Self-Oscillating Mode of a Nanoresonator

The paper proposes a new graphene resonator circuit which operates on the principle of a self-oscillator and has no drawbacks typical of nanoresonators as mass detectors and associated with their law quality factor, eigenfrequency errors (measurements from resonance curves), and dependence of quench frequency on oscillation frequency (curves with quenching for nonlinear systems). The proposed circuit represents a self-oscillator comprising an amplifier, a graphene resonator, and a positive feedback loop with a graphene oscillation transducer, and its major advantage is in self-tuning to resonance frequency at slowly varying resonator parameters, compared to oscillation periods. The graphene layer with a conducting substrate beneath it forms a capacitor which is recharged by a dc voltage source as its capacitance varies due to graphene deformation, and the recharge current is an oscillation- dependent signal transmitted from the transducer to the amplifier input. The graphene layer is placed in a magnetic field and is deformed when a current from the amplifier output is passed through. By properly choosing the magnetic field direction and the amplifier gain, it is possible to provide swinging oscillation whose amplitude is limited by the amplifier nonlinearity. For the proposed system we present an electromechanical model, dimensionless equations of motion, and numerical data demonstrating the generation of steady-state oscillations with eigenfrequency. Also presented is an analysis showing that the system can have only one limit cycle and that this cycle is always stable. The proposed resonator circuit can be used as a mass detector which determines the added mass from a change in self-oscillation frequency.     

A differential graphene-based resonator

We describe a new, in principle, layout of a graphene resonator—a differential resonator, which makes it possible to increase substantially its sensitivity to the mass deposited on it. The differential resonator consists of two parallel graphene films, which are fastened in insulating supports; the lower film is arranged over the conducting surface. The force coupling between the films is performed by the electrostatic field in the space between them. Several equilibrium positions are possible in such a mechanical system. Small free oscillations near the stable equilibrium position are considered. The field strength is selected so that the mechanical system of two graphene films would have two close eigenfrequencies. The free oscillations of such a system have the form of intrinsic frequencies of the system much lower that the partial frequency of each film. When depositing the particle on the upper film, the partial eigenfrequency of this film decreases. In this case, the characteristic envelope frequency also decreases, and a small variation in the partial eigenfrequency leads to considerable variation in the characteristic envelope frequency. This provides higher sensitivity to the mass of the revealed particle for the differential resonator compared with the resonator based on one film.     

Oscillation stop as a way to determine spectral characteristics of a graphene resonator

A nanoresonator based on a graphene layer is investigated as an electromechanical oscillatory system. Mechanical oscillations are excited in it by a high-frequency alternating electric field. A nanoresonator is considered as a capacitor with kinematically varying capacity of the determined transverse deformation of the graphene layer as one of its plates. In the case of small ratios of energy accumulated in a capacitor to the amplitude of energy of mechanical oscillations and the time constant of the capacitor charge to the period of free oscillations, excitation of both common and parametric resonances is possible. It is shown that upon decreasing the external frequency lower than the half-frequency of free oscillations, the cessation of forced oscillations of the nanolayer is observed. This makes it possible to determine more reliably the variations in the intrinsic frequency of the nanoresonator upon deposition of a nanoparticle on it.     

微波谐振器系统的调谐实验研究

圆台谐振腔和微波产生及传输装置可以形成一套和外界独立的微波谐振器系统.由于壁面上电磁压强差的作用,圆台谐振腔可能产生净电磁力,这需要从实验上给予证明.为此首先应对独立的微波谐振器系统进行调谐实验研究,使系统时刻处于谐振状态,这是实验证明净电磁力存在的重要保证.为此,本文对圆台谐振腔进行低信号调谐实验,同时配合调谐元件,准确地调试2.45 GHz频率下的谐振状态,分析温度对谐振状态的影响.实验结果表明该微波谐振器谐振频率2.44895 GHz、品质因数117495.0823,而且当腔体壁温升高时谐振频率减小、品质因数出现周期性振荡.     

品质因子可调的石墨烯纳米机械振子

纳米机械振子尺寸小,质量轻,可以用来制作探测力、质量等微小物理量的超灵敏探测器.石墨烯拥有质量轻、密度低和杨氏模量高等特性,被认为是制作纳米机械振子的理想材料.石墨烯纳米机械振子因其具有的谐振频率高、品质因子高和谐振频率可调性高等优势,近年来得到了人们的广泛关注.作为表征纳米机械振子性能的一个重要指标,品质因子越高,意味着纳米机械振子耗散越低,纳米机械振子的灵敏度越高.本文通过微纳加工的工艺制备出一种谐振频率随栅压可调(调节的范围为73MHz~90MHz)的石墨烯纳米机械振子样品,研究其在极低温高真空环境下的品质因子与栅极电压之间的关系.实验表明通过栅压调节振子的内部应力,能够使石墨烯纳米机械振子品质因子从220提高到1000.我们的结果为二维材料纳米机械振子的耗散研究提供了一种新的研究思路.     

基于石墨烯谐振沟道晶体管的高频纳米机电系统信号读取研究

结合石墨烯场效应晶体管和机械谐振原理,研究了基于本地背栅石墨烯谐振沟道晶体管(RCT) 的高频机械信号直接读取方法.利用机械剥离法获得的石墨烯,提出了一种基于刻蚀技术的器件制备方法, 并实现了栅长和栅宽分别为1 μm的本地背栅RCT.实验结果表明,在室温下RCT的谐振频率范围为57.5–88.25 MHz.研究结果对加速石墨烯纳米机电系统和高频低噪声器件的应用有着重要作用. 关键词： 石墨烯 谐振沟道晶体管 纳米机电系统     

Electrothermal Oscillatory Instability in Spherical Ferroelectric Resonators. Three-Mode Case

We consider the equations of interaction between electromagnetic oscillations and the temperature in a nonlinear dielectric resonator and study the dynamics of the oscillatory instability in the system. The threshold conditions (power and self-modulation frequency) of electrothermal excitation are calculated for microwave potassium-tantalate resonators for the case of three-mode interaction. The conditions for observing electrothermal excitation in the three-mode case are found to be quite favorable. In this case, the threshold power of excitation of temperature oscillations is smaller than that in the two-mode case and can amount to a few microwatts.     

Laser-assisted spin-polarized transport in graphene tunnel junctions

The Keldysh nonequilibrium Green's function method is utilized to theoretically study spin-polarized transport through a graphene spin valve irradiated by a monochromatic laser field. It is found that the bias dependence of the differential conductance exhibits successive peaks corresponding to the resonant tunneling through the photon-assisted sidebands. The multi-photon processes originate from the combined effects of the radiation field and the graphene tunneling properties, and are shown to be substantially suppressed in a graphene spin valve which results in a decrease of the differential conductance for a high bias voltage. We also discuss the appearance of a dynamical gap around zero bias due to the radiation field. The gap width can be tuned by changing the radiation electric field strength and the frequency. This leads to a shift of the resonant peaks in the differential conductance. We also demonstrate numerically the dependences of the radiation and spin valve effects on the parameters of the external fields and those of the electrodes. We find that the combined effects of the radiation field, the graphene and the spin valve properties bring about an oscillatory behavior in the tunnel magnetoresistance, and this oscillatory amplitude can be changed by scanning the radiation field strength and/or the frequency.     

A theoretical study of pump–probe experiment in single-layer,bilayer and multilayer graphene

The pump–probe experiment is typically used to study relaxation phenomena in nonlinear optical systems. Here we use it as a tool to study the phenomenon of anomalous Rabi oscillations in graphene that was predicted recently in single-layer graphene. Unlike conventional Rabi oscillations, anomalous Rabi oscillations are unique to graphene (and possibly to surface states of topological insulators (TIs)), attributable to the pseudospin (conventional spin for TI) degree of freedom and Dirac-fermion character of the graphene system. A pump pulse of a finite duration long enough to contain a large number of cycles induces a current density that oscillates with the frequency of the pump pulse. The amplitude associated with these fast oscillations is seen to exhibit much slower oscillations with a frequency given by \({ 2 \omega ^2_{\mathrm {R}} }/{ \omega } \) – the anomalous Rabi frequency, where ω _R is the conventional Rabi frequency and ω is the frequency of the external pump field. This effect is easily probed by a probe pulse subsequent to the pump, where it manifests itself as periodic oscillations of the probe susceptibility as a function of pump duration at each probe frequency. Alternatively, it is also seen as an oscillatory function of the pump–probe delay with other variables remaining fixed. This period corresponds to the anomalous Rabi frequency. An analysis of the previously reported experimental data confirms the presence of anomalous Rabi oscillations in graphene.     

Theorie der parametrischen Vier-Photonen-Wechselwirkung. III. Verstärkung und Oszillation bei Berücksichtigung der Rückwirkung auf die Pumpwelle

The processes of parametric amplification and oscillation in a medium with cubic polarization are investigated theoretically taking into consideration the depletion of the pump wave. We suppose that phase-matching is realized exactly (a possible nonlinear detuning of the exact phase-matching should be compensated by a suitable subsequent adjustment of the frequencies). A consequence of linear losses is the appearance of a threshold for the parametric amplification. There exist a maximum length, a minimum length and an optimum length of the nonlinear medium for the process of parametric amplification. The threshold intensity, the optimum length of the nonlinear medium and the optimum reflection coefficient for outcoupling are determined for two arrangements of the double resonant parametric four-photon oscillator (ring resonator, FABRY -PEROT resonator). It is shown that for the above mentioned arrangements of the single resonant and the double resonant four-photon oscillator the efficiency is a monotonous function of the threshold excess. On the contrary in case of the three-photon oscillator there exists an optimum value of the threshold excess.     

On the application of radio frequency voltages to ion traps via helical resonators

Ions confined using a Paul trap require a stable, high voltage and low noise radio frequency (RF) potential. We present a guide for the design and construction of a helical coil resonator for a desired frequency that maximises the quality factor for a set of experimental constraints. We provide an in-depth analysis of the system formed from a shielded helical coil and an ion trap by treating the system as a lumped element model. This allows us to predict the resonant frequency and quality factor in terms of the physical parameters of the resonator and the properties of the ion trap. We also compare theoretical predictions with experimental data for different resonators, and predict the voltage applied to the ion trap as a function of the Q factor, input power and the properties of the resonant circuit.     

Nonlinear frequency mixing in a resonant cavity: Numerical simulations in a bubbly liquid

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.     

Material and device properties of ZnO-based film bulk acoustic resonator for mass sensing applications

Zinc oxide based film bulk acoustic resonator as mass sensor was fabricated by multi-target magnetron sputtering under optimized deposition condition. Each layer of the device was well crystallized and highly textural observed by transmission electron microscopy and X-ray diffraction measurement. Through piezoelectric test, the device vibrated with significant distance. The influence of top electrode on resonant frequency and the bio-specimen of mass loading effect were investigated. Data show that the device has qualified properties as mass biosensor, with a resonant frequency of 3-4 GHz and a high sensitivity of 8-10 kHz cm²/ng.     

Frequency measurement study of resonant vibratory gyroscopes

In this paper, frequency measurement methods of resonant vibratory gyroscopes are studied. First, the working principle and dynamic output characteristics of the resonant vibratory gyroscope are introduced, which provide a theoretical analysis base to analyze the dynamic frequency output characteristic of the resonant vibratory gyroscope. Moreover, some relevant frequency measurement methods are introduced, a frequency measurement method based on dynamic output characteristics has been proposed for the purpose of investigating the modulated output signal of resonant vibratory gyroscopes. Finally, in order to verify the feasibility of the proposed frequency measurement method, resonator oscillator and dynamic frequency measurement experiments of the resonant vibratory gyroscopes are built. It is concluded from the resonator oscillator result that the designed and observed resonant frequency of the resonator have a good match, which shows the design of resonator oscillator is feasible. It is concluded from the dynamic frequency measurement result that correlation coefficient of output fitted curve is 99.95%, and the output characteristic of the gyroscope is linear frequency output, which shows the effectiveness of the proposed frequency measurement method.     

Nonlinear Spherical Standing Waves in an Acoustically Excited Liquid Drop

Nonlinear evolution of a standing acoustic wave in a spherical resonator with a perfectly soft surface is analyzed. Quadratic approximation of nonlinear acoustics is used to analyze oscillations in the resonator by the slowly varying amplitude method for the standing wave harmonics and slowly varying profile method for the standing wave profile. It is demonstrated that nonlinear effects may lead to considerable increase in peak pressure at the center of the resonator. The proposed theoretical model is used to analyze the acoustic field in liquid drops of an acoustic fountain. It is shown that, as a result of nonlinear evolution, the peak negative pressure may exceed the mechanical strength of the liquid, which may account for the explosive instability of drops observed in experiments.     

Thermal effects on mass detection sensitivity of carbon nanotube resonators in nonlinear oscillation regime

A mass sensor using a nano-resonator has high detection sensitivity, and mass sensitivity is higher with smaller resonators. Therefore, carbon nanotubes (CNTs) are the ultimate materials for these applications and have been actively studied. In particular, CNT-based nanomechanical devices may experience high temperatures that lead to thermal expansion and residual stress in devices, which affects the device reliability. In this letter, to demonstrate the influence of the temperature change (i.e., thermal effect) on the mass detection sensitivity of CNT-based mass sensor, dynamic analysis is carried out for a CNT resonator with thermal effects in both linear and nonlinear oscillation regimes. Based on the continuum mechanics model, the analytical solution method with an assumed deflection eigenmode is applied to solve the nonlinear differential equation which involves the von Karman nonlinear strain–displacement relation and the additional axial force associated with thermal effects. A thermal effect on the fundamental resonance behavior and resonance frequency shift due to adsorbed mas, i.e., mass detection sensitivity, is examined in high-temperature environment. Results indicate a valid improvement of fundamental resonance frequency by using nonlinear oscillation in a thermal environment. In both linear and nonlinear oscillation regimes, the mass detection sensitivity becomes worse due to the increasing of temperature in a high-temperature environment. The thermal effect on the detection sensitivity is less effective in the nonlinear oscillation regime. It is concluded that a temperature change of a mass sensor with a CNT-based resonator can be utilized to enhance the detection sensitivity depending on the CNT length, linear/nonlinear oscillation behaviors, and the thermal environment.     

Noise-enabled precision measurements of a duffing nanomechanical resonator

We report quantitative measurements of the nonlinear response of a radio frequency mechanical resonator with a very high quality factor. We measure the noise-free transitions between the two basins of attraction that appear in the nonlinear regime, and find good agreement with theory. We measure the transition rate response to controlled levels of white noise, and extract the basin activation energy. This allows us to obtain precise values for the relevant frequencies and the cubic nonlinearity in the Duffing oscillator, with applications to parametric sensing.     

New designed helical resonator to improve measurement accuracy of magic radio frequency

Based upon the new designed helical resonator, the resonant radio frequency (RF) for trapping ions can be consecutively adjusted in a large range (about 12 MHz to 29 MHz) with high Q-factors (above 300). We analyze the helical resonator with a lumped element circuit model and find that the theoretical results fit well with the experimental data. With our resonator system, the resonant frequency near magic RF frequency (where the scalar Stark shift and the second-order Doppler shift due to excess micromotion cancel each other) can be continuously changed at kHz level. For ⁸⁸Sr⁺ ion, compared to earlier results, the measurement accuracy of magic RF frequency can be improved by an order of magnitude upon rough calculation, and therefore the net micromotion frequency shifts can be further reduced. Also, the differential static scalar polarizability Δα₀ of clock transition can be experimentally measured more accurately.     

Finite-amplitude standing acoustic waves in a cubically nonlinear medium

The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted “forced” waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.     

Dual-wavelength, two-crystal, continuous-wave optical parametric oscillator

We report a cw optical parametric oscillator (OPO) in a novel architecture comprising two nonlinear crystals in a single cavity, providing two independently tunable pairs of signal and idler wavelengths. Based on a singly resonant oscillator design, the device permits access to arbitrary signal and idler wavelength combinations within the parametric gain bandwidth and reflectivity of the OPO cavity mirrors. Using two identical 30 mm long MgO:sPPLT crystals in a compact four-mirror ring resonator pumped at 532 nm, we generate two pairs of signal and idler wavelengths with arbitrary tuning across 850-1430 nm, and demonstrate a frequency separation in the resonant signal waves down to 0.55 THz. Moreover, near wavelength-matched condition, coherent energy coupling between the resonant signal waves, results in reduced operation threshold and increased output power. A total output power >2.8 W with peak-to-peak power stability of 16% over 2 h is obtained.