High Q-factor Resonances Research Articles

Sensing and frequency selecting with toroidal resonance in metasurface

A double M-shaped metasurface is proposed and produced to realize a high Q-factor resonance at 13 GHz. The numerical and experimental results show that the high Q excitation of the structure is caused by the strong toroidal dipole. The novel toroidal metasurface can be a refractive index sensor with a high sensitivity of 3.2 GHzRIU−1. In addition, the double layer metasurface can achieve frequency selection with a bandwidth of 0.27 GHz. The proposed metasurface further extends the application of toroidal dipole in the field of sensing, frequency selective surface and so on.

A mechanically coupled MEMS filter with high-Q width extensional mode resonators

This work presents a novel radio frequency (RF) narrowband Si micro-electro-mechanical systems (MEMS) filter based on capacitively transduced slotted width extensional mode (WEM) resonators. The flexibility of the plate leads to multiple modes near the target frequency. The high Q-factor resonators of around 100 000 enable narrow bandwidth filters with small size and simplified design. The 1-wavelength and 2-wavelength WEMs were first developed as a pair of coupled modes to form a passband. To reduce bandwidth, two plates are coupled with a λ-length coupling beam. The 79.69 MHz coupled plate filter (CPF) achieved a narrow bandwidth of 8.8 kHz, corresponding to a tiny 0.011%. The CPF exhibits an impressive 34.84 dB stopband rejection and 7.82 dB insertion loss with near-zero passband ripple. In summary, the RF MEMS filter presented in this work shows promising potential for application in RF transceiver front-ends.

Ultra-high Q-factor quasi-BIC BaTiO3 metasurface for electro-optic modulation

Metasurfaces play a crucial role in trapping electromagnetic waves with specific wavelengths, serving as a significant platform for enhancing light–matter interactions. In all kinds of dynamic modulation metasurfaces, electro-optic modulation metasurfaces have attracted much attention due to its advantages of fast, stable and high efficiency. In order to respond to the extremely weak refractive index change of the electro-optical effect of the materials, the metasurfaces are required to support optical signals with high Q values. The quasi-bound state in the continuum (Q-BIC) is often used to enhance the light-field modulation capability of metasurfaces and to improve the modulation sensitivity of electro-optic modulators due to its ability to generate high Q-factor resonances. However, the design of an electro-optic modulation metasurface that facilitates the application of voltage and achieves modulation efficiency of nearly 100% is still in urgent need of development. In this study, single-crystal BTO metasurfaces are modeled using finite-difference time-domain method, and the structural symmetry is broken to introduce a Q-BIC resonance to generate a high Q-factor optical signal of 2.45 × 104 for high-depth electro-optic modulation. By simulating an applied electric field of 143 V/mm on the metasurface, a slight refractive index change of BTO of 8 × 10−4 was produced, leading to an electro-optical intensity modulation depth of 100%. Furthermore, the nanostructure of the metasurface was carefully designed to facilitate nano-fabrication and voltage application, and it is ideal for the development of low-power, CMOS-compatible, and miniaturized electro-optic modulation devices. Although the results of this study are based on simulations, they provide a crucial theoretical basis and guidance for the realization of efficient and realistic design of dynamic metasurfaces.

Control of the Dynamic Regimes of a Superconducting Nanointerferometer

An analytical solution has been found to describe dynamic processes in a superconducting nanointerferometer with negligibly low inductances that is included in a high-Q factor resonator. The effect of nonlinearity in the system, as well as the effect of external parametric pumping, has been analyzed. The screening of detected dynamic modes in the studied nanostructure in the resonator is performed in a wide range and their positions on the plane of the parameters have been determined. A significant influence of phase effects on the evolution of the system has been demonstrated and phase relations allowing one to control the output signal intensity have been evaluated. The detected effects open new possibilities for developing and testing basic elements of modern quantum computing systems.

Coupling-Based Multiple Bound States in the Continuum and Grating-Assisted Permittivity Retrieval in the Terahertz Metasurface.

The terahertz (THz) metasurfaces that support bound states in the continuum (BICs) provide a promising platform for various applications due to their high Q-factor resonance. In this study, we experimentally demonstrate multiple BICs with different resonance symmetries in the THz metasurface based on mode coupling. The proposed metasurface is composed of 2 × 2 split ring resonators (SRRs) metamolecules. The SRRs of two different gap angles in the metamolecule lattice provide intrinsic resonance with different frequencies, and the coupling between them exhibits high transmission quasi-BIC resonance, which can be tuned by varying the gap angle. The arrangement of SRRs in the 2 × 2 metamolecule lattice determines the types of coupling that govern the resonance symmetry of quasi-BIC. More interestingly, the multiple quasi-BICs enabled by different couplings can be simultaneously achieved in a metasurface. Apart from tuning the gap angles, the permittivity in the vicinity of SRRs also changes the resonance frequency. Consequently, quasi-BIC can be artificially formed by deliberately constructing the permittivity difference of the dielectric environment on the SRRs. In view of this, we introduce the scheme of permittivity retrieval for the dispersive analyte, assisted by the fixed-permittivity gratings. In addition, we experimentally demonstrate the metasurface in combination with the microfluidic chip for the sensing of the glucose solution concentration. Our findings offer a possible strategy for the existing manufactured metasurface to achieve quasi-BIC resonance and provide a promising candidate for approaching the spectral analysis of the biochemical.

Modal Phase-Matched Bound States in the Continuum for Enhancing Third Harmonic Generation of Deep Ultraviolet Emission.

Coherent deep ultraviolet (DUV) light sources are crucial for various applications such as nanolithography, biomedical imaging, and spectroscopy. DUV light sources can be generated by using conventional nonlinear optical crystals (NLOs). However, NLOs are limited by their bulky size, inadequate transparency at the DUV regime, and stringent phase-matching requirements for harmonic generation. Recently, dielectric metasurfaces support high Q-factor resonances and offer a promising approach for efficient harmonic generation at short wavelengths. In this study, we demonstrated a crystalline silicon (c-Si) metasurface simultaneously exciting modal phase-matched bound states in the continuum (BIC) resonance at the fundamental wavelength of 840 nm with a higher degree of freedom for precise control of the BIC resonance and a plasmonic resonance at the wavelength of 280 nm in the DUV to enhance third harmonic generation (THG). We experimentally achieved a Q-factor of ∼180 owing to the relatively large refractive index of the c-Si and the geometric symmetry breaking of the structure. We realized THG at a wavelength of 280 nm with a power of 14.5 nW by using a peak power density of 15 GW/cm2 excitation. The measured THG power is 14 times higher than the state-of-the-art THG dielectric metasurfaces using the same peak power density in the DUV regime, and the maximum obtained THG power enhancement factor is up to 48. This approach relies on the significant third-order nonlinear susceptibility of c-Si, the interband plasmonic nature of the c-Si in the DUV, and the strong field confinement of BIC resonance to boost overall nonlinear conversion efficiency to 5.2 × 10-6% in the DUV regime. Our work shows the potential of c-Si BIC metasurfaces for developing efficient and ultracompact DUV light sources using high-efficacy nonlinear optical devices.

Polarization-Independent High Q-Factor Resonance Achieved by Efficiently Selecting and Perturbing the Unit Cell of Nanostructure

Polarization-Independent High Q-Factor Resonance Achieved by Efficiently Selecting and Perturbing the Unit Cell of Nanostructure

Ultra-high Q-factor and amplitude-tunable Fano resonance in vanadium dioxide-silicon hybrid metamaterials.

As the resonance response in magnetic systems usually occurs at low frequencies, previously known as terahertz high Q-factor resonances, are mainly excited by electrical resonances. In this paper, we present a metamaterial based on vanadium dioxide-silicon arrays capable of achieving a Q-factor of up to 165 198; the ultra-high Q-factor Fano resonance excited by the proposed metamaterial is mainly affected by strong magnetic resonance. The analysis of diffractive coupling theory, electric field, magnetic field and current distribution shows that strong magnetic resonance is mainly realized by coupling localized plasmon resonance with the lattice resonance. Due to the conductivity-tunable nature of vanadium dioxide, the proposed metamaterial features an amplitude tunable function with a modulation depth of 98.8%. The spectral response of the analyte demonstrates the capability of the proposed metamaterial for application as a sensor with a maximum sensitivity of 69.52 GHz per RIU and a figure of merit of 15 456. The ultra-high Q-factor performance and amplitude tunability of the proposed structure can be applied to terahertz devices, such as ultrasensitive sensors, filters and optical switches.

