Silicon Disk Resonators Research Articles

Silicon double-disk optomechanical resonators from wafer-scale double-layered silicon-on-insulator

Whispering Gallery Mode (WGM) optomechanical resonators are a promising technology for the simultaneous control and measurement of optical and mechanical degrees of freedom at the nanoscale. They offer potential for use across a wide range of applications such as sensors and quantum transducers. Double-disk WGM resonators, which host strongly interacting mechanical and optical modes co-localized around their circumference, are particularly attractive due to their high optomechanical coupling. Large-scale integrated fabrication of silicon double-disk WGM resonators has not previously been demonstrated. In this work, we present a process for the fabrication of double-layer silicon-on-insulator wafers, which we then use to fabricate functional optomechanical double silicon disk resonators with on-chip optical coupling. The integrated devices present experimentally observed optical quality factors of the order of 105 and a single-photon optomechanical coupling of approximately 15 kHz.

Coupled mode theory-based analytical model of a ring resonator refractive index sensor incorporating bending loss and dispersion

This paper presents an analytical model of a silicon nitride-based 2D ring resonator refractive index (RI) sensor using coupled mode theory (CMT). The proposed model decomposes the ring resonator into two coupling regions and employs coupled-mode equations to describe input and output amplitudes via scattering matrix analysis. The proposed sensor, operating with varying refractive indices in the background cladding, demonstrates a sensitivity of 218 nm/RIU and a total quality factor of 1198. A comprehensive analysis of the bending loss in the proposed sensor is conducted, elucidating its impact on sensitivity, coupling quality factor, and intrinsic quality factor. This analysis aids in the selection of optimal ring resonator parameters, including radius, width, and gap, to achieve superior sensing performance. Furthermore, the paper examines the effect of dispersion on sensitivity and quality and compares the results with those obtained from CMT-based silicon core ring resonator and disk resonator RI sensors. This study provides valuable insights for the design and optimization of high-performance silicon nitride-based RI sensors for various applications.

Measurement of the temperature dependence of mechanical losses induced by an electric field in undoped silicon disk resonators

Test masses of future laser interferometric gravitational-wave detectors will be made of high-purity silicon and cooled, in particular, to 123 K in the LIGO Voyager project. Electrostatic actuators are supposed to be used to tune the test mass position. Capacitive coupling of the actuator electrodes with the silicon test mass results in the mechanical loss caused by electric currents flowing in silicon having a finite resistivity. This loss is a cause of additional thermal noise. In this study, we present the results of temperature dependence of the electric field induced loss in the bending vibration mode of commercial disk-shaped undoped silicon wafers in the temperature range of 100–295 K.

Design of a Multiple Folded-Beam Disk Resonator with High Quality Factor.

This paper proposes a new multiple folded-beam disk resonator whose thermoelastic quality factor is significantly improved by appropriately reducing the beam width and introducing integral-designed lumped masses. The quality factor of the fabricated resonator with (100) single crystal silicon reaches 710 k, proving to be a record in silicon disk resonators. Meanwhile, a small initial frequency split of the order-3 working modes endows the resonator with great potential for microelectromechanical systems (MEMS) gyroscopes application. Moreover, the experimental quality factor of resonators with different beam widths and relevant temperature experiment indicate that the dominating damping mechanism of the multiple folded-beam disk resonator is no longer thermoelastic damping.

A wide bandwidth real-time MEMS optical power meter with high resolution and linearity

This paper presents a new type of wide bandwidth real-time micromechanical optical power meter based on a micro silicon disk resonator. The resonant frequency of micromechanical resonator is ultrasensitive with its heat absorption, which is verified by both simulation and experiment, including the open-loop and closed-loop testings. The resonant frequency of both the elliptical mode and contour mode of the disk resonator will shift when lasers of 488 nm and 1550 nm with different power are irradiated. The detector shows different heat absorption efficiency depending on the wavelength of the measured optical signal. The heat absorption efficiency was tested with 488 nm and 1550 nm laser irradiation in our experiments. According to our closed-loop experiments, the resolution of our detector could reach 78 nW, and a high linearity of R2 = 0.99605 for the 488 nm target optical signal.

Using silicon disk resonators to measure mechanical losses caused by an electric field.

Several projects of the next generation gravitational-wave detectors use the high purity monocrystalline silicon test masses. The electric field of the actuator that is applied to correct the position of the silicon test mass causes additional mechanical losses and associated noise. Disk mechanical resonators are widely used to study mechanical losses in multilayer optical coatings that are deposited on the test masses of gravitational-wave detectors. We use silicon disk resonators to study losses caused by an electric field. In particular, the dependence of mechanical losses on the resistivity of silicon is investigated. The resonator is a thin commercial silicon wafer in which a low frequency nodal diameter mode is excited. A DC voltage is applied between the wafer and a nearby electrode. We use two measurement configurations. In the first configuration, the dependence of losses on the resistance in the voltage supply circuit is investigated. The dependence of losses on the resistivity of silicon is investigated in the second configuration. We propose a model that relates the electric field induced mechanical loss in disk resonators to the resistivity of the material. Measurements are carried out for low and high resistivity silicon wafers. The measurement results are compared with calculations. Based on these studies, it is possible to estimate the loss and noise of the test masses of gravitational-wave detectors associated with electrostatic actuators.

Influence of the Surface Roughness of a Silicon Disk Resonator on Its Q-Factor

This article presents a silicon disk resonator of the whispering-gallery-mode (WGM) type. The calculated Q-factor of the silicon WGM resonator was 107. Two methods of studying the surface roughness of a silicon WGM resonator with a nonlinear profile by means of Helios 650 scanning electron microscope and Bruker atomic force microscope (AFM) are presented. The results obtained by the two methods agreed well with each other. A comparison of the surface roughness values of WGM resonators manufactured using different technological approaches is presented. Based on the obtained data, a preliminary estimated Q-factor calculation of the resonators was performed, which was refined by numerical calculation using the finite-difference time-domain (FDTD) method. The effect of the surface roughness of the resonator on its Q-factor was found. Reducing the surface roughness of the resonator from 30 nm to 1–2 nm led to an increase in its Q-factor from 104 to 107.

0.015 Degree-Per-Hour Honeycomb Disk Resonator Gyroscope

High performance Microelectromechanical system (MEMS) gyroscopes are in great demand in the fields of precise navigation, automatic driving and precise attitude measurement. Honeycomb disk resonator gyroscope(HDRG) which works on wineglass-modes has many advantages including higher immunity to fabrication errors, better resonant mode consistency and better inner electrode arrangement, showing excellent potentials to be the next-generation MEMS gyroscope with high performance and good robustness. In this paper, a new HDRG prototype is designed based on the comprehensive optimizations of resonant structure and electrode configuration. The main structure parameters and the lumped-mass configuration are optimized systematically through the finite element simulation, while the configuration and arrangement of the inner electrodes are optimized based on the vibration amplification effect, offering systematic reference for the optimizations of other MEMS gyroscopes. The new HDRG is fabricated through a SOI fabrication technique and tested with a close-loop digital circuit. Quality factor of the optimized HDRG prototype reaches 650k, proving to be a record in silicon disk resonator gyroscopes. The bias instability of the optimized gyroscope reaches 0.015°/h under room temperature without any compensation, approaching the accuracy of navigation grade. Scale factor nonlinearity reached around 120ppm in the range of ±300°/s without compensation. The comprehensive performance is at the forefront of MEMS resonant gyroscopes.

All-optical nanophotonic resonant element for switching and routing applications exploiting graphene saturable absorption

A silicon disk resonator overlaid with a uniform graphene layer in an add-drop configuration is proposed as an all-optical routing element. Operation is based on the saturable absorption effect provided by the graphene layer. The element is thoroughly analyzed as a two-channel device in the context of an appropriate nonlinear framework combining perturbation theory and temporal coupled-mode theory. Taking into consideration the primary nonlinear effect, which is graphene saturable absorption, a design path is carefully developed that eventually leads to a traveling-wave resonant element with low-power requirements, low insertion loss, high extinction ratio, and sufficient bandwidth. In a subsequent step, other important nonlinear effects originating from graphene and the silicon disk, including the Kerr effect and free-carrier effects, are considered and means for counterbalancing their action are demonstrated. A low control power of 9mW together with a bandwidth of 20GHz is shown possible, with the insertion loss of almost 3dB and an extinction ratio over 10dB in both ports (add and drop).

Research of Constructive and Technological Methods for Forming a Silicon Disk Resonator with Whispering Gallery Modes

This article presents the results of a computer simulation of whispering gallery modes in the structure of a silicon disk resonator with a wedge-shaped profile made on a silicon-on-isolator base (SOI). The rationale for the choice of silicon as a material for its manufacturing is given. The results of the study of the influence of the wedge angle on the whispering gallery mode parameters (WGM) are presented. The optimum wedge angle of a silicon disk resonator is determined, which ensures the minimum loss and maximum mode stability. The technological aspects of plasma-chemical etching processes for forming a wedge-shaped profile of the edge of a silicon disk resonator are studied.

Toward Physically Unclonable Functions From Plasmonics-Enhanced Silicon Disc Resonators

The omnipresent digitalization trend has enabled a number of related malicious activities, ranging from data theft to disruption of businesses, counterfeiting of devices, and identity fraud, among others. Hence, it is essential to implement security schemes and to ensure the reliability and trustworthiness of electronic circuits. Toward this end, the concept of physically unclonable functions (PUFs) has been established at the beginning of the 21st century. However, most PUFs have eventually, at least partially, fallen short of their promises, which are unpredictability, unclonability, uniqueness, reproducibility, and tamper resilience. That is because most PUFs directly utilize the underlying microelectronics, but that intrinsic randomness can be limited and may thus be predicted, especially by machine learning. Optical PUFs, in contrast, are still considered as promising---they can derive strong, hard-to-predict randomness independently from microelectronics, by using some kind of "optical token." Here we propose a novel concept for plasmonics-enhanced optical PUFs, or peo-PUFs in short. For the first time, we leverage two highly nonlinear phenomena in conjunction by construction: (i) light propagation in a silicon disk resonator, and (ii) surface plasmons arising from nanoparticles arranged randomly on top of the resonator. We elaborate on the physical phenomena, provide simulation results, and conduct a security analysis of peo- PUFs for secure key generation and authentication. This study highlights the good potential of peo-PUFs, and our future work is to focus on fabrication and characterization of such PUFs.

Side-Supported Radial-Mode Thin-Film Piezoelectric-on-Silicon Disk Resonators.

In this paper, anisotropy of single-crystalline silicon (SCS) is exploited to enable side-supported radial-mode thin-film piezoelectric-on-substrate (TPoS) disk resonators. In contrast to the case for isotropic material, it is demonstrated that the displacement of the disk periphery is not uniform for the radial-mode resonance in SCS disks. Specifically, for high-order harmonics, nodal points are formed on the edges, creating an opportunity for placing suspension tethers and enabling side-supported silicon disk resonators at the very high-frequency band with negligible anchor loss. In order to thoroughly study the effect of material properties and the tether location, anchor loss is simulated using a 3-D perfectly matched layer in COMSOL. Through modeling, it is shown that eighth-harmonic side-supported SCS disk resonators could potentially have orders of magnitude lower anchor loss in comparison to their nanocrystalline diamond (NCD) disk resonator counterparts given the tethers are aligned to the [100] crystalline plane of silicon. It is then experimentally demonstrated that in TPoS disk, resonators fabricated on an 8- [Formula: see text] silicon-on-insulator (SOI) wafer, unloaded quality factor improves from ~450 for the second-harmonic mode at 43 MHz to ~11500 for the eighth-harmonic mode at 196 MHz if tethers are aligned to [100] plane. The same trend is not observed for NCD disk resonators and SCS disk resonators with tethers aligned to [110] plane. Finally, the temperature coefficient of frequency is simulated and measured for the radial-mode disk resonators fabricated on the 8- [Formula: see text]-thick degenerately n-type doped SCS, and the TFC data are utilized to guarantee proper identification of the harmonic radial-mode resonance peaks among others.

Surface Area Enhancement of Nanomechanical Disk Resonators Using MWCNT for Mass-Sensing Applications.

This work presents fabrication of thermal-piezoresistive nanoelectromechanical silicon disk resonators and their characterization as highly sensitive mass sensors. Forest of multiwall carbon nanotubes (MWCNTs) has been grown on the top surface of the fabricated devices, increasing the resonator effective surface area, which, in turn, increases the adsorption capacity and, therefore, the frequency shift of the sensor in molecular or particulate detection applications. To investigate the effect of the enhanced surface area on frequency shift, devices with and without MWCNTs were exposed to an aqueous solution of manganese sulfate for different deposition times and the resonance frequency shift was recorded accordingly. The measured frequency shift for the devices covered with MWCNTs was 14× higher than similar bare silicon devices. Furthermore, mass loading experiments were performed using gold nanoparticles as the loading mass. A novel way to attach gold nanoparticles on the carbon nanotubes (CNTs) wall was developed here. Oxygen plasma treatment introduced dangling bonds on the MWCNTs walls to facilitate the bonding between them and trimethoxysilane aldehyde molecules, forming the self-assembled monolayer (SAM). After functionalization of the device with SAM and antiinfluenza H1N1 viruses (AB), the device was exposed to a solution of Antimouse IgG (whole molecule)-gold antibody produced in goat products. The results showed more than three times response enhancement for the resonators with MWCNTs.

0.04 degree-per-hour MEMS disk resonator gyroscope with high-quality factor (510\u2009k) and long decaying time constant (74.9\u2009s)

The disk resonator gyroscope is an attractive candidate for high-performance MEMS gyroscopes. This gyroscope consists of a sensor and readout electronics, and the characteristics of the sensor directly determine the performance. For the sensor, a high-quality factor and long decaying time constant are the most important characteristics required to achieve high performance. We report a disk resonator gyroscope with a measured quality factor of 510 k and decaying time constant of 74.9 s, which is a record for MEMS silicon disk resonator gyroscopes, to the best of our knowledge. To improve the quality factor of the DRG, the quality factor improvement mechanism is first analyzed, and based on this mechanism two stiffness-mass decoupled methods, i.e., spoke length distribution optimization and lumped mass configuration design, are proposed and demonstrated. A disk resonator gyroscope prototype is fabricated based on these design strategies, and the sensor itself shows an angle random walk as low as 0.001°/√h, demonstrating true potential to achieve navigation-grade performance. The gyroscope with readout electronics shows an angle random walk of 0.01°/√h and a bias instability of 0.04°/h at room temperature without compensation, revealing that the performance of the gyroscope is severely limited by the readout electronics, which should be further improved. We expect that the quality factor improvement methods can be used in the design of other MEMS gyroscopes and that the newly designed DRG can be further improved to achieve navigation-grade performances for high-end industrial, transportation, aerospace, and automotive applications.

Vertically emitting silicon disk resonators with periodic shape modulation

It is shown by direct numerical modeling, using the 3D FDTD method, that a disk resonator with a sinusoidal modulation of its boundary has not only a modified frequency spectrum, but also a greater proportion of its optical radiation is directed normal to its surface. Simulations are carried out for a set of disk resonators on a typical silicon-on-insulator structure with a 250-nm silicon core and a disk diameter of about 2.6μm with the 5% sinusoidal boundary perturbation. Depending on the optical wavelength, the far-field radiation pattern looks either like a quasihomogeneous optical beam or a torus, having a maximum or minimum intensity at its center, respectively.

Stiffness-mass decoupled silicon disk resonator for high resolution gyroscopic application with long decay time constant (8.695 s)

We propose a stiffness-mass decoupling concept for designing large effective mass, low resonant frequency, small size, and high quality factor micro/nanomechanical resonators. This technique is realized by hanging lumped masses on the frame structure. An example of a stiffness-mass decoupled silicon disk resonator for gyroscopic application is demonstrated. It shows a decay time constant of 8.695 s, which is at least 5 times longer than that of the pure frame silicon disk resonator and is even comparable with that of the micromachined three-dimensional wine-glass resonators made from diamond or fused silica. The proposed design also shows a Brownian noise induced angle random walk of 0.0009°/√h, which is suitable for making an inertial grade MEMS gyroscope.

Designing Multipolar Resonances in Dielectric Metamaterials.

Dielectric resonators form the building blocks of nano-scale optical antennas and metamaterials. Due to their multipolar resonant response and low intrinsic losses they offer design flexibility and high-efficiency performance. These resonators are typically described in terms of a spherical harmonic decomposition with Mie theory. In experimental realizations however, a departure from spherical symmetry and the use of high-index substrates leads to new features appearing in the multipolar response. To clarify this behavior, we present a systematic experimental and numerical characterization of Silicon disk resonators. We demonstrate that for disk resonators on low-index quartz substrates, the electric and magnetic dipole modes are easily identifiable across a wide range of aspect-ratios, but that higher order peaks cannot be unambiguously associated with any specific multipolar mode. On high-index Silicon substrates, even the fundamental dipole modes do not have a clear association. When arranged into arrays, resonances are shifted and pronounced preferential forward and backward scattering conditions appear, which are not as apparent in individual resonators and may be associated with interference between multipolar modes. These findings present new opportunities for engineering the multipolar scattering response of dielectric optical antennas and metamaterials, and provide a strategy for designing nano-optical components with unique functionalities.

Plasmofluidic Disk Resonators.

Waveguide-coupled silicon ring or disk resonators have been used for optical signal processing and sensing. Large-scale integration of optical devices demands continuous reduction in their footprints, and ultimately they need to be replaced by silicon-based plasmonic resonators. However, few waveguide-coupled silicon-based plasmonic resonators have been realized until now. Moreover, fluid cannot interact effectively with them since their resonance modes are strongly confined in solid regions. To solve this problem, this paper reports realized plasmofluidic disk resonators (PDRs). The PDR consists of a submicrometer radius silicon disk and metal laterally surrounding the disk with a 30-nm-wide channel in between. The channel is filled with fluid, and the resonance mode of the PDR is strongly confined in the fluid. The PDR coupled to a metal-insulator-silicon-insulator-metal waveguide is implemented by using standard complementary metal oxide semiconductor technology. If the refractive index of the fluid increases by 0.141, the transmission spectrum of the waveguide coupled to the PDR of radius 0.9 μm red-shifts by 30 nm. The PDR can be used as a refractive index sensor requiring a very small amount of analyte. Plus, the PDR filled with liquid crystal may be an ultracompact intensity modulator which is effectively controlled by small driving voltage.

Predicting the closed-loop stability and oscillation amplitude of nonlinear parametrically amplified oscillators

This work investigates the closed-loop operation of microelectromechanical oscillators in the presence of both cubic (Duffing) nonlinearities and parametric amplification. We present a theoretical model for this system that enables us to predict oscillation amplitude and instability and experimentally verify it using a silicon disk resonator with a quality factor (Q) of 85 000 and a natural frequency of 251 kHz. We determine that, contrary to previous understanding gained from analyzing the open-loop system, the presence of cubic nonlinearities does not limit the maximum stable oscillation amplitude if the resonator is operated in a closed loop. In addition, the stability and amplitude behavior predicted by our theoretical model are independent of the presence or severity of cubic nonlinearities, or on drive amplitude.

All-optical switching of silicon disk resonator based on photothermal effect in metal-insulator-metal absorber.

Efficient narrowband light absorption by a metal-insulator-metal (MIM) structure can lead to high-speed light-to-heat conversion at a micro- or nanoscale. Such a MIM structure can serve as a heater for achieving all-optical light control based on the thermo-optical (TO) effect. Here we experimentally fabricated and characterized a novel all-optical switch based on a silicon microdisk integrated with a MIM light absorber. Direct integration of the absorber on top of the microdisk reduces the thermal capacity of the whole device, leading to high-speed TO switching of the microdisk resonance. The measurement result exhibits a rise time of 2.0μs and a fall time of 2.6μs with switching power as low as 0.5mW; the product of switching power and response time is only about 1.3 mW·μs. Since no auxiliary elements are required for the heater, the switch is structurally compact, and its fabrication is rather easy. The device potentially can be deployed for new kinds of all-optical applications.