Monolayer graphene exhibits exceptional electronic and mechanical properties, making it a very promising material for nanoelectromechanical devices. Here, we conclusively demonstrate the piezoresistive effect in graphene in a nanoelectromechanical membrane configuration that provides direct electrical readout of pressure to strain transduction. This makes it highly relevant for an important class of nanoelectromechanical system (NEMS) transducers. This demonstration is consistent with our simulations and previously reported gauge factors and simulation values. The membrane in our experiment acts as a strain gauge independent of crystallographic orientation and allows for aggressive size scalability. When compared with conventional pressure sensors, the sensors have orders of magnitude higher sensitivity per unit area.

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Electromechanical Piezoresistive Sensing in Suspended Graphene Membranes

Optomechanical systems couple light stored inside an optical cavity to the motion of a mechanical mode. Recent experiments have demonstrated setups, such as photonic crystal structures, that in principle allow one to confine several optical and vibrational modes on a single chip. Here we start to investigate the collective nonlinear dynamics in arrays of coupled optomechanical cells. We show that such ``optomechanical arrays'' can display synchronization, and that they can be described by an effective Kuramoto-type model.

Collective dynamics in optomechanical arrays.

This review provides a summary of the work completed to date on the nonlinear dynamics of resonant micro- and nanoelectromechanical systems (MEMS/NEMS). This research area, which has been active for approximately a decade, involves the study of nonlinear behaviors arising in small scale, vibratory, mechanical devices that are typically integrated with electronics for use in signal processing, actuation, and sensing applications. The inherent nature of these devices, which includes low damping, desired resonant operation, and the presence of nonlinear potential fields, sets an ideal stage for the appearance of nonlinear behavior, and this allows engineers to beneficially leverage nonlinear dynamics in the course of device design. This work provides an overview of the fundamental research on nonlinear behaviors arising in micro/nanoresonators, including direct and parametric resonances, parametric amplification, impacts, selfexcited oscillations, and collective behaviors, such as localization and synchronization, which arise in coupled resonator arrays. In addition, the work describes the active exploitation of nonlinear dynamics in the development of resonant mass sensors, inertial sensors, and electromechanical signal processing systems. The paper closes with some brief remarks about important ongoing developments in the field.

/pdf/nonlinear-dynamics-and-its-applications-in-micro-and-2d8rp19sh4.pdf

Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

Summary form only given. The field of optomechanics [1] seeks to explore the interaction between light and mechanical motion. Optomechanical system are typically composed of a single mechanical and a single optical mode interacting via radiation pressure: Ĥint = -ħg0 â†â(b + b†), where â/b are the photon/phonon operators. In this talk, we will introduce arrays of optomechanical cells, and discuss our first theoretical results on the nonlinear dynamics of such a setup [2,3].First we have studied the classical nonlinear dynamics of optomechanical arrays. For blue-detuned laser drive, a Hopf bifurcation towards self-sustained mechanical oscillations takes place. For static disorder of the frequencies in the array, we have shown that there can be a transition towards phase-locking. The slow dynamics of the mechanical oscillation phase field is described by a specific modification of the Kuramoto equation known in synchronization physics: in the simplest case δ φ = -δΩ - Ksin(2δφ), for the phase difference δφ between two cells with frequency difference δΩ, corresponding to a particle sliding down in a tilted washboard potential.In a second step, we have turned towards the quantum dynamics of arrays without static disorder [3]. There, the effects of the fundamental quantum noise can lead to phase diffusion. Upon increasing the coupling between cells, we observe a transition between incoherent mechanical oscillations and a collective phase-coherent mechanical state. To study the driven-dissipative dynamics, we employ a mean-field approach based on the Lindblad master equation, as well as semiclassical Langevin equations. We will also discuss the prospects of observing this non-equilibrium dynamics in an experimental implementation based on currently available setups. Very promising candidates in this regard are optomechanical crystal setups, where defects in photonic crystal structures are used to generate co-localized optical and mechanical modes in a two-dimensional geometry [4].

/pdf/collective-dynamics-in-optomechanical-arrays-4y23pzx4cm.pdf

Collective dynamics in optomechanical arrays

By virtue of their low mass and stiffness, atomically thin mechanical resonators are attractive candidates for use in optomechanics. Here, we demonstrate photothermal back-action in a graphene mechanical resonator comprising one end of a Fabry–Perot cavity. As a demonstration of the utility of this effect, we show that a continuous wave laser can be used to cool a graphene vibrational mode or to power a graphene-based tunable frequency oscillator. Owing to graphene’s high thermal conductivity and optical absorption, photothermal optomechanics is efficient in graphene and could ultimately enable laser cooling to the quantum ground state or applications such as photonic signal processing.

https://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/nl302036x.pdf

Photothermal Self-Oscillation and Laser Cooling of Graphene Optomechanical Systems

We demonstrate synchronization of laser-induced self-sustained vibrations of radio-frequency micromechanical resonators by applying a small pilot signal either as an inertial drive at the natural frequency of the resonator or by modulating the stiffness of the oscillator at double the natural frequency. By sweeping the pilot signal frequency, we demonstrate that the entrainment zone is hysteretic and can be as wide as 4% of the natural frequency of the resonator, 400 times the 1/Q∼10−4 half-width of the resonant peak. Possible applications are discussed based on the wide range of frequency tuning and the power gain provided by the large amplitude of self-oscillations (controlled by a small pilot signal).

/pdf/frequency-entrainment-for-micromechanical-oscillator-ud7ltd8is7.pdf

Frequency entrainment for micromechanical oscillator

Optically actuated radio frequency microelectromechanical system (MEMS) devices are seen to self-oscillate or vibrate under illumination of sufficient strength (Aubin, Pandey, Zehnder, Rand, Craighead, Zalalutdinov, Parpia (Appl Phys Lett 83, 3281–3283, 2003)) These oscillations can be frequency locked to a periodic forcing, applied through an inertial drive at the forcing frequency, or subharmonically via a parametric drive, hence providing tunability In a previous work~(Aubin, Zalalutdinov, Alan, Reichenbach, Rand, Zehnder, Parpia, Craighead (IEEE/ASME J Micromech Syst 13, 1018–1026, 2004)), this MEMS device was modeled by a three-dimensional system of coupled thermo-mechanical equations requiring experimental observations and careful finite element simulations to obtain the model parameters The resulting system of equations is relatively computationally expensive to solve, which could impede its usage in a complex network of such resonators In this paper, we present a simpler model that shows similar behavior to the MEMS device We investigate the dynamics of a Mathieu–van der Pol–Duffing equation, which is forced both parametrically and nonparametrically It is shown that the steady-state response can consist of either 1:1 frequency locking, or 2:1 subharmonic locking, or quasiperiodic motion The system displays hysteresis when the forcing frequency is slowly varied We use perturbations to obtain a slow flow, which is then studied using the bifurcation software package AUTO

Frequency locking in a forced Mathieu–van der Pol–Duffing system

http://audiophile.tam.cornell.edu/randpdf/manoj_CNSNS.pdf

Perturbation analysis of entrainment in a micromechanical limit cycle oscillator

Thin, planar, radio frequency microelectromechanical systems (MEMS) resonators have been shown to self-oscillate in the absence of external forcing when illuminated by a direct current (dc) laser of sufficient amplitude. In the presence of external forcing of sufficient strength and close enough in frequency to that of the unforced oscillation, the device will become frequency locked, or entrained, by the forcing. In other words, it will vibrate at the frequency of the external forcing. Experimental results demonstrating entrainment for a disk-shaped oscillator under optical and mechanical excitation are reviewed. A thