Showing papers on "Parametric oscillator published in 2012"

A Wideband, Low-Noise Superconducting Amplifier with High Dynamic Range

Abstract: Amplifiers are ubiquitous in electronics and play a fundamental role in a wide range of scientific measurements. From a user's perspective, an ideal amplifier has very low noise, operates over a broad frequency range, and has a high dynamic range - it is capable of handling strong signals with little distortion. Unfortunately, it is difficult to obtain all of these characteristics simultaneously. For example, modern transistor amplifiers offer multi-octave bandwidths and excellent dynamic range. However, their noise remains far above the fundamental limit set by the uncertainty principle of quantum mechanics. Parametric amplifiers, which predate transistor amplifiers and are widely used in optics, exploit a nonlinear response to transfer power from a strong pump tone to a weak signal. If the nonlinearity is purely reactive, ie. nondissipative, in theory the amplifier noise can reach the quantum-mechanical limit. Indeed, microwave frequency superconducting Josephson parametric amplifiers do approach the quantum limit, but generally are narrow band and have very limited dynamic range. In this paper, we describe a superconducting parametric amplifier that overcomes these limitations. The amplifier is very simple, consisting only of a patterned metal film on a dielectric substrate, and relies on the nonlinear kinetic inductance of a superconducting transmission line. We measure gain extending over 2 GHz on either side of an 11.56 GHz pump tone, and we place an upper limit on the added noise of the amplifier of 3.4 photons at 9.4 GHz. Furthermore, the dynamic range is very large, comparable to microwave transistor amplifiers, and the concept can be applied throughout the microwave, millimeter-wave and submillimeter-wave bands.

Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

Abstract: A global nonlinear distributed-parameter model for a piezoelectric energy harvester under para- metric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geomet- ric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler- Lagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the per- formance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester's behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a sub- critical pitchfork bifurcation.

Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance

Abstract: In this paper, the generalized harmonic balance method is presented for approximate, analytical solutions of periodic motions in nonlinear dynamical systems. The nonlinear damping, periodically forced, Duffing oscillator is studied as a sample problem. The approximate, analytical solution of period-1 periodic motion of such an oscillator is obtained by the generalized harmonic balance method. The stability and bifurcation analysis of the HB2 approximate solution of period-1 motions in the forced Duffing oscillator is carried out, and the parameter map for such HB2 solutions is achieved. Numerical illustrations of period-1 motions are presented. Similarly, the same ideas can be extended to period-k motions in such an oscillator. The methodology presented in this paper can be applied to other nonlinear vibration systems, which are independent of small parameters.

Nonlinear tides in close binary systems

Abstract: We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.

Parametric resonance in dynamical systems

Abstract: An Introduction to Parametric Resonance.- Part I Detection and Estimation of Parametric Resonance: Detection of Parametric Roll for Ships.- Estimation of Parametric Roll in Random Seaways.- Part II Parametric Roll: Trimaran Vessels and Parametric Roll.- Probability of Parametric Roll in Random Seaways.- Domains of Parametric Roll Amplification for Different Hull Forms.- Probabilistic Properties of Parametric Roll.- Experience from Parametric Rolling of Ships.- Ship Model for Parametric Roll Incorporating the Effects of Time-Varying Speed.- Part III Control of Parametric Resonance in Ships: Frequency Detuning Control by Doppler Shift.- Optimal Speed and Heading Control for Stabilization of Parametric Oscillations in Ships.- A U-Tank Control System for Ships in Parametric Roll Resonance.- Part IV Control of Parametric Resonance in Mechanical Systems: Parametric and Direct Resonances in a Base-Excited Beam Carrying a Top Mass.- A Study of the Onset and Stabilization of Parametric Roll by using an Electro-Mechanical Device.- Controlling Parametric Resonance: Induction and Stabilization of Unstable Motions.

Qubit-assisted thermometry of a quantum harmonic oscillator

Abstract: We use the theory of quantum estimation in two different qubit-boson coupling models to demonstrate that the temperature of a quantum harmonic oscillator can be estimated with high precision by quantum-limited measurements on the qubit. The two models that we address embody situations of current physical interest due to their connection with ongoing experimental efforts on the control of mesoscopic dynamics. We show that population measurements performed over the qubit probe are near optimal for a broad range of temperatures of the harmonic oscillator.

Parametric noise squeezing and parametric resonance of microcantilevers in air and liquid environments.

Abstract: In this work, parametric noise squeezing and parametric resonance are realized through the use of an electronic feedback circuit to excite a microcantilever with a signal proportional to the product of the microcantilever's displacement and a harmonic signal. The cantilever's displacement is monitored using an optical lever technique. By adjusting the gain of an amplifier in the feedback circuit, regimes of parametric noise squeezing/amplification and the principal and secondary parametric resonances of fundamental and higher order eigenmodes can be easily accessed. The exceptionally symmetric amplitude response of the microcantilever in the narrow frequency bandwidth is traced to a nonlinear parametric excitation term that arises due to the cubic nonlinearity in the output of the position-sensitive photodiode. The feedback circuit, working in both the regimes of parametric resonance and noise squeezing, allows an enhancement of the microcantilever's effective quality-factor (Q-factor) by two orders of magnitude under ambient conditions, extending the mass sensing capabilities of a conventional microcantilever into the sub-picogram regime. Likewise, experiments designed to parametrically oscillate a microcantilever in water using electronic feedback also show an increase in the microcantilever's effective Q-factor by two orders of magnitude, opening the field to high-sensitivity mass sensing in liquid environments.

Dispersion-stabilized highly-nonlinear fiber for wideband parametric mixer synthesis.

Abstract: Conventional highly-nonlinear fiber (HNLF) designs are optimized for high field-confinement but are also inherently susceptible to dispersion fluctuations. The design compromise prevents fiber-optical parametric mixers from possessing high power efficiency and extended operating bandwidth simultaneously. Using a new fiber waveguide design, we have fabricated and tested a new class of HNLF that possesses a significantly lower level of dispersion fluctuations while maintaining a high level of field-confinement comparable to that in conventional HNLFs. The fiber was used to demonstrate an all-fiber parametric oscillator operating in short-wavelength infrared (SWIR) band with a watt-level pump, for the first time.

Parametric resonance: Amplification and damping in MEMS gyroscopes

Abstract: The attainable resolution of inertial sensors is ultimately limited by the cumulated noise level generated in both the mechanical domain (mechano-thermal noise) and the frontend of the electrical readout circuit, provided that deterministic errors, such as quadrature errors in the case of gyroscopes, are kept under control. Improving the resolution performance of MEMS structures mounts to being able to either increase the minimum detectable signal through an increased sensitivity, or to improve the signal-to-noise ratio (SNR). This paper reports on parametric amplification and damping employed in a MEMS gyroscope. Experiments confirm that parametric modulation through electro-mechanical coupling leads to both an increase in spectral selectivity and a reduction of the equivalent input noise angular rate (from 0.0046 ∘ / ( s Hz ) to 0.0026 ∘ / ( s Hz ) for a parametric gain of 5). In a more general analysis of a MEMS resonant structure, electro-mechanical parametric amplification decreases the mechano-thermal noise associated with the resonant mode motion – the equivalent input noise acceleration was diminished from 0.033 m s−2 to 0.022 m s−2 for a parametric gain of 5. Either signal amplification or an attenuation of undesired signal components can be achieved by tuning the phase difference between the driving force and the parametric coupling. Therefore, the technique can be applied as well to reduce the quadrature error signal, which strongly constrains the maximum gain of the sensing circuit. Our experiments show a 2.2 improvement factor in SNR using a parametric amplification with a gain of 25.

Parametric oscillators based on superconducting circuits

Abstract: A parametric oscillator is an oscillating system in which one of the parameters, typically either the resonance frequency or damping, can be modulated by an external pump. Parametric oscillations can be found in a wide variety of systems including radiofrequency circuits, optical and mechanical systems, and even single electrons in a Penning trap. In recent years, interest in parametric oscillators has revived in many areas of physics, ranging from basic physics to applications. For instance, they are being used as quantum-limited amplifiers in an increasingly large number of experiments in quantum information and computing. At the same time, interest in their basic physics in the quantum regime, in which they are a model system for driven, nonlinear systems, has grown commensurately. This chapter gives a largely self-contained introduction to the theoretical description of the dynamics of parametric oscillators, both classical and quantum, and reviews some of the recent experimental work in superconducting circuits.

Tunable modulational instability sidebands via parametric resonance in periodically tapered optical fibers

Abstract: We analyze the modulation instability induced by periodic variations of group velocity dispersion and nonlinearity in optical fibers, which may be interpreted as an analogue of the well-known parametric resonance in mechanics. We derive accurate analytical estimates of resonant detuning, maximum gain and instability margins, significantly improving on previous literature on the subject. We also design a periodically tapered photonic crystal fiber, in order to achieve narrow instability sidebands at a detuning of 35 THz, above the Raman maximum gain peak of fused silica. The wide tunability of the resonant peaks by variations of the tapering period and depth will allow to implement sources of correlated photon pairs which are far-detuned from the input pump wavelength, with important applications in quantum optics.

Tunable 2-μm optical vortex parametric oscillator.

Abstract: We generated tunable 2-μm optical vortex pulses with a topological charge of 1 or 2 in the wavelength range 1.953–2.158 μm by realizing anisotropic transfer of the topological charge from the pump beam to the signal output in a vortex-pumped half-symmetric optical parametric oscillator. A maximum vortex output energy of 2.1 mJ was obtained at a pump energy of 22.8 mJ, which corresponds to a slope efficiency of 15%. The topological charges of the signal and idler output were investigated using a shearing interferometric technique employing a low-spatial-frequency transmission grating.

High power ultra-widely tuneable femtosecond pulses from a non-collinear optical parametric oscillator (NOPO).

Abstract: We present an ultra-widely tunable non-collinear optical parametric oscillator with an average output power of more than 3 W and a repetition frequency of 34 MHz. The system is pumped by the second harmonic of a femtosecond Yb:KLu(WO4)2 thin-disk laser oscillator. The wavelength of the signal pulse can be rapidly tuned over a wide range from the visible to the NIR just by scanning the resonator length.

Discontinuous dynamics of a non-linear, self-excited, friction-induced, periodically forced oscillator

Abstract: The discontinuous dynamics of a non-linear, friction-induced, periodically forced oscillator is studied. The analytical conditions for motion switchability at the velocity boundary in such a nonlinear oscillator are developed to understand the motion switching mechanism. Using such analytical conditions of motion switching, numerical predictions of the switching scenarios varying with excitation frequency and amplitude are carried out, and the parameter maps for specific periodic motions are presented. Chaotic and periodic motions are illustrated through phase planes and switching sections for a better understanding of motion mechanism of the nonlinear friction oscillator. The periodic motions with switching in such a nonlinear, frictional oscillator cannot be obtained from the traditional analysis (e.g., perturbation and harmonic balance method).

Parametric resonances in a base-excited double pendulum

Abstract: Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.

Statistics of radiation at Josephson parametric resonance

Abstract: Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson-junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts, each encompassing 2N photons; this accounts for the bunching of the photon pairs produced in the course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.

