Order Resonance Research Articles

Reliability Study of MEMS Resonator: A Review

Reliability study is required for all the industrial applications to understand the behavior and functionality of device with respect to technological, environmental and operational issues. This paper aim to study and analyzed the exiting contribution related to MEMS resonator in order to explore the reliability issues. It also explored the reliability related to packaging, designing and functioning of MEMS resonator. It summarized the analysis of Environmental effect, design parameters, intermolecular forces, varying electrical load and vibrations etc. An approach and methodology for testing and simulation of MEMS resonator in view of reliability analysis is presented.

Optimization of Anchor Placement in TPoS MEMS Resonators: Modeling and Experimental Validation

In this paper, a semi-analytical model is derived to calculate the anchor loss of TPoS resonators operating in higher-order length extensional modes. This model provides valuable insights on the effect of order, device dimensions, position and number of anchors on the quality factor (Q) of these resonators. Results from this model are in close agreement with the FEM simulations. The optimum position, dimension, and the number of anchors to deliver the highest Q are also discussed. Predictions of the model are validated through characterization of TPoS resonators fabricated to operate at a resonant frequency of around 1 GHz with different number of anchor pairs and position. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$23^{rd}$ </tex-math></inline-formula> order resonator with a W/L ratio of 1.5 with three pairs of anchors placed at positions suggested by the model gave a loaded Q of 4431, which is 65% more than the conventional case where anchors are uniformly placed towards the edge, and also an improvement in the insertion loss by 5.5 dB compared to the latter. For resonators where the anchor loss is predominant, our results show that the performance can be improved by placing the anchors at the optimum position, closer to the middle of the resonator than the conventional scheme where anchors are uniformly placed towards the edge.

An asymmetric CPW-fed ultra miniaturized epsilon negative triple-band antenna with improved gain using complimentary closed ring resonators

In this paper, an ultra-miniaturized triple-band antenna based on an epsilon negative transmission line (ENG-TL) approach is presented. The proposed antenna has a miniaturized electrical size of 0.247λ0×0.185λ0×0.019λ0 at 3.71 GHz which has been achieved by means of zeroth-order resonance (ZOR). This is recognized as an attractive technique to achieve compactness. It is observed from measured results that the proposed antenna is performing well over 3.63–3.81, 5.21–5.33, and 6.79–7.09 GHz. The novelty of this work lies in the fact that the peak gain has been improved by 1.73 dBi at the lowest order resonant mode. The antenna is able to exhibit measured peak gain of 1.97, 1.09, and 3.42 dBi in the broadside direction at 3.72, 5.27, and 6.92 GHz, respectively. Hence proposed antenna is suitable to work for Wi-MAX 3.5 GHz (3.4–3.8 GHz), WLAN/Wi-Fi 5.2 GHz (5.15–5.35 GHz), mobile/satellite (E-S) (6.875–7.075 GHz) applications.

Sensitivity enhancement analysis of frequency tuned-SAW resonator with temperature for sensor applications

Cooling of quartz-SAW devices leads to a noticeable increase in sensitivity. However, the effect of heating on the output characteristics of quartz-SAW resonators in terms of sensitivity has not yet been studied. Here we examine the inverse parabolic temperature characteristics of a quartz-SAW resonator in order to study the effect of temperature rise on the sensitivity. Various characteristics of a quartz SAW resonator are measured such as frequency shifts, phase, and group delay by Vector Network Analyzer (VNA) over a temperature range of 5 °C to 150 °C. It is shown that the sensitivity could be increased at certain combinations when the operating frequency (fo) is tuned away from the centre frequency (fc) along with temperatures higher or lower than room temperature. Sensitivity increases up to 24-fold was achieved when T > 120 °C and fo > fc. This study of temperature tuning of SAW device will be useful for enhancing the sensitivity in various SAW sensing applications for various industrial purposes.

Wideband Compartment Shielding Technique for Miniaturized Packages Based on Electrically Small Single-Negative Meta-Diaphragm

This article focuses on realizing wideband compartment shielding in the shielding can packages of miniaturized high-speed chip modules and circuits. Because the conventional diaphragms with a low profile are difficult to cope with the high-order mode interference and evanescent wave interference, a new &#x201C;meta-diaphragm,&#x201D; which is based on the single-negative (SNG) metamaterial, is proposed to address these inherent problems. It is demonstrated that benefitting from the large propagation attenuation introduced by the proposed meta-diaphragm, a good shielding performance can be achieved at the first higher order resonance mode. Moreover, by elaborately embedding resistors in the meta-diaphragm, the additional interferences at other resonance frequencies can be significantly suppressed. Furthermore, the structure of the meta-diaphragm is optimized with two approaches: evolving from the single-band SNG structure to the double-band one and integrating with the parasitic patches. The two approaches enable its independent controlling ability at different frequency ranges and enhancement of low-frequency shielding performance. Based on the proposed technique, an experiment is implemented to suppress the resonance-dominated interference between the passive traces in a shielding can. The result agrees well with those from theoretical prediction. The final experimental shielding can&#x2019;s profile and width are 5 and 20 mm, respectively; the meta-diaphragm&#x2019;s profile is only 1.5 mm, i.e., &#x003C; 1/3 of shielding can&#x2019;s profile, and its electrically length is only 3 mm, i.e., <inline-formula> <tex-math notation="LaTeX">$0.1\lambda _{0}$ </tex-math></inline-formula> at 10 GHz, and the measured (simulated) meta-diaphragm can significantly suppress radio frequency interference (RFI) within 10.2&#x2013;17 GHz (10&#x2013;16.9 GHz) and realize <inline-formula> <tex-math notation="LaTeX">$&lt; -33.5$ </tex-math></inline-formula> dB (<inline-formula> <tex-math notation="LaTeX">$&lt; -40$ </tex-math></inline-formula> dB) coupling within 100 kHz&#x2013;18 GHz (dc-to-20 GHz). The miniaturized dimension and wideband results indicate that our proposed technique could meet the compartment shielding requirement of a series of miniaturized packages in the practical radio frequency (RF) chip modules and circuits.

Emergence and Ordering of Polygonal Breathers in Polariton Condensates.

We show that the simultaneous driving of a polariton condensate with both nonresonant and nth order resonant pump frequencies allows for a generic mechanism of breather formation. From this we construct for the second order resonance a family of exotic breathers with nontrivial discrete order of rotational symmetry. Finally, we demonstrate the spontaneous emergence of both crystalline and glassy orderings of lattices of polygonal breathers, depending on the degree of polygonal excitations at the lattice sites.

Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems

ABSTRACT Non-restricted hierarchical three-body configurations are common in various scales of astrophysical systems. Dynamical structures of the quadrupole-order resonance (the von Zeipel–Lidov–Kozai resonance) and the octupole-order resonance (the apsidal resonance) under the non-restricted hierarchical planetary systems are investigated in this work by taking advantage of perturbative treatments. Under the quadrupole-order Hamiltonian model, the distribution of libration and circulation regions as well as the distribution of flipping region are analytically explored in the parameter space spanned by the conserved quantities. The fundamental frequencies of system are produced and then the nominal location of octupole-order resonance is identified. From the viewpoint of perturbative theory, the quadrupole-order Hamiltonian determines the unperturbed dynamical model and the octupole-order Hamiltonian plays a role of perturbation to the quadrupole-order dynamics. The resonant Hamiltonian for octupole-order resonances is formulated by means of averaging theory, giving rise to a new constant of motion. Phase portraits are produced to analyse dynamical structures of octupole-order resonance, including resonant centres, saddle points, dynamical separatrices and islands of libration. By analysing phase portraits, it is found that there are four branches of libration centre and eight libration zones in the considered space. Applications to orbit flips show that there are five flipping regions.

Shape- and Size-Dependent Refractive Index Sensing and SERS Performance of Gold Nanoplates.

Plasmonic sensors are promising for ultrasensitive chemical and biological analysis. Gold nanoplates (Au NPLs) show unique geometrical structures with high ratios of surface to bulk atoms, which display fascinating plasmonic properties but require optimization. This study presented a systematic investigation of the influence of different parameters (shape, aspect ratio, and resonance mode) on localized surface plasmon resonance properties, refractive index (RI, n) sensitivities, and surface-enhanced Raman scattering (SERS) enhancement ability of different types of Au NPLs through finite-difference time-domain (FDTD) simulations. As a proof of concept, triangular, circular, and hexagonal Au NPLs with varying aspect ratios were fabricated via a three-step seed-mediated growth method by the experiment. Both FDTD-simulated and measured experimental results confirm that the RI sensitivities increase with the aspect ratio. Furthermore, choosing a lower order resonance mode of Au NPLs benefits higher RI sensitivities. The SERS enhancement abilities of Au NPLs also predicted to be highly dependent on the shape and aspect ratio. The triangular Au NPLs showed the highest SERS enhancement ability, while it drastically decreased for circular Au NPLs after the rounding process. The SERS enhancement ability gradually became more intense as the hexagonal Au NPLs overgrown on circular Au NPLs with increasing volumes of HAuCl4 solution. The results are expected to help develop effective biosensors.

Three port photonic and plasmonic demultiplexers based on Cross and U-shaped stub structures: Application for filtering and sensing

We propose the design of three port photonic and plasmonic demultiplexers where filtering toward the two outputs is based on the phenomena of Fano resonances and electromagnetically induced transparency (EIT). We use a Cross-shape resonator in one output and a U-shape resonator composed of two stubs in the other output. We give a theoretical demonstration of the geometrical parameters of both resonators in order to filter one wavelength in one output while leaving the other output unperturbed. These results are confirmed by experimental validation in the radio frequency domain and a numerical simulation in the infrared (IR) domain using plasmonic metal–insulator–metal waveguides. The Cross resonator in the first output can give rise to an EIT resonance, whereas the U-shaped resonator in the second output may exhibit both EIT and Fano resonances depending on the lengths chosen for the stubs. Therefore, different demultiplexing schemes can be proposed such as achieving a Fano resonance in one output and an EIT in the other, or EIT resonances in both outputs. The Fano resonance is obtained by bringing resonance close to transmission zero, whereas the EIT results from the squeezing of resonance between two transmission zeros. When the widths of the resonances tend to zero, they transform to trapped or bound states in the continuum with an infinite lifetime. We show that the crosstalk between the two channels can be reduced to −82 dB and the sensitivity can reach 2390.8 nm/RIU, RIU is the refractive index units. Finally, we highlight the performance of our design as a high sensitive filter and sensor in the IR domain. In this work, the analytical calculations and demonstrations are performed by using Green’s function approach, the experimental verifications are realized by means of coaxial cables operating in the radio frequency range and the numerical simulations are obtained using the finite element method via Comsol Multiphysics software.

Manipulation of resonance orders and absorbing materials for structural colors in transmission with improved color purity.

We present an improved color purity of additive transmissive structural color filters by controlling a resonance order and by inserting a highly absorbing material. The proposed structure consists of a single metal sandwiched by two transparent dielectric media serving as a cavity to minimize the ohmic loss in the metal mirrors, which is distinctly different from a conventional Fabry-Perot (FP) cavity that is in general designed to have two metal mirrors. Low reflections at an air-dielectric interface cause a quality-factor of a resonance to be reduced, causing a degraded color purity, which can be improved by employing a 1st order resonance that exhibits a narrower bandwidth than a fundamental FP resonant mode (0th order). For a red color with the improved purity, introducing an ultrathin absorbing layer in the middle of a top cavity enables the 1st resonance to be trivially influenced while selectively suppressing a 2nd order resonance appearing at the shorter wavelength region. Moreover, angle-insensitive performances up to 60° are attained by utilizing a cavity material with high index of refraction. Besides, the fabrication of the structural coloring devices involves a few deposition steps, thus rendering the approach suitable for applications over the large area. The described concept could be applied to diverse applications, such as colored solar panels, sensors, imaging devices, and decorations.

Instability from high-order resonant chains in wide-separation massive planet systems

ABSTRACT Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term evolution of model planetary systems, made up of three equal mass giant planets on initially eccentric orbits. The range of separations studied is dominated by secular processes, but intersects chains of high-order mean-motion resonances. Over time-scales of 108 orbits, the secular evolution of the simulated systems is predominantly regular. High-order resonant chains, however, can be a significant source of angular momentum deficit (AMD), leading to instability. Using a time series analysis based on a Hilbert transform, we associate instability with broad islands of chaotic evolution. Previous work has suggested that first-order resonances could modify the AMD of nominally secular systems and facilitate secular chaos. We find that higher order resonances, when present in chains, can have similar impacts.

Mass identification of multiple particles on a doubly clamped resonator

The shift of resonant frequencies is the working mechanism of a mass resonator sensor. The shift is due to the adsorption of particles, which can change the mass, stiffness and damping of the sensor. Based on the Timoshenko beam model, an analytical model and mathematical solution are proposed to explain the frequency shifts due to the adsorption of multiple particles. The model shows a better accuracy in the scenarios of the high order resonance, the vibration in the viscous environment and under high tension. The inverse problem of identifying multi-particle mass is solved by an iteration algorithm, whose performance is also evaluated for the measured noise and adsorption areas. The mass identification of multiple particles shows a better sensitivity and robustness than that of single particle, which is somewhat surprising but beneficial to mass sensing. The results in this study provide a theoretical basis for the mass identification of multiple particles and are of some help to the practical application.

A Micromechanical Transmitter with Only One BAW Magneto-Electric Antenna.

Implantable medical devices have been facing the severe challenge of wireless communication for a long time. Acoustically actuated magnetoelectric (ME) transducer antennas have attracted lots of attention due to their miniaturization, high radiation efficiency and easy integration. Here, we fully demonstrate the possibility of using only one bulk acoustic wave (BAW) actuated ME transducer antenna (BAW ME antenna) for communication by describing the correspondence between the BAW ME antenna and components of the traditional transmitter in detail. Specifically, we first demonstrate that the signal could be modulated by applying a direct current (DC) magnetic bias and exciting different resonance modes of the BAW ME antenna with frequencies ranging from medium frequency (MF) (1.5 MHz) to medium frequency (UHF) (2 GHz). Then, two methods of adjusting the radiation power of the BAW ME antenna are proposed to realize signal amplification, including increasing the input voltage and using higher order resonance. Finally, a method based on electromagnetic (EM) perturbation is presented to simulate the transmission process of the BAW ME antenna via the finite element analysis (FEA) model. The simulation results match the radiation pattern of magnetic dipoles perfectly, which verifies both the model and our purpose.

The dynamics of the TRAPPIST-1 system in the context of its formation

ABSTRACT TRAPPIST-1 is an 0.09 M⊙ star, which harbours a system of seven Earth-sized planets. Two main features stand out: (i) all planets have similar radii, masses, and compositions; and (ii) all planets are in resonance. Previous works have outlined a pebble-driven formation scenario where planets of similar composition form sequentially at the H2O snowline (∼0.1 au for this low-mass star). It was hypothesized that the subsequent formation and migration led to the current resonant configuration. Here, we investigate whether the sequential planet formation model is indeed capable to produce the present-day resonant configuration, characterized by its two-body and three-body mean motion resonances structure. We carry out N-body simulations, accounting for type-I migration, stellar tidal damping, disc eccentricity-damping, and featuring a migration barrier located at the disc’s inner edge. Due to the sequential migration, planets naturally form a chain of first-order resonances. But to explain the period ratios of the b/c/d-system, which are presently in higher order resonances, we find that planets b and c must have marched across the migration barrier, into the gas-free cavity, before the disc has dispersed. We investigate both an early and late cavity infall scenario and find that the early infall model best matches the constraints, as well as being more probable. After the dispersal of the gaseous disc, stellar tidal torque also contributes towards a modest separation of the inner system. We outline how the insights obtained in this work can be applied to aid the understanding of other compact resonant planet systems.

Polarization Independent Simultaneous Excitation of Odd and Even Order Resonances in Plasmonic Metasurfaces

Polarization Independent Simultaneous Excitation of Odd and Even Order Resonances in Plasmonic Metasurfaces

Polarization Engineered Second Harmonic Generation Enhancement from Amorphous Silicon - Gallium Nitride Heterogeneous Resonant Metasurface

We experimentally demonstrate second harmonic generation (SHG) enhancement from a heterogeneous resonant metasurface consisting of amorphous silicon sub-wavelength gratings supporting resonances within an underlying gallium nitride (GaN) layer. Electromagnetic design studies used to choose the sub-wavelength grating dimensions, corresponding spectral resonances, its angular sensitivity, electric field and non-linear polarization profiles are discussed. The efficient excitation of second-order nonlinearities within the GaN layer requiring longitudinal fundamental field component and efficient extraction of on-axis SHG using in-plane nonlinear polarization components are simultaneously satisfied for fundamental excitation polarized at 45^o, resulting in excitation of TE and TM-like resonances. Experimental studies on the fabricated structures characterizing the linear and nonlinear SHG properties including power, polarization, and spectral dependence are also discussed. The SHG spectral measurements show 1300-times enhancement for 1460 nm fundamental excitation. The SHG enhancement observed for the higher order resonance at 1460 nm is attributed to the trade-off between the increase in the in-plane to out-of-plane nonlinear polarization ratio, resulting in relative increase in on-axis SHG radiation and the decrease in quality factor of the resonances, which lowers the resonance field strength with increasing guided-mode order.

Balancing of Coupled Piezoelectric NEMS Resonators

Micro and Nano Electro Mechanical systems (M/NEMS) have a lot of potential to be used for sensing in different schemes and operation modes. We focus here on the use of coupled resonators for sensing and address the major limitation that these systems face, which stems from a compromise between dynamic range and responsivity. When the system becomes unbalanced, the responsivity drops. To solve this issue, we propose the use of piezoelectric-based stress tuning of the stiffness of the resonators in order to rebalance the system of resonators. With this approach we expect to be able to extend the dynamic range of such systems by some orders of magnitude.

Tunable color gamut based a symmetric microcavity governed by Sb[formula omitted]S[formula omitted

Dynamically structural color has great attraction and practicability in display. By introducing a phase change material Sb2S3 (SS23), which exhibits significantly different optical properties in different crystalline states, we have theoretically studied the active gamut regulation using symmetric optical microcavities. When SS23 is embedded in the oxide layer of the traditional symmetric optical microcavity, the high order resonance is suppressed, resulting in a wide color gamut. Moreover, switching SS23 from the amorphous state to the crystalline state also produces resonant damping, resulting in a high purity transmission color, further increasing the gamut to 128% of sRGB. The influence of incident angle and machining error on the color gamut when SS23 is crystal state is also investigated in CIE 1931 chromaticity diagram. Our work provides a way to achieve dynamic gamut modulation using optical microcavity.

Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.

Superscattering for non-spherical objects

In this work we generalize the notion of superscattering and associate it with a symmetry group of a scattering object. Using the group theory approach we describe a way to spectrally overlap several eigenmodes of a resonator in order to achieve scattering enhancement. Importantly, this can be done by simple variation of geometric parameters of the system, implying that the symmetry is preserved. We also demonstarte that a scattering cross-section limit of a spherical object is not valid for the case of non-spherical geometries. As an example, we use finite-size ceramic cylinder and demonstrate that a dipolar scattering cross-section limit of a spherical object can be exceeded by more then 3 times. The obtained results may be promising for design of antennas and radio frequency identification systems.