the electrodes. In this study we develop a device enabling changes in the electric boundary conditions (EBC) from one condition to another by making use of switches driven by a microcontroller. This device agility is exploited to perform dynamic control of the crystal properties. To our knowledge, this is the first study devoted to the dynamic modulation of Lamb-type guided waves. Here, we do not simply change the EBCs as a function of time, but we create a "wave" of modulation of properties. Broadband translation of Lamb-wave dispersion curves in the frequency-wavenumber space (f, k) are observed, depending on the modulation speed. Experimentally, the translation of the S0 mode is detected. The relationship between the position of static bands and the position of bands after temporal modulation obeys a very simple vector rule in the (f, k) space. [1] Phys. Rev. B 99, 094302 (2019).

Dispersion and bandgap feature of coupled Bloch waves in one-dimensional piezoelectric semiconductor phononic crystal with PN junction

Dispersion and bandgap feature of coupled Bloch waves in one-dimensional piezoelectric semiconductor phononic crystal with PN junction

Investigating the impact of shear and bulk viscosity on the damping of confined acoustic modes in phononic crystal sensors

Phononic crystal (PnC) sensors are recognized for their capability to control acoustic wave propagation through periodic structures, presenting considerable potential across various applications. Despite advancements, the effects of fluid viscosity on PnC performance remain intricate and inadequately understood. This study theoretically investigates the influence of shear (dynamic) and bulk viscosity on acoustic wave damping in defective one-dimensional phononic crystal (1D PnC) sensors designed for detecting liquid analytes. Acetic acid with varying viscosities is considered to fill a cavity layer intermediated by a multilayer stack of lead and epoxy. The effects of dynamic and bulk viscosity on the resonance characteristics of the defective mode were analyzed. Numerical results reveal that increased dynamic viscosity leads to substantial broadening and decreased intensity of resonance peaks, accompanied by a shift to higher frequencies due to enhanced elastic wave attenuation and damping. At low dynamic viscosity (η = 0.2 ηd), numerous resonance peaks with varying intensities are observed. However, at higher viscosities (η = 2.0 ηd to η = 10.0 ηd), only one prominent peak appears in the spectrum. The intensity of this resonant peak starts at 98% for η = 2 ηd and decreases to 58.8% as the dynamic viscosity increases to η = 10 ηd. Additionally, the combined effect of dynamic and bulk viscosity introduces further damping, causing a strong shift of the resonance peak to higher frequencies, along with an increase in the full width at half maximum (FWHM) and a decrease in the quality factor (QF). These findings emphasize the necessity of incorporating both shear and bulk viscosity in the design of PnC sensors to enhance their sensitivity and accuracy in practical applications. This theoretical framework provides critical insights for optimizing sensor performance and bridging gaps between theoretical predictions and experimental observations, especially in 1D PnCs, offering potential solutions to challenges in real-world PnC sensor applications.

Ultra-sensitive optimized one-dimensional phononic crystal as a fluidic sensor to enhance the measurement of acetic acid concentration

The current investigation theoretically presents a one-dimensional phononic crystal (PnC) as a fluidic sensor. The sensor under consideration aims to distinguish the concentration of acetic acid. The primary configuration of the proposed sensor is constructed with lead, epoxy, and a defect layer in the middle of the structure, that is filled with acetic acid (vinegar). As a result of the rise in density and decline in the speed of sound at a 100% concentration of acetic acid in comparison to pure water, the peak frequency of the output has shifted towards lower frequencies. Given that the maximum permissible concentration of acetic acid in water for vinegar is above 30%, sensor simulations were conducted within the concentration range of 25–35% with a step size of 1%. Interestingly, the sensitivity of the sensor exhibits a polynomial change in response to the concentration of acetic acid. Consequently, the highest level of sensitivity, which corresponds to the lowest concentration of vinegar, is recorded as 48.44 × 106 (Hz). The proposed system exhibits a remarkable value of the quality factor of 2802.91. Furthermore, the optimal figure of merit (FOM) is achieved when the concentration is at its lowest, with a value of 94.00. Furthermore, the temperature effects are taken into account for a wide range between 10 and\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{and}$$\\end{document} 60 °C. A pronouncing sensitivity is obtained for all temperatures changes and the highest one reached the value of 1.57 × 106 (Hz/°C) at a temperature of 25 °C. Considering the present circumstances, the suggested sensor configuration has the potential to cater to a diverse array of other fluids, specifically their concentration and temperature, thereby offering a broad scope of applications.