Frequency Studies and Scaling Effects of Jet Interaction in a Feedback-Free Fluidic Oscillator

Abstract: The work presented in this paper focuses on understanding the effects of scaling on fluidic oscillator performance, with a particular emphasis on the relationship between flow rate and oscillation frequency. The jet interaction feedback-free type of fluidic oscillator used in this investigation is a strong candidate for a flow control actuator, as it has high bandwidth, no moving parts, and high momentum capability. The aim of this study is to understand the basic fluid dynamics of fluidic oscillators, as well as to provide an engineering database of information for future oscillator designs. Results presented in this paper detail the frequency response of the fluidic oscillator under various geometric and supply fluid conditions. Scaling studies were performed in order to establish the operating range of the device. Oscillators were built and tested with different fluids in gas and liquid phases over a range of magnitude in flow rate and frequency response. Frequency maps of the oscillator response indicate a flow field that is rich in high-frequency content, with up to the 7 th harmonic visible in the spectra. Three different flow regimes were observed with particle image velocimetry with a refractive index matched fluid. An interesting modehopping behavior was also observed which varied with the size of the oscillator, aspect ratio, and test fluid.

Quantum dynamics of the damped harmonic oscillator

Abstract: The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys the Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.

An Improved Performance Ring Oscillator Design

Abstract: This paper presents a new technique to improve frequency performance of CMOS ring oscillator. It is based on the addition of MOS transistor to boost switching speed of the oscillator delay cell. The method can be used for simple and differential oscillator and offers a simple way to implement frequency tuning without introduction of any additional phase noise. Using 0.35 µm CMOS technology, simulation results show that applying the technique to the simple ring oscillator allows a frequency oscillation improvement of 80%. Also, simulations show that frequency improvement can reach 300 % if the technique is associated to a positive feedback.

Demonstration of polarization pulling using a fiber-optic parametric amplifier

Abstract: We report the observation of all-optical polarization pulling of an initially polarization-scrambled signal using parametric amplification in a highly nonlinear optical fiber. Broadband polarization pulling has been achieved both for the signal and idler waves with up to 25 dB gain using the strong polarization sensitivity of parametric amplifiers. We further derive the probability distribution function for the final polarization state, assuming a randomly polarized initial state, and we show that it agrees well with the experiments.

Stability in parametric resonance of an axially moving beam constituted by fractional order material

Abstract: The stability of an axially moving beam constituted by fractional order material under parametric resonances is investigated. The governing equation is derived from Newton’s second law and the fractional derivative Kelvin constitutive relationship. The time-dependent axial speed is assumed to vary harmonically about a constant mean velocity. The resulting principal parametric resonances and summation resonances are investigated by the multi-scale method. It is found that instabilities occur when the frequency of axial speed fluctuations is close to two times the natural frequency of the beam or when the frequency is close to the sum of any two natural frequencies. Moreover, Numerical results show that the larger fractional order and the viscoelastic coefficient lead to the larger instability threshold of speed fluctuation for a given detuning parameter. The regular axially moving beam displays a higher stability than the beam constituted by fractional order material.

Stability analysis of a new class of MEMS gyroscopes with parametric resonance

Abstract: In this paper, a parametrically resonated MEMS gyroscope is considered, and the effect of its parameters on the system stability is studied. Unlike the general case of MEMS gyroscopes with harmonic excitation, in this new class of gyroscopes with parametric excitation, the origin is one stationary point of the system. The study starts with the stability analysis of the origin, and then it goes on to analyze the effect of each parameter on the stability of periodic orbits. Stabilities are studied by means of Floquet theory. As the results indicate, presence of a non-trivial response for the system is closely interconnected to the stabilities (and instabilities) of the system. It is demonstrated that the stability of the origin always contributes to a zero response for the sensor, and hence the instability of origin is required for the occurrence of parametric resonance. In contrast, stability of a periodic orbit does not necessarily guarantee a resonant response for the gyroscope, and again it is the instability of the origin which is required for this purpose. Because in the case of linear stiffness—linear parametric excitation the instability of the origin results in instability of the system, it is concluded that nonlinearities are required for a parametrically actuated gyroscope.

Oscillator with random trichotomous mass

Abstract: In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable.

Theory of polarization attraction in parametric amplifiers based on telecommunication fibers

Abstract: We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing (FWM) in standard (randomly birefringent) optical fibers. We show that in the small-signal case these equations can be solved analytically, and permit us to predict the gain experienced by the signal beam as well as its state of polarization (SOP) at the fiber output. We find that, independently of its initial value, the output SOP of a signal within the parametric gain bandwidth is solely determined by the pump SOP. We call this effect of pulling the polarization of the signal towards a reference SOP the polarization attraction, and we call the parametric amplifier the FWM polarizer (which can equivalently be called the fiber-optic parametric amplifier polarizer). Our theory is valid beyond the zero polarization mode dispersion (PMD) limit, and it takes into account moderate deviations of the PMD from zero. In particular, our theory is capable of analytically predicting the rate of degradation of the efficiency of the parametric amplifier, which is caused by the detrimental PMD effect.

On the analysis of bipolar transistor based chaotic circuits: case of a two-stage colpitts oscillator

Abstract: We perform a systematic analysis of a system consisting of a two-stage Colpitts oscillator. This well-known chaotic oscillator is a modification of the standard Colpitts oscillator obtained by adding an extra transistor and a capacitor to the basic circuit. The two-stage Colpitts oscillator exhibits better spectral characteristics compared to a classical single-stage Colpitts oscillator. This interesting feature is suitable for chaos-based secure communication applications. We derive a smooth mathematical model (i.e., sets of nonlinear ordinary differential equations) to describe the dynamics of the system. The stability of the equilibrium states is carried out and conditions for the occurrence of Hopf bifurcations are obtained. The numerical exploration reveals various bifurcation scenarios including period-doubling and interior crisis transitions to chaos. The connection between the system parameters and various dynamical regimes is established with particular emphasis on the role of both bias (i.e., power supply) and damping on the dynamics of the oscillator. Such an approach is particularly interesting as the results obtained are very useful for design engineers. The real physical implementation (i.e., use of electronic components) of the oscillator is considered to validate the theoretical analysis through several comparisons between experimental and numerical results.

The Noisy Oscillator: Random Mass, Frequency, Damping

Abstract: Deterministic and Random Oscillators White and Color Noise Brownian Motion Overdamped Harmonic Oscillator with Additive Noise Overdamped Harmonic Oscillator with Multiplicative Noise Overdamped Single-Well Oscillator Overdamped Double-Well Oscillator Harmonic Oscillator with Additive Noise Nonlinear Oscillator with Additive Noise Harmonic Oscillator with Random Frequency Harmonic Oscillator with Random Damping Linear vs Quadratic Noise Nonlinear Oscillator with Multiplicative Noise Harmonic Oscillator with Random Mass In the Future.

Experimental characterization of a phase-sensitive four-mode fiber-optic parametric amplifier

Abstract: Four-mode phase-sensitive amplification is experimentally introduced for the first time. In a proof-of-principle realization using a dual-pump fiber-optic parametric amplifier we achieve nearly 20-dB gain. The influence of the individual phases of the six interacting waves on the signal gain is investigated.

Sensitivity Enhancement of Remotely Coupled NMR Detectors using Wirelessly Powered Parametric Amplification

Abstract: A completely wireless detection coil with an integrated parametric amplifier has been constructed to provide local amplification and transmission of MR signals. The sample coil is one element of a parametric amplifier using a zero-bias diode that mixes the weak MR signal with a strong pump signal that is obtained from an inductively coupled external loop. The NMR sample coil develops current gain via reduction in the effective coil resistance. Higher gain can be obtained by adjusting the level of the pumping power closer to the oscillation threshold, but the gain is ultimately constrained by the bandwidth requirement of MRI experiments. A feasibility study here shows that on a NaCl/D2O phantom, 23Na signals with 20 dB of gain can be readily obtained with a concomitant bandwidth of 144 kHz. This gain is high enough that the integrated coil with parametric amplifier, which is coupled inductively to external loops, can provide sensitivity approaching that of direct wire connection. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.