Multilevel Feature Extraction Method for Adaptive Fault Diagnosis of Railway Axle Box Bearing

Railway axle box bearing fault signal contains high Q-factor resonance and low Q-factor transient shock components with periodic transient shock features that can characterize bearing faults. However, extracting fault features is usually difficult due to noise, transmission paths, and high-amplitude accidental shocks. Therefore, to address the abovementioned problems, the multilevel feature extraction method for adaptive fault diagnosis of railway axle box bearing was proposed. This paper used the maximum second-order cyclostationary blind convolution (CYCBD) to weaken the influence of disturbances, enhancing weak transient shock components. Resonant sparse decomposition(RSSD) is used for the selection of quality factor Q due to its excellent fault feature separation property. Considering the strict fault frequency component periodicity in the envelope spectrum, the envelope spectrum multipoint kurtosis (ESMK) is proposed as a metric. The Q factor is optimized using the gray wolf optimization algorithm (GWO) to obtain an adaptive sparse decomposition method (GWO-RSSD) for extracting bearing transient fault shocks to eliminate the signal effects of high-amplitude disturbance shocks and background noise. The simulation results and measured signal analysis of railway axle box bearing show that ESMK can effectively measure periodic transient shocks under strong shock interference compared with the MED-RSSD method. Thus, GWO-RSSD can adaptively separate the optimal low-Q resonance components, verifying the methods’ effectiveness and superiority.

Highly efficient second harmonic generation assisted by the quasi-bound states in the continuum from AlGaAs meta-gratings

Due to the design freedom of metasurfaces in tailoring wavefronts, they have become a general platform for miniaturized functional nonlinear optics. Recently, with the help of the quasi-bound states in the continuum (Q-BIC), the all-dielectric resonance metasurfaces with high quality factor (Q) boost the interaction between pump light and dielectric structure, which have become an effective way to achieve high nonlinear efficiency. Here, an asymmetric grating structure composed of AlGaAs is utilized to enhance the second harmonic generation (SHG) near Q-BIC. By breaking the symmetry of the grating structure, a simple normal incidence linearly polarized plane wave can be treated to excite stronger localized fields within the metasurfaces, allowing strong light–matter​ interactions in nonlinear metasurfaces. Numerical investigations depict that the Q-factor and resonant field enhancement noticed on the metasurface are intimately related to the asymmetric structure of the system. In addition, the high Q-factor resonance facilitates the SHG conversion process in AlGaAs metasurfaces. Especially, for the AlGaAs metasurface with Q-factor of 4.0314 × 104, the conversion efficiency of SHG can reach 10.5% when the pumping intensity is 5 MW/cm 2. This study is of great importance for analyzing the efficient nonlinear metasurfaces with high Q-factors.

Optical-microwave sensor for real-time measurement of water contamination in oil derivatives

This paper presents a novel microwave sensor using optical activation for measuring in real-time the water contamination in crude oil or its derivatives. The sensor is constructed from an end-coupled microstrip resonator that is interconnected to two pairs of identical fractal structures based on Moore curves. Electromagnetic (EM) interaction between the fractal curves is mitigated using a T-shaped microstrip-stub to enhance the performance of the sensor. The gap in one pair of fractal curves is loaded with light dependent resistors (LDR) and the other pair with microwave chip capacitors. The chip capacitors were used to increase the EM coupling between the fractal gaps to realize a high Q-factor resonator that determines the sensitivity of the sensor. Empirical results presented here show that the insertion-loss of the sensor is affected by the change in LDR impedance when illuminated by light. This property is used to determine the amount of water contaminated oil. The sensitivity of the sensor was optimized using commercial 3D EM solver. The measurements were made by placing a 30 mm diameter petri dish holding the sample on top of the sensor. The petri dish was filled up to a height of 10 mm with the sample of water contaminated crude oil, and the measurements were done in the range between 0.76 GHz and 1.2 GHz. The Q-factor of the oil sample with no water contamination was 70 and the Q-factor declined to 20 for 100% contamination. The error in the measurements was less than 0.024%. The sensor has dimensions of 0.127λo × 0.127λo × 0.004 λo and represents a new modality. Compared to existing techniques, the proposed sensor is simple to use, readily portable and is more sensitive.

Anapole-assisted ultra-narrow-band lattice resonance in slotted silicon nanodisk arrays

Anapole modes supported by well-designed dielectric nanostructures have attracted extensive attention in the field of nanophotonic applications owing to their unique strong near-field enhancement and non-radiative far-field scattering characteristics, yet it is still difficult to achieve high Q-factor resonance features with a narrow linewidth. In this work, a periodic slotted silicon nanodisk array is theoretically proposed to realize narrow linewidth and high Q-factor resonance in the near-infrared wavelength range. Through introducing the coupling between the anapole modes in the single dielectric nanostructure and the diffractive wave mode arising from the periodic array, the as-designed dielectric nanostructure synchronously manifests excellent spectral features with a bandwidth as narrow as about 2.0 nm, a large Q-factor of 599, an almost-perfect transmission amplitude of 96% and a relatively high electric field intensity (>2809 times) in the middle of the slotted silicon nanodisk. The as-designed nanostructure possessing these outstanding optical features can work as a high-efficiency refractive index sensor, whose sensitivity can reach 161.5 nm RIU−1 with its figure of merit attaining 80.8 RIU−1, efficiently distinguishing an index change of less than 0.01. The proposed slotted silicon nanodisk array exhibits tremendous potential for expanding applications such as label-free biochemical sensing, plasmonic refractive index sensing and surface enhancement spectroscopy.

