Noise suppression for micromechanical resonator via intrinsic dynamic feedback

We study a dynamic mechanism to passively suppress the thermal noise of a micromechanical resonator through an intrinsic self-feedback that is genuinely non-Markovian. We use two coupled resonators, one as the target resonator and the other as an ancillary resonator, to illustrate the mechanism and its noise reduction effect. The intrinsic feedback is realized through the dynamics of coupling between the two resonators: the motions of the target resonator and the ancillary resonator mutually influence each other in a cyclic fashion. Specifically, the states that the target resonator has attained earlier will affect the state it attains later due to the presence of the ancillary resonator. We show that the feedback mechanism will bring forth the effect of noise suppression in the spectrum of displacement, but not in the spectrum of momentum.     

Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED

We investigate theoretically the dynamical behavior of a qubit obtained with the two ground eigenstates of an ultrastrong coupling circuit-QED system consisting of a finite number of Josephson fluxonium atoms inductively coupled to a transmission line resonator. We show a universal set of quantum gates by using multiple transmission line resonators (each resonator represents a single qubit). We discuss the intrinsic "anisotropic" nature of noise sources for fluxonium artificial atoms. Through a master equation treatment with colored noise and many-level dynamics, we prove that, for a general class of anisotropic noise sources, the coherence time of the qubit and the fidelity of the quantum operations can be dramatically improved in an optimal regime of ultrastrong coupling, where the ground state is an entangled photonic "cat" state.     

Coherent interference induced transparency in self-coupled optical waveguide-based resonators

We propose a self-coupled optical waveguide (SCOW)-based resonator to generate an optical resonance analogous to electromagnetically induced transparency (EIT). The EIT-like effect is formed by the coherent interference between two resonance paths inherent to the SCOW resonator. For cascaded SCOW resonators, the spectrum they produce is significantly affected by the phase shift between them, with the EIT-like peak flattened or split as the two extreme cases. We also investigate the dispersion characteristics of an infinite array of SCOW resonators and show that the dispersion relation and group index in the EIT subband can be greatly changed by a small phase shift between the SCOW resonators.     

Development of a resonator with automatic tuning and coupling capability to minimize sample motion noise for in vivo EPR spectroscopy

EPR spectroscopy has been applied to measure free radicals in vivo; however, respiratory, cardiac, and other movements of living animals are a major source of noise and spectral distortion. Sample motions result in changes in resonator frequency, Q, and coupling. These instabilities limit the applications that can be performed and the quality of data that can be obtained. Therefore, it is of great importance to develop resonators with automatic tuning and automatic coupling capability. We report the development of automatic tuning and automatic coupling provisions for a 750-MHz transversely oriented electric field reentrant resonator using two electronically tunable high Q hyperabrupt varactor diodes and feedback loops. In both moving phantoms and living mice, these automatic coupling control and automatic tuning control provisions resulted in an 8- to 10-fold increase in signal-to-noise ratio.     

Development of a Resonator with Automatic Tuning and Coupling Capability to Minimize Sample Motion Noise for in Vivo EPR Spectroscopy

EPR spectroscopy has been applied to measure free radicals in vivo; however, respiratory, cardiac, and other movements of living animals are a major source of noise and spectral distortion. Sample motions result in changes in resonator frequency, Q, and coupling. These instabilities limit the applications that can be performed and the quality of data that can be obtained. Therefore, it is of great importance to develop resonators with automatic tuning and automatic coupling capability. We report the development of automatic tuning and automatic coupling provisions for a 750-MHz transversely oriented electric field reentrant resonator using two electronically tunable high Q hyperabrupt varactor diodes and feedback loops. In both moving phantoms and living mice, these automatic coupling control and automatic tuning control provisions resulted in an 8- to 10-fold increase in signal-to-noise ratio.     

Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.     

Axisymmetric eigenmodes of magnetic type in an open resonator with spherical mirrors

We develop a rigorous mathematical model describing axisymmetric eigenmodes of magnetic type of open resonators with spherical mirrors. On the assumption that the spectrum of complex eigenfrequencies of an open resonator exists, it is proved that this spectrum is discrete and has finite multiplicity with a single accumulation point at infinity. Theoretical analysis of the spectral characteristics of an open resonator is performed in the case where the wavelength is comparable with the resonator sizes. The limits of applicability of the well-known asymptotic models of open resonators are established. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 9, pp. 787–798, September 2006.     

Toward broadband electroacoustic resonators through optimized feedback control strategies

This paper presents a methodology for the design of broadband electroacoustic resonators for low-frequency room equalization. An electroacoustic resonator denotes a loudspeaker used as a membrane resonator, the acoustic impedance of which can be modified through proportional feedback control, to match a target impedance. However, such impedance matching only occurs over a limited bandwidth around resonance, which can limit its use for the low-frequency equalization of rooms, requiring an effective control at least up to the Schroeder frequency. Previous experiments have shown that impedance matching can be achieved over a range of a few octaves using a simple proportional control law. But there is still a limit to the feedback gain, beyond which the feedback-controlled loudspeaker becomes non-dissipative. This paper evaluates the benefits of using PID control and phase compensation techniques to improve the overall performance of the electroacoustic resonator. More specifically, it is shown that some adverse effects due to high-order dynamics in the moving-coil transducer can be mitigated. The corresponding control settings are also identified with equivalent electroacoustic resonator parameters, allowing a straightforward design of the controller. Experimental results using PID control and phase compensation are finally compared in terms of sound absorption performances. As a conclusion the overall performances of electroacoustic resonators for damping the modal resonances inside a duct are presented, along with general discussions on practical implementation and the extension to actual room modes damping.     

串联双微环湿度传感器光谱特性研究

提出了一种基于串联双微环谐振器的新型聚酰亚胺(Polyimide,PI)湿度传感器,采用传输矩阵法和耦合模的理论计算微环谐振器的传递函数,并对比了传统单微环与串联不同半径的双微环的输出光谱特性。外界湿度变化使得聚酰亚胺SOI波导吸收水汽后折射率发生变化,从而引起微环输出光谱发生漂移,通过探测光谱漂移量来测湿度值,得到了串联双微环传感器的灵敏度和测量范围,并且分析了感湿部位不同时谐振器输出光谱特性。理论结果表明：串联不同半径的微环谐振器的自由光谱范围（FSR）要比单微环有所提高,而且串联双微环谐振器整体感湿比单个微环单独感湿的传感性能更优良,可作为最佳的湿敏元件。与传统的单微环传感器相比,串联不同半径的微环结构可提高系统的测量范围和灵敏度,半径为30和50 μm的串联微环谐振器的FSR可达到0.15 μm,传感器测量湿度范围为10%RH～80%RH,灵敏度可达到0.001 7 μm·(%RH)-1。因此串联不同半径的双微环谐振器为制备成本低、结构简单、高灵敏度、可集成的微型湿度传感器件提供一定理论基础。     

Modeling and analysis of silicon-on-insulator elliptical microring resonators for future high-density integrated photonic circuits

We propose a novel resonator containing an elliptical microring based on a silicon-on-insulator platform. Simulations using the three-dimensional finite-difference time-domain method show that the novel elliptical microring can efficiently enhance the mode coupling between straight bus waveguides and resonator waveguides or between adjacent resonators while preserving relatively high intrinsic quality factors with large free spectral range. The proposed resonator would be an alternative choice for future high-density integrated photonic circuits.     

Noise control in enclosures: modeling and experiments with T-shaped acoustic resonators

This paper presents a theoretical and experimental study of noise control in enclosures using a T-shaped acoustic resonator array. A general model with multiple resonators is developed to predict the acoustic performance of small resonators placed in an acoustic enclosure. Analytical solutions for the sound pressure inside the enclosure and the volume velocity source strength out of the resonator aperture are derived when a single resonator is installed, which provides insight into the physics of acoustic interaction between the enclosure and the resonator. Based on the understanding of the coupling between the individual resonators and enclosure modes, both targeted and nontargeted, a sequential design methodology is proposed for noise control in the enclosure using an array of acoustic resonators. Design examples are given to illustrate the control performance at a specific or at several resonance peaks within a frequency band of interest. Experiments are conducted to systematically validate the theory and the design method. The agreement between the theoretical and experimental results shows that, with the help of the presented theory and design methodology, either single or multiple resonance peaks of the enclosure can be successfully controlled using an optimally located acoustic resonator array.     

Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency

We provide the first experimental observation of structure tuning of the electromagnetically induced transparency-like spectrum in integrated on-chip optical resonator systems. The system consists of coupled silicon ring resonators with 10 microm diameter on silicon, where the coherent interference between the two coupled resonators is tuned. We measured a transparency-resonance mode with a quality factor of 11,800.     

光纤环形谐振腔的频率锁定及其特性

基于可调分束比的光纤分束器,制作了光纤环形谐振腔并通过调节分束比实现了对光纤环形谐振腔的欠耦合、临界耦合和过耦合的状态控制.实验测量了腔最小反射率与腔损耗之间的关系,获得光纤环形谐振腔的腔内衰减率为κ_0=2π×(1.60±0.03) MHz ,品质因子为Q=(1.10±0.02)×10.8.在此基础上,结合了压电陶瓷拉伸光纤以控制腔长和Pound-Drever-Hall锁频两大技术优势,克服了之前温度反馈控制等方法的反馈带宽窄、噪声大和稳定性差等问题,实现了对光纤环形谐振腔共振频率的快速、灵敏的控制和锁定.结果表明,锁频过程中相位调制功率与相位调制引起腔反射光的强度调制之间的关系为线性关系,进而通过降低相位调制信号的功率以减小相位调制对腔反射光强度调制的影响.当调制功率设定最低为–9 dBm时,光纤环形谐振腔仍能被稳定锁定.该光纤环形谐振腔为其与原子、金刚石色心等发光粒子相互作用的腔量子电动力学实验研究奠定了坚实的基础.     

Experimental investigation of the sound absorption performance of compartmented Helmholtz resonators

An experiment was derived in the present study to investigate the effects of coupling up two Helmholtz resonators on their overall sound absorption performance. The effect of compartmenting the cavity of a resonator on its sound absorption property was also discussed. Such cavity compartmentation in fact creates a coupled resonator with a front and a rear resonator. The results show that the coupling in many cases can improve the sound absorption capacity and widen the working bandwidth of the resonators provided that the uncoupled resonance frequency of the front resonator is larger than or equal to that of the rear resonator. Results also suggest that the best compartmentation is that with these uncoupled resonance frequencies very close to each other. It is also found that the undamped plane wave approach is sufficient to predict the resonance frequencies of the coupled resonators within engineering tolerance.     

I/f noise in systems showing stochastic resonance

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.     

激光调制参数对光纤环型谐振腔光谱特性影响

谐振光学环型腔作为光学陀螺的核心敏感单元,其光学调制谱和与之对应的鉴频曲线的特性成为提高光学陀螺系统检测灵敏度的关键。为了研究光学陀螺的调制和鉴频谱线特性,优化陀螺性能,设计并搭建了实验测试系统,光纤环形谐振腔采用分光比为50∶50、直径17 cm的保偏光纤,总长2.2 m。使用直流高压放大器扫描窄线宽激光器（线宽小于1 kHz）的压电转化模块,扫描频率和电压分别选取20 Hz和1 V,使用模拟比例积分电路进行锁频并反馈给激光器的压电转化模块,使激光器的输出频率跟踪谐振腔实时变化。研究分析了光纤环型谐振腔在两种情况下所对应的透射谱和鉴频曲线:第一种情况为调制电压分别为2 V和4 V,对应调制频率从100 kHz到4 MHz变化;第二种情况为当调制频率为900 kHz,调制电压从2 V到10 V变化。通过实验,得到了不同调制参数下光学陀螺谱线的谐振深度、半高全宽、线性带宽、动态范围、品质因数、标度因数以及对应的锁频精度七种物理量的详细变化情况,并进一步得到了静态测试条件下三种陀螺的最佳调制频率及与之所匹配的调制电压。为进一步研究激光调制对光纤环型谐振腔光谱的影响提供指导。     

基于新型三环谐振器的诱导透明效应分析

针对谐振式微腔的应用需求, 提出了一种新型三环谐振式微腔结构, 类似于原子系统中的电磁诱导透明, 耦合诱导透明(CRIT)效应在一个新的光学微腔系统中已被实验证明. 该结构在硅基上由三个尺寸完全一样的微环腔组成, 通过理论分析、制备和实验测试, 能够观察到CRIT现象, 其频谱具有低群速的狭窄透明峰, 与光栅耦合器的耦合效率为34%, 并且谐振器的品质因数达到了0.65×10⁵, 同时, 失谐的谐振波长可以通过温度变化来控制, 这在旋转传感、光滤波器、光存储器等方面的应用有重要意义.     

Instabilities in coupled photorefractive ring cavities and self-pumped phase conjugators

We investigate the temporal instabilities of mode intensities in two coupled unidirectional photorefractive ring resonators. The first resonator is driven by an external laser beam via photorefractive two-wave mixing. The internal oscillating beam is then employed to drive the second ring resonator. The second ring resonator provides a nonlinear loss mechanism for the coupled system. Complete spatial-temporal equations for describing the coupled system are derived and mean-field approximation is employed to simplify the transient analysis. The results of linear stability analysis indicate that the coupled system exhibits instability in the off-state and steady-state operation. The instability is explained in terms of competition between nonlinear gain and loss. The results are presented and discussed.Part II on Numerical Results will be published in a forthcoming issue of Applied Physics B     

Wave propagation in a duct with a periodic Helmholtz resonators array

Helmholtz resonator is often used to reduce noise in a narrow frequency range. To obtain a broader noise attenuation band, combing several resonators is a possible way. This paper presents a theoretical study of sound propagation in a one-dimensional duct with identical side-branch resonators mounted periodically. The analysis of each resonator was based on a distributed-parameter model that considered multi-dimensional wave propagation in its neck-cavity interface. This model provided a more accurate prediction of the resonant frequency of the resonator than traditional lumped-parameter model. Bloch wave theory and the transfer matrix method were used to investigate wave propagation in these spatially periodic resonators. The results predicted by the theory fit well with the computer simulation using a three-dimensional finite element method and the experimental results. This study indicates that the wave coupling in this periodic system results in the dispersion of the frequency band into the stop and the pass bands. The long-term significance is that periodic resonators may more effectively control noise in ducts by broadening the bandwidth they attenuate and increasing the magnitude of sound attenuation.     

Field quantization for chaotic resonators with overlapping modes

Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.