Topological rainbow trapping of shear horizontal waves in a phononic crystal plate with tapered surface

Topological interface states have localized field enhancement characteristics. Integrating them with the concept of rainbow trapping undoubtedly be a more effective method for elastic energy localization and collection. In this paper, the tunable interface state of shear horizontal (SH) waves is realized in a one-dimensional (1D) phononic crystal (PC) plate by modifying the structural parameters of unit cells with tapered surfaces, where the interface state emerges in the overlapping band gaps of two types of unit cells with different Zak phases. Furthermore, we assembled seven types of unit cells with gradient variations, achieving topological rainbow trapping. Meanwhile, the robustness of the rainbow state has been demonstrated, and more separated frequencies are obtained by changing the order of these unit cells. The results of the study demonstrate that the highly localized, compact, and broadband tunable topological rainbow system we designed holds promise for applications in areas such as elastic energy harvesting, filtering, and multi-frequency signal processing.

Duality of a coiled phononic crystal enables reflectionless interfaces

Recently, it has been demonstrated that one-dimensional bar-based phononic crystals can exhibit subwavelength Bragg bandgaps by coiling the bars and locking the nodal rotational degrees of freedom to create what is termed a coiled phononic crystal (CPnC) [C. L. Willey et al., Phys. Rev. Appl. 18, 014035 (2022)]. Here, it is shown that the CPnC exhibits duality of its dispersion curves relative to its coiling/twist angle, meaning that the dispersion curves are symmetric about a particular coiling/twist angle defined configuration. An exciting implication of this finding is that under a certain set of constraints, segments of dual unit cells with perpendicular wave propagation directions can be connected such that their wave transmission is equivalent to a finite CPnC entirely composed of identical unit cells with parallel wave propagation directions. The ability to link unit cells with different wave propagation orientations, but the same dispersion/dynamic stiffness, is used to create an elastic hierarchically coiled phononic crystal based on a fractal space-filling curve design. The novelty of this work is that it numerically demonstrates reflectionless wave propagation in large fractal architectures (created from specific combinations of dual unit cells) such that regular phononic properties (i.e., passbands and bandgaps) are preserved, allowing for propagation of broadband signals and filtering.

Fano resonance in one-dimensional quasiperiodic topological phononic crystals towards a stable and high-performance sensing tool

Phononic crystals (PnCs) emerge as an innovative sensor technology, especially for high-performance sensing applications. This study strives to advance this field by developing new designs of PnC structures that exhibit stability in the face of construction imperfections and deformations, focusing on the evolution of topological PnCs (TPnCs). These designs could be promising to overcome the problem of instability involved in most of the theoretical PnC sensors when they emerge in experimental verification. In particular, the fabrication process of any design could collide with some fluctuations in controlling the size of each component. Thus, Fano resonance is introduced through a one-dimensional (1D) quasiperiodic TPnC. To the best of the author’s knowledge, this study is the first to observe Fano modes in liquid cavities through 1D PnCs. Various quasiperiodic PnC designs are employed to detect the temperature of alcohols (specifically propanol) across an extensive temperature range (160–240 °C). The effects of many geometrical parameters on the sensor stability, such as material thicknesses, are studied. Numerical findings demonstrated that the designed quasiperiodic topological PnCs based on Fibonacci sequence of the second order proved superior performance. This sensing tool provides sensitivity, quality factor and figure-of-merit values of 104,533.33 Hz/°C, 223.69 and 0.5221 (/°C), respectively, through temperature detection of propanol in the range of 160–240 °C.

