Shell Resonator Research Articles

Silicon-Au nanowire resonators for high-Q multiband near-infrared wave absorption

Semiconductors have been widely utilized to fabricate optoelectronic devices. Nevertheless, it is still a challenging task to achieve high-quality (Q) resonant light absorption using the high refractive index semiconductors. In this work, we propose a facile scheme for multi-band perfect absorption in the near-infrared range using an array of core–shell cylinder-shaped resonators which are composed of gold nanowires and thin silicon shells. Based on the cooperative effects between the photonic modes of the semiconductor cavity and the plasmonic resonances of the metal resonator, five sharp absorption peaks are observed with the maximal absorption close to 100% (99.98%) and a high Q factor up to 208. The multi-band sharp absorption is observed to be angle-insensitive and polarization-adjustable. Absorption efficiency can be quantitatively tuned via the polarization states following the classical Malus law. Moreover, different semiconductors such as gallium arsenide, indium arsenide, indium phosphide have been exploited to reproduce the sharp perfect absorption in this core–shell resonators platform. The remarkable features make the proposed system potential for multiple applications such as multispectral filtering, photo-detection and hot electron generation.

Thermoelastic Dissipation in Diamond Micro Hemispherical Shell Resonators

Maximizing quality factor (Q) is essential to improve the performance of micro hemispherical shell resonators (μHSRs) which can be used in microelectromechanical system (MEMS) gyroscopes to measure angular rotation. Several energy dissipation mechanisms limit Q, where thermoelastic dissipation (TED) is the major one and studied in this paper. Fully coupled thermo-mechanical equations for calculating TED are formulated, and then temperature distribution in a deformed μHSR and its quality factor related to TED (QTED) are obtained by solving the equations through a finite-element method (FEM). It has been found that different fabrication process conditions can obtain various geometrical parameters in our previous studies. In order to provide guidelines for the design and fabrication of μHSRs, the effects of their geometry on resonant frequency (f0) and QTED are studied. The change of anchor height and small enough anchor radius have no effect on both f0 and QTED, but the shell size including its radius, thickness and height has significant impact on f0 and QTED. It is found that whether a μHSR has lower f0 and higher QTED or higher f0 and higher QTED can be achieved by changing these geometrical parameters. The results presented in this paper can also be applied to other similar resonators.

Whispering-Gallery-Mode Optical Microshell Resonator Infrared Detector

We demonstrate a thermal infrared (IR) detector based on a high quality-factor (Q) whispering gallery mode (WGM) borosilicate glass microspherical shell resonator and investigate its performance to detect IR radiation in 1 – 20 ${\mu }\text{m}$ wavelength range. The resonator exhibits a temperature sensitivity of 1.17 GHz/K with a Q-factor of 3 million and can be configured as a high sensitivity infrared sensor. The microspherical shell IR sensor exhibited a responsivity of 7.88 kHz/nW and achieved a noise-equivalent-power (NEP) of 19 nW/ $\sqrt {Hz}$ experimentally. A laser Doppler vibrometer (LDV) is used to measure the physical expansion of the microspherical glass resonator when IR radiation is absorbed. Based on the experimentally measured diametric expansion of the shell per unit IR power absorbed, the NEP of 19 nW/ $\sqrt {Hz}$ corresponds to a dimensional change of 2 pm which can be resolved using the resonator. Using COMSOL modeling, thermal expansion analysis was performed for the absorbed IR Power. Using these values of dimension change of the microspherical shell, the dependence of resonance frequency shift on absorbed IR power was simulated. These models show that a NEP of 690 pW/ $\sqrt {Hz}$ can be achieved for the microspherical shell with a diameter of 2 mm and a thickness of 2 ${\mu }\text{m}$ .

Development of 3D Fused Quartz Hemi-Toroidal Shells for High-Q Resonators and Gyroscopes

In this paper, recent developments in the design and fabrication of micromachined fused quartz hemi-toroidal shells are presented. The fabrication is based on micro glassblowing process, demonstrated to enable the realization of high-Q MEMS resonators and gyroscopes. The design optimization of the shell geometry is performed using parametric finite element analysis. The effect of geometric parameters on the scaling of the resonant frequencies and energy dissipation are discussed. Three variations of the micro-glassblowing process are studied in the paper, concluding that shell resonators with a broad operational frequency range without losing the symmetry and Q-factor are feasible. Finite element models are presented to simulate the presented glassblowing processes, which are used to predict the final geometry of shell resonators accurately. Operational frequency as low as 5 kHz and Q-factor as high as 1.7 million is demonstrated on the fabricated shell resonators. The proposed process modifications demonstrate a low-cost and scalable fabrication of 3D shells for resonators and gyroscopes, which can be used in inertial navigation and timing applications. [2019-0179]

Strong exciton–plasmon couplings dependent on two localized modes in cuboid dielectric–metal core–shell resonators

In this paper, the strong exciton–plasmon couplings dependent on two localized modes are numerically and theoretically investigated in cuboid dielectric–metal core–shell resonators. For different resonance wavelengths, the electric fields of different modes can be highly localized in the dielectric gap layer, bringing about very small mode volumes. Through the active control of core–shell cavity parameters, the Rabi splitting and the anti-crossing dispersion are observed in the extinction spectrum, confirming the realization of strong coupling Both the multimode interference coupled mode theory and the Bloch equation are applied to explain the strong coupling in this system. After replacing the shell metal from silver to gold, the large red shift of resonance peaks exactly makes the high order mode strongly coupled with the same J-aggregate molecules, thus inducing slight spatial changes and reducing the required minimum number of the coupled excitons.

Three-dimensional micromachined diamond birdbath shell resonator on silicon substrate

This paper proposes a novel three-dimensional (3-D) micromachined birdbath shell resonator ($$\mathrm {\upmu }$$-BSR) fabricated from polycrystalline diamond on silicon substrate for potential MEMS gyroscope. Design, modal simulation, MEMS fabrication process and vibration test of the micromachined diamond birdbath shell resonator are presented. Key features of the 3-D fabrication process are the etching of the bulk silicon mold and deposition of high-Q polycrystalline diamond films onto the mold. The birdbath shell resonator is fabricated with a good structural symmetry, owing to its supporting anchor and shell are integrated manufactured through the MEMS fabrication process. By using piezoelectric actuation and optical characterization, the M = 2 elliptical vibration mode is determined to be at about 80.61 kHz with a normalized frequency split ($$\varDelta {f_{M = 2}}/{f_{M = 2}}$$) of 0.32%. The frequency separation between the M = 2 elliptical mode and the closest parasitic tilting mode of the $$\upmu $$-BSR is relatively large, which makes the resonator less sensitive to vibration and improves shock resistance. These resonators show great promise for being used as micro birdbath resonator gyroscopes ($$\upmu $$-BRGs) on a chip.

A Novel High Transduction Efficiency Micro Shell Resonator Gyroscope With 16 T-Shape Masses Using Out-of-Plane Electrodes

A novel micro shell resonator gyroscope (MSRG) with 16 T-shape masses using out-of-plane electrodes is proposed in this paper. The T-shape masses are designed for high transduction efficiency. Out-of-plane electrodes are used to drive and detect the spatial deformation of the resonator. The finite element method (FEM) is applied to evaluate the influence of the T-shape mass on transduction efficiency. Compared with the MSRG without the T-shape masses, the FEM results reveal that the MSRG with T-shape masses has shown an increase of 42% on effective mass ( ${M}_{ {eff}}$ ) and a decrease of 8% on ${f}_{ {n=2}}$ . For the MSRG without T-shape mass, spherical–cylindrical, spherical, and out-of-plane electrodes have been applied to drive and sense n = 2 wineglass modes. Compared with the MSRG without T-shape using out-of-plane electrodes, the MSRG with T-shape masses has showed the improvement of 334%, 522%, and 598% on driving efficiency ( ${S}_{ {d}}$ ), detection efficiency ( ${S}_{ {s}}$ ), and mechanical sensitivity ( ${S}_{ {mech}}$ ) due to large ${M}_{\text {eff}}$ and electrode area. In addition, the improvement of 15% in the thermal noise of a gyroscope (ARW $_{\text {mech}}$ ) is dominated by a large effective mass, contributing to the improvement of signal-to-noise ratio. The process of micro blow torching with the whirling platform and femtosecond ablation is presented to fabricate the MSRG with T-shape masses. The performance of MSRG is demonstrated experimentally with out-of-plane capacitive transduction. The MSRG is operated in the force-rebalance mode, which demonstrates a scale factor of 0.107V/(°/s), an angle random walk of 0.099°/ $\text{h}^{{1/2}}$ , and a bias instability of 0.46°/h, showing a great potential for high-performance gyroscopic application.