Thermoelastic damping in micro-scale T-, U- and Z-shaped frame structures using wave propagation approach

Studying the thermo-mechanical coupling behavior and establishing the thermoelastic damping (TED) model are essential for improving the quality factor of the microelectromechanical resonator. In this work, an analytical TED model for planar frame resonators is first developed using the wave propagation approach. The method is illustrated for typical T-, U- and Z-shaped frame structures and can be extended to more complex frame structures. The frame is viewed as a set of beam segments interconnected by rigid joints, each following the Euler-Bernoulli beam theory. Based on the wave propagation approach, the wave transmission and reflection properties at discontinuities are determined taking into account the flexural and longitudinal motions. The displacement fields of the frame structure are established for both free and forced vibrations. The coupled temperature field of the frame is obtained by solving for the temperature variation arising from the flexural and longitudinal vibrations separately. Finally, the expression of TED is achieved by its energy definition. The validity of the present TED model is confirmed by comparison with finite element (FE) simulations. Numerical results indicate that the TED behavior of frame structures is too complicated to be predicted by previous TED models of simple structures. The often-overlooked longitudinal motion will cause a dramatic TED reduction around specific frequencies. The overall TED is determined by all segments together, and the influence of a segment is reflected by its energy share. Moreover, the effects of different boundary conditions and geometric parameters on TED are evaluated. Practical conclusions to guide the design of high Q-factor resonators are drawn based on the TED behavior of frame structures as summarized from the numerical study.

Active quasi-BIC metasurfaces assisted by epsilon-near-zero materials.

Active devices play a critical role in modern electromagnetic and photonics systems. To date, the epsilon (ε)-near-zero (ENZ) is usually integrated with the low Q-factor resonant metasurface to achieve active devices, and enhance the light-matter interaction significantly at the nanoscale. However, the low Q-factor resonance may limit the optical modulation. Less work has been focused on the optical modulation in the low-loss and high Q-factor metasurfaces. Recently, the emerging optical bound states in the continuum (BICs) provides an effective way for achieving high Q-factor resonators. In this work, we numerically demonstrate a tunable quasi-BICs (QBICs) by integrating a silicon metasurface with ENZ ITO thin film. Such a metasurface is composed of five square holes in a unit cell, and hosts multiple BICs by engineering the position of centre hole. We also reveal the nature of these QBICs by performing multipole decomposition and calculating near field distribution. Thanks to the large tunability of ITO's permittivity by external bias and high-Q factor enabled by QBICs, we demonstrate an active control on the resonant peak position and intensity of transmission spectrum by integrating ENZ ITO thin films with QBICs supported by silicon metasurfaces. We find that all QBICs show excellent performance on modulating the optical response of such a hybrid structure. The modulation depth can be up to 14.8 dB. We also investigate how the carrier density of ITO film influence the near-field trapping and far-field scattering, which in turn influence the performance of optical modulation based on this structure. Our results may find promising applications in developing active high-performance optical devices.

Asymmetric tetramer metasurface sensor governed by quasi-bound states in the continuum

Abstract Asymmetric metasurfaces supporting quasi-bound states in the continuum (BICs) with high Q-factors and strong light–matter interaction properties are attractive platforms for label-free biosensing applications. Recently, various meta-atom geometries have been exploited to support sharp high-Q quasi-BIC resonance. However, which meta-atom design may be a better practical choice remains unclear. Here, we compared several established meta-atom designs to address this issue by conducting an extensive theoretical discussion on sensing capability and fabrication difficulty. We theoretically revealed that the tetramer meta-atom geometry produces a higher surface sensitivity and exhibits a larger size-to-wavelength ratio than other meta-atom schemes. Furthermore, we found that metasurfaces with a higher depth considerably enhance surface sensitivity. The performance of two asymmetric tetramer metasurfaces (ATMs) with different heights was demonstrated experimentally. Both shallow and thick ATM structures exhibit sharp high Q-factor resonances with polarization-insensitive features. Notably, the surface sensitivity is 1.62 times for thick ATM compared to that for shallow ones. The combination of properties opens new opportunities for developing biosensing or chemical-sensing applications with high performance.

Terahertz high-Q magnetic dipole resonance induced by coherent Fano interactions

High Q-factor resonance holds great promise for bio-chemical sensing and enhanced light–matter interaction. However, terahertz (THz) magnetic resonances usually demonstrate low Q-factors, resulting in huge energy radiation loss particularly in high frequency bands. Here, we show that high Q-factor magnetic dipole resonance at THz frequencies can be achieved by exploiting the coherent Fano interactions with strong field enhancements in an array composed of single metallic split-ring resonators, working at Wood–Rayleigh anomalies. It can give rise to ultrahigh Q-factor beyond 104 in the THz regime. Experimentally, the measured Q-factor of dominant magnetic dipole resonance can achieve no less than a level of ∼261 by Lorentzian fitting to the experimental data. In addition, a high Q-factor of the fundamental-order magnetic dipole resonance is demonstrated beyond 30. High-Q magnetic dipole resonance is closely associated with ultralow-damping and negative permeability in the THz band. The measurements of magnetic dipole resonances are in good agreement with the theoretical analyses. Our scheme suggests a feasible route to suppress radiative loss for enhanced THz field-matter interaction.

E-shaped split ring resonator used for metasurface-based structure with an ultra-high Q-factor for terahertz application

Plasmonic devices based on split ring resonator (SRR) of ultra-low-loss performance (high Q-factor) are significant for a broad range of applications and studies. However, due to the inevitable ohmic and radiation losses, it has always been a challenge to design various types of plasmonic devices with high Q-factor. Here, we theoretically present a unique E-shaped SRR that can destructively suppress dipole radiation by adjusting the grating-arm position to produce asymmetry. Meanwhile, the proposed terahertz metasurface structure formed by periodically arranged E-shaped SRRs can give rise to high Q-factor resonances. The results show that an ultra-high Q-factor beyond 104 can be obtained in the terahertz frequency region by optimizing the structural parameters. The sensing characteristics of such a metasurface-based structure served as a refractive-index sensor are investigated as well, demonstrating its advantage of high sensitivity. Unique radiation properties of the metasurface-based structure enable it to use in the design of novel low-loss, ultra-sensitive sensors, narrowband filters, and other plasmonic devices.

Stability of symmetry-protected BICs in dielectric metasurfaces

Optical metasurfaces with high Q -factors have attracted much attention due to their sharp spectral features and significant field enhancement. The excitation of symmetry-protected bound states in the continuum (SP-BICs) is an efficient way to achieve a high Q -factor resonator. The experimental Q -factors of resonant quasi-SP-BIC metasurfaces are currently not high. In this work, we numerically demonstrate the stability of SP-BICs in silicon metasurfaces. The two SP-BICs are transformed into quasi-SP-BICs by breaking the in-plane symmetry of the structure, and their resonance properties are discussed by far-field radiation and near-field distribution. Moreover, the effects of different periods, sizes, substrate refractive indices, and shape factors on the SP-BICs are explored, and the Q -factors of quasi-SP-BICs always exhibit the same inverse quadratic dependence on asymmetry parameters, which demonstrates the stability of the SP-BIC. Our results may provide theoretical support for the experimental realization of ultrahigh Q -factor quasi-SP-BICs.

Reactive ion etching of ZERO CTE glass for MEMS resonator

In this paper, the reactive ion etching (RIE) of a glass with zero coefficient of thermal expansion (CTE) is reported, which can be used for a high Q-factor resonator used in timing resonators and gyroscopes. ZERO CTE glass can be used for a high Q-factor resonator, which is a key element for gyroscopes. SF6 and Xe were selected as etching gases. A thick Ni film was used as an etching mask. Experimental results show that ZERO CTE glass can be patterned by RIE at an etching rate similar to that of quartz glass. Due to the impurities which were used to control the CTE, the etched surface become rough and the sidewall tilted at about 20 degree. The minimum etching width as small as 30 μm could be achieved.

Trapped mode resonances in symmetric rectangular-hole tetramers

High Q-factor trapped mode resonances are mostly supported by weakly asymmetric metamolecules. In this paper, we study theoretically and experimentally a planar all-metallic metamaterial comprising highly symmetric metamolecules (rectangular-hole tetramers in a freestanding metallic plate) and find that high Q-factor trapped mode resonances can also be realized. The effect comes from the destructive interference between two anti-phased excitations: the electric dipole modes of the two inner and two outer rectangular holes within individual tetramers. Here, the high Q-factor resonance is dominated by the hole separation that affects greatly the coupling and radiation. At the resonance, a huge enhancement of electric field in each hole appears, accompanied by a significant slow-wave effect in the reflection process. Our design has potential applications in constructing high Q-factor filters, highly sensitive sensors and slow-wave devices.