Локализованные акустические волны в одномерных периодически модулированных структурах

A number of one-dimensional phononic crystals, which are periodic thin-film structures of various geometries, consisting of sets of columns and metal inclusions located on a piezoelectric half-space, have been proposed and studied. The features of propagation in such structures of acoustic waves localized near the free surface and inhomogeneous inclusions have been studied. An unusual behavior of the dispersion curves for the studied localized modes was discovered. Particular attention is drawn to the so-called forbidden zones, i.e. frequency ranges in which there are no propagating localized modes. The influence of mechanical and electrical boundary conditions on the spectrum of the waves under study is discussed in detail.

Tunable bandpass filters using a defective phononic crystal shunted to synthetic negative capacitance for longitudinal waves

This study illustrates the successful achievement of tunable defect bands in one-dimensional defective phononic crystals (PnCs) through the incorporation of piezoelectric defects with synthetic negative capacitances (SNCs) for the first time. The efficacy of SNCs in creating tunable bandpass filters across a broad frequency range is thoroughly examined using the proposed analytical and numerical models. A newly developed electroelastically coupled transfer matrix that incorporates SNCs is presented, considering either series or parallel connection between bimorph piezoelectric elements. Defect band and transmittance analyses are conducted using the transfer matrix and S-parameter methods. Two key findings emerge from this investigation. First, when the total equivalent capacitance of the bimorph piezoelectric elements and SNC becomes zero, the defect band representing the point-symmetric defect-mode shape can be customized throughout the entire phononic bandgap. Second, the constant transmittance value, resembling short-circuit conditions, highlights the remarkable ability of SNCs to tune defect bands without energy dissipation, paving the way for fully tunable bandpass filters. To propel this research forward, future investigations could explore expanding the design space with double defects, adopting enhanced modeling techniques to account for lateral and shear effects, developing a control algorithm for the automatic optimization of SNC values in actively tunable bandpass filters, and incorporating artificial intelligence into design methods for piezoelectric defects with electrical connections.

Tunable topological edge states and energy harvesting of piezoelectric-inductance phononic crystals based on Su-Schrieffer-Heeger model

Based on Su-Schrieffer-Heeger (SSH) model, a one-dimensional tunable topological phononic crystal (PnC) was designed. Piezoelectric column with an inductance was designed as a scatterer embedded in the epoxy resin matrix. And the introduce of an inductance into each piezoelectric column resulted in a new Dirac point in band structure. Subsequently, the new Dirac point was operated to open/close by altering the intracell distance, and the trivial and non-trivial phase transition occurred simultaneously, which demonstrated the topological properties of PnC. The results showed that the obvious edge state was observed at the frequencies of 16.334–27.226 kHz by varying the inductance from 2.5mH to 9.5mH. And the immune of the edge state to the local defects was also verified. Furthermore, the energy harvesting of the wave propagation was performed, and the energy harvesting efficiency of the edge state case was about 40 times larger than that of bulk state case.

Band gap of shear horizontal waves for one-dimensional phononic crystals with chiral materials.

Extensive applications of chiral lattice structures in the field of acoustic wave manipulation and vibration modulation show the effectiveness of chirality route to the design of phononic crystals. However, how and to what extent the material chirality affects the band gap properties of phononic crystals remains unclear. In this study, one-dimensional phononic crystals made of chiral materials is proposed, and a theoretical model of shear horizontal (SH) wave propagation in the chiral phononic crystals is developed based on the noncentrosymmetric micropolar elasticity theory. Through the transfer matrix method, the dispersion relationship of SH wave propagation is obtained and the effects of material chirality on the band-gap properties are investigated. Our work demonstrates that the change of material chirality can significantly affect the dispersion relationship of phononic crystals, leading to the wide band gap and low frequency. In a unit cell, when the chiral coefficients of the two parts have opposite signs but the same magnitude and the chiral directions are consistent with the vibrational direction, it is the most favorable for the phononic crystals to achieve the lowest frequency and widest band gap. This study suggests that the material chirality can be harnessed to effectively tune the band-gap properties of phononic crystals. The present study provides insight for the chirality route to the design of phononic crystals.