Fabrication and characterisation of microscale hemispherical shell resonator with diamond electrodes on the Si substrate

A self-aligned fabrication method is employed for microscale hemispherical shell resonator with integrated diamond electrodes on a silicon (Si) substrate. The millimetre-scale three-dimensional (3D) hemispherical shell resonator, with integrated electrostatic excitation and capacitive detection transducers for full control of the resonator, is fabricated on the Si substrate by employing a microelectromechanical systems process. The eight integrated diamond electrodes evenly distributed outside the hemispherical shell are fabricated using a self-aligned method, which ensures uniform capacitive gap along the whole circumference. The Boron-doped polycrystalline diamond, a material with low thermo-elastic damping and low surface losses to reach the high quality, is used as the millimetre-scale 3D hemispherical shell resonator with integrated electrodes. The fabrication process enables the production of almost perfect hemisphere mould (<2% roundness variation) with an average surface roughness of 3 nm. Vibration modes and frequencies are carried out by a scanning laser Doppler vibrometer; the elliptical mode frequency is determined to be at 81.3 kHz, with the two M = 2 degenerate modes having a relative frequency mismatch of 0.86%. This process can be further optimised to fabricate high-quality and full-symmetric microscale hemispherical resonator gyroscopes in batch.

The Synthesis Model of Flat-Electrode Hemispherical Resonator Gyro.

The Hemispherical Resonator Gyro (HRG) is a solid-state and widely used vibrating gyroscope, especially in the field of deep space exploration. The flat-electrode HRG is a new promising type of gyroscope with simpler structure that is easier to be fabricated. In this paper, to cover the shortage of a classical generalized Coriolis Vibration Gyroscope model whose parameters are hard to obtain, the model of flat-electrode HRG is established by the equivalent mechanical model, the motion equations of unideal hemispherical shell resonator are deduced, and the calculation results of parameters in the equations are verified to be reliable and believable by comparing with finite element simulation and the reported experimental data. In order to more truthfully reveal the input and output characteristics of HRG, the excitation and detection models with assemble errors and parameters are established based on the model of flat-electrode capacitor, and they convert both the input and output forms of the HRG model to voltage changes across the electrodes rather than changes in force and capacitance. An identification method of assemble errors and parameters is proposed to evaluate and improve the HRG manufacturing technology and adjust the performance of HRG. The average gap could be identified with the average capacitance of all excitation and detection capacitors; fitting the approximate static capacitor model could identify the inclination angle and direction angle. With the obtained model, a firm and tight connection between the real HRG system and theoretical model is established, which makes it possible to build a fully functional simulation model to study the control and detection methods of standing wave on hemispherical shell resonator.

Research on precise mechanical trimming of a micro shell resonator with T-shape masses using femtosecond laser ablation

This paper presents a novel method to achieve permanent frequency trimming between wineglass modes of micro shell resonator (MSR) with T-shape masses (T-masses) using femtosecond laser ablation. Trimming effects on stiffness and mass distribution around the rim are analyzed by finite element method (FEM). Stiffness and mass trimming can be achieved by grooves ablating in different positions. A systematic frequency trimming process including stiffness and mass modification is proposed. FEM simulation is further applied to estimate the variation of cross coupling and frequency split during the trimming process. High resolution trimming without surface deterioration is achieved by using a low-power femtosecond laser. Finally, frequency trimming experiments were implemented on imperfect resonators. Test results show that frequency split can be effectively reduced to less than 0.5Hz within several steps, demonstrating the effectiveness of this method.

基于硅各向同性腐蚀工艺的三维曲面壳体微谐振器制备技术

基于硅各向同性腐蚀工艺的三维曲面壳体微谐振器制备技术

Highly tunable multiple narrow emissions of dyed dielectric-metal core–shell resonators: towards efficient fluorescent labels

We report a potential efficient fluorescent label based on the dyed dielectric-metal core–shell resonators (DMCSRs). By utilizing the near-field coupling between the dyes and the multipolar sharp cavity plasmon resonances, the dyed DMCSRs with diameter of 1.02 μm are demonstrated to be capable of supporting multiple spontaneous emission peaks with the linewidths as narrow as ∼ 10 nm in visible range, and these reshaped fluorescent emissions are insensitive to the surrounding dielectric environment. Furthermore, these multiple narrow emission peaks show a precise tunability on the spectrum by simply separating a nanometric dielectric layer between the dielectric core and the metallic shell, which may provide an attractive spectral multiplexing strategy in the fields of cell biology and medical sciences.

Electromagnetic field analysis of shielded composite dielectric spherical shell resonator in infrared and visible regions

In this paper, we have presented an electromagnetic field analysis of shielded composite dielectric spherical shell resonator. The resonator studied in this work is considered for the first time as no study on such resonators is available in the published literature to the best of the author's information. This shielded composite dielectric spherical shell resonator is composed of two concentric metal spheres with different dielectric material has been made. The whole assembly is shielded by a perfectly conducting concentric spherical metal. The expression for the resonant frequencies and quality factors have been calculated using numerical methods for both the TEnmℓand TMnmℓ modes for an infrared and visible regions. It is found that as the outer radius of the shielded composite dielectric spherical shell resonator increases, the quality factor Q of the resonator increases monotonically. It is also found that if we change the radius of the inner dielectric sphere, there is no appreciable change in resonant frequency of the concerned mode is observed. This is due to the small difference in the permittivities of the materials of the inner and the outer dielectric spheres. It has also been observed that an inner concentric superconducting sphere within a dielectric spherical resonator is a more effective controlling parameter of the resonant frequency than the other parameters.

Chip-scale high Q-factor glassblown microspherical shells for magnetic sensing.

A whispering gallery mode resonator based magnetometer using chip-scale glass microspherical shells is described. A neodynium micro-magnet is elastically coupled and integrated on top of the microspherical shell structure that enables transduction of the magnetic force experienced by the magnet in external magnetic fields into an optical resonance frequency shift. High quality factor optical microspherical shell resonators with ultra-smooth surfaces have been successfully fabricated and integrated with magnets to achieve Q-factors of greater than 1.1 × 107 and have shown a resonance shift of 1.43 GHz/mT (or 4.0 pm/mT) at 760 nm wavelength. The main mode of action is mechanical deformation of the microbubble with a minor contribution from the photoelastic effect. An experimental limit of detection of 60 nT Hz−1/2 at 100 Hz is demonstrated. A theoretical thermorefractive limited detection limit of 52 pT Hz−1/2 at 100 Hz is calculated from the experimentally derived sensitivity. The paper describes the mode of action, sensitivity and limit of detection is evaluated for the chip-scale whispering gallery mode magnetometer.

Microsacle PolySilicon Hemispherical Shell Resonating Gyroscopes with Integrated Three-dimensional Curved Electrodes

A novel approach for fabrication of polysilicon hemispherical resonator gyroscopes with integrated 3-D curved electrodes is developed and experimentally demonstrated. The 3-D polysilicon electrodes are integrated as a part of the hemispherical shell resonator’s fabrication process, and no extra assembly process are needed, ensuring the symmetry of the shell resonator. The fabrication process and materials used are compatible with the traditional semiconductor process, indicating the gyroscope has a high potential for mass production and commercial development. Without any trimming or tuning of the n=2 wineglass frequencies, a 28 kHz shell resonator demonstrates a 0.009% frequency mismatch between two degenerate wineglass modes, and a 13.6 kHz resonator shows a frequency split of 0.03%. The ring-down time of a fabricated resonator is 0.51 s, corresponding to a Q of 22000, at 0.01 Pa vacuum and room temperature. The prototype of the gyroscope is experimentally analyzed, and the scale factor of the gyro is 1.15 mV/°/s, the bias instability is 80 °/h.

Fused Silica Micro Shell Resonator With T-Shape Masses for Gyroscopic Application

This paper presents a novel micro shell resonator (MSR) with T-shape masses based on fused silica using out-of-plane electrode structures. Eight circular-distributed T-shape masses are designed along the rim of resonator shell to improve transduction efficiency, including drive efficiency and detection efficiency. The dynamic parameters and transduction efficiency are calculated and optimized with finite element method, revealing 3.76 times improvement in drive efficiency, 4.65 times improvement in detection efficiency, and 17.81 times increase in mechanical sensitivity. In addition, it is feasible to trim the frequency by adding or removing mass on the T-shape masses. The key feature of the process is based on micro blow-torching process and whirling platform, which form the resonator structure with smooth roughness and good structure uniformity. Femtosecond laser ablation is used to release the T-shape masses for good symmetry and high processing quality. Then, metalized MSR with T-shape masses is assembled on a glass substrate. Electrostatic transduction is used to detect spatial deformation of resonators by out-of-plane electrodes, which reveals a frequency mismatch of 0.175% at 6904.4 Hz and 6916.5 Hz with quality factors of 20.39 k ( $\tau =0.94$ s) and $Q = 36.94$ k ( $\tau =1.7\text{s}$ ). [2017-0086]

The Application of Chemical Foaming Method in the Fabrication of Micro Glass Hemisphere Resonator.

Many researchers have studied the miniaturization of the hemisphere resonator gyroscope for decades. The hemisphere resonator (HSR), as the core component, has a size that has been reduced to the submillimeter level. We developed a method of batch production of micro-hemisphere shell resonators based on a glass-blowing process to obtain larger hemisphere shells with a higher ratio of height to diameter (H/D), we introduced the chemical foaming process (CFP) and acquired an optimized hemisphere shell; the contrasted and improved H/D of the hemisphere shell are 0.61 and 0.80, respectively. Finally, we increased the volume of glass shell resonator by 51.48 times while decreasing the four-node wineglass resonant frequencies from 7.24 MHz to 0.98 MHz. The larger HSR with greater surface area is helpful for setting larger surrounding drive and sense capacitive electrodes, thereby enhancing the sensitivity of HSR to the rotation. This CFP method not only provides more convenience to control the shape of a hemisphere shell but also reduces non-negligible cost in the fabrication process. In addition, this method may inspire some other research fields, e.g., microfluidics, chemical analysis, and wafer level package (WLP).

Investigation on Eigenfrequency of a Cylindrical Shell Resonator under Resonator-Top Trimming Methods.

The eigenfrequency of a resonator plays a significant role in the operation of a cylindrical shell vibrating gyroscope, and trimming is aimed at eliminating the frequency split that is the difference of eigenfrequency between two work modes. In this paper, the effects on eigenfrequency under resonator-top trimming methods that trim the top of the resonator wall are investigated by simulation and experiments. Simulation results show that the eigenfrequency of the trimmed mode increases in the holes-trimming method, whereas it decreases in the grooves-trimming method. At the same time, the untrimmed modes decrease in both holes-trimming and grooves-trimming methods. Moreover, grooves-trimming is more efficient than holes-trimming, which indicates that grooves-trimming can be a primary trimming method, and holes-trimming can be a precision trimming method. The rigidity condition after grooves-trimming is also studied to explain the variation of eigenfrequency. A femtosecond laser is employed in the resonator trimming experiment by the precise ablation of the material. Experimental results are in agreement with the simulation results.

Simulation of Blowtorch Reflow of Fused Silica Micro-Shell Resonators

Fabrication of high-precision micro-shell 3-D resonators is a challenging task. We report a non-isothermal model and finite-element simulation results for the prediction of geometries of fused silica micro-shell resonators fabricated with a blowtorch molding process. The model considers coupling between thermal and mechanical aspects of the reflowing process and heat transfer at the fused silica/mold interface, which dramatically controls the final shape of the resonator. The model is successfully applied to investigate the production details of 3-D hemi-ellipsoidal shells of revolutions with eccentricity, such as birdbath shell resonators. Comparisons of numerical results with experimental observations demonstrate that the model can predict an overall trend of thickness distribution. The numerical model can be used to optimize shell geometry and thickness by changing different fabrication parameters, such as surface heat flux, conductivity of the mold material, and initial temperature of the mold. The simulation technique also allows the mold shape and design to be optimized to fabricate different micro-shell geometries and dimensions. The model clarifies the blowtorch molding capabilities and limitations for fabrication of hollow 3-D shell resonators. [2016-0251]

Thermoelastic Dissipation in Micromachined Birdbath Shell Resonators

Many MEMS gyroscopes rely on micro mechanical resonators to measure angular rotation. Maximizing their quality factor ( $Q$ ) will help improve accuracy. There are several energy dissipation mechanisms that limit $Q$ . This paper studies the role of thermoelastic dissipation (TED) in micro birdbath shell resonators. Fully coupled thermo-mechanical equations of physical behavior are solved for these shells using a finite-element method. Furthermore, an analytical model is developed to predict TED. The effects of material properties, shell geometry, edge chipping around the shell rim, trimming approaches, thin-film coatings, and operating temperature on thermoelastic $Q$ ( $Q_{{TED}})$ are studied. It is found that the shell material properties and rim thickness have significant impact on $Q_{{TED}}$ . However, edge chipping and most of the shell geometrical parameters do not have large impact. Additionally, this paper shows that some trimming approaches, such as forming grooves along the rim, can improve $Q_{{TED}}$ . A study of the effect of metal coatings on the resonator on $Q$ shows that the coating thickness and material are important factors affecting $Q$ and $Q_{{TED}}$ . The results presented in this paper provide guidelines for the design of other similar high- $Q$ resonators. [2016–0027]