Tunable non-reciprocity of elastic waves in one-dimensional magnetoelastic phononic crystal plate with oblique incident angle

In this work, non-reciprocal A0 wave in a one-dimensional (1D) magnetoelastic phononic crystal (PC) plate is observed by adjusting the magnitude of the external static magnetic field and the angle of incidence of the elastic wave. This phenomenon arises from the both breaking of time-reversal and spatial-inversion symmetries. When the angle between the applied in-plane magnetic field and the wave vector direction is greater than 0°, the spin waves exhibit a small non-reciprocity. The non-reciprocal spin waves couples with the elastic wave to form a non-reciprocal bandgap, which is distinct from the asymmetric transmission of elastic waves in non-periodic structures. Our research provides robust way to manipulate the transmission characteristics of A0-Lamb waves and has potential application in the design of diodes in seismic exploration and material testing.

Surface impedance and topologically protected interface modes in one-dimensional phononic crystals

When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry, the bulk-boundary correspondence claims that the existence of interface modes is given by a topological invariant computed from the bulk properties of the PC, which ensures strong stability properties. This one-dimensional bulk-boundary correspondence has been proven in various works. Recent attempts have exploited the notion of surface impedance, relying on analytical calculations of the transfer matrix. In the present work, the monotonic evolution of surface impedance with frequency is proven for all one-dimensional PCs with mirror symmetry. This result allows us to establish a stronger version of the bulk-boundary correspondence that guarantees not only the existence but also the uniqueness of a topologically protected interface state. This correspondence is extended to a larger class of one-dimensional models that include imperfect interfaces, array of resonators, or dispersive media. Numerical simulations are proposed to illustrate the theoretical findings.

One-dimensional synthetic waterborne phononic crystals

Underwater acoustics has wide applications in underwater communication, underwater positioning, underwater navigation, and so on. Inspired by the concept of topological physics, the study of topological states in waterborne phononic crystals provides a brand-new way for innovatively controlling underwater waves, which has both basic research value and important application prospects. In this work, we design a one-dimensional bilayer iron grid waterborne phononic crystal to realize a synthetic two-dimensional Dirac point by considering the relative lateral translation between the two layers as a synthetic dimension. Through changing the relative lateral translation, the double degenerate band opens a gap, which is characterized by the valley Chern number. As the band gap opens, closes and reopens, the bulk band undergoes a band inversion, that is, a topological phase transition from one valley topological phase to another. At the interface formed by two phononic crystals with distinct valley topological phases, the valley Chen number ensures the deterministic existence of the interface state. Experimental measurements are in good agreement with numerical simulations, both showing the bulk bands of waterborne phononic crystals at different valley topological phases and the interface state dispersion between them. The waterborne phononic crystal proposed in this work has a simple structure. With the help of the concept of synthetic dimension, it provides an effective way to study the topological properties of high-dimensional systems in low-dimensional real space systems, and gives new ideas for designing topological functional underwater acoustic devices. In addition, we can expand the real space system to two or even three dimensions, and introduce more synthetic dimensions to study the topological states and associated transport characteristics of higher-dimensional systems.

Surface acoustic waves in the continuous spectrum of Bloch waves in piezoelectric one-dimensional phononic crystals.

This paper theoretically investigates surface acoustic waves (SAWs) which emerge within the continuous spectrum of bulk Bloch waves in piezoelectric one-dimensional phononic crystals. Accordingly, these SAWs may be treated as an example of the bound states in the continuum (BIC). The equationswhich determine the existence of such BIC-SAWs have been derived. Unlike SAWs in the frequency intervals forbidden for bulk Bloch waves, BIC-SAWs are governed not by a single purely real dispersion equationbut by sets of equations, so BIC-SAWs prove to be robust only to a consistent change of a definite number of free parameters characterizing the wave propagation. The form of the derived equationsallows the establishment of the conditions on the frequency and other parameters under which the BIC-SAW exists. The number of conditions depends on the number of bulk waves in the frequency interval under consideration. In the case of generic crystallographic symmetry, there are three, five, and seven conditions which have to be fulfilled for a BIC-SAWs to coexist with one pair, two pairs, and three pairs of bulk Bloch waves, respectively. It is shown that the crystallographic symmetry may reduce the number of conditions to two, three and four, respectively. Numerical computations confirm analytic results.

Angular wave propagation through one-dimensional phononic crystals made of functionally graded auxetic nanocomposites

Composites reinforced with graphene origami nanofillers possess negative Poisson's ratio and obtain multifunctional features offering unique mechanical properties such as tunable auxeticity, high impact resistance, better indentation resistance, and improved fracture toughness. This paper introduces such novel nanocomposites into functionally graded multilayered phononic crystals and numerically investigates the propagation characteristics of normally and obliquely incident waves in the structures containing components with negative Poisson's ratio. Theoretical models of present structures are formulated and solved by the state space approach. The transfer matrix method is used to obtain dispersion relations of normally and obliquely incident waves. A comprehensive parametric study is conducted to discuss the propagation characteristics of elastic waves in the structures with auxetic and non-auxetic components which can be tuned by the weight fraction and hydrogen coverage of graphene origami fillers. The results indicate that introducing components with negative Poisson’ ratio into unit cells can significantly affect wave propagation features. Wave modes have different sensitivities to the weight fraction and hydrogen coverage of graphene origami fillers. Weigh fraction can manipulate all wave modes simultaneously, while hydrogen coverage only influences longitudinal modes and keeps transverse modes nearly undisturbed. Theoretical results shed insights into the design of high-performance multifunctional phononic crystals.

Experimental evidence of nonreciprocal propagation in space-time modulated piezoelectric phononic crystals

A nonreciprocal system composed of a one-dimensional piezoelectric phononic crystal whose periodic electrical conditions are modulated in time is presented. One-way longitudinal wave propagation is studied experimentally and compared to finite element temporal simulations. The modulation is performed by prescribing grounded or floating potential conditions on a periodic set of electrodes through external circuits. This approach makes it possible to consider a wide range of modulation speeds, and the large number of unit cells of the phononic crystal allows us to characterize experimentally the full dispersion curves of the system. This permits to observe the presence of directional bandgaps and to follow the shift in frequencies of these bandgaps as a function of the modulation speed. The experiments show the linear evolution of the central position of the bandgaps with the increase in the modulation speed, as well as their progressive closure, over a wide range of frequencies. Experiments are also used to estimate the evolution of bandgaps in a dispersive system, a problem discussed in several theoretical works but never observed experimentally. This work may constitute the foundation for experimental analysis of Floquet acoustic metamaterials, accelerated-modulation space-time metamaterials, or acoustic analog of the event horizon.

Elastic wave propagation in one-dimensional phononic crystal with defects

The possibilities of manipulating the behavior of propagating waves using only the appropriate choice of materials is a field of interest in engineering. Phononic Crystals (PnCs) come precisely as a proposal for a device to work with waves, defined as artificial materials obtained from a periodic arrangement of unit cells. This configuration can provide frequency bands where waves cannot propagate (bandgaps). However, this property can be directly influenced by the break in the periodicity pattern of the structure when geometric and/or material parameters are changed in a single part of the unit cell. New propagating modes appear inside the bandgaps, presenting characteristics of localized modes. Different length and diameter combinations are applied to establish the defective cell and verify the existence of defect modes that reveal the degree of influence on the creation of these new modes within the bandgap region. Spectral Element (SEM) and Finite Element (FE) methods are adopted to model the PnCs analysis and the frequency response functions (FRFs). The initial results show that the PnCs with geometric defects have an expressive sensitivity to variations in geometric parameters, mainly variations in the length of the defective cell. A break in periodicity in terms of material will also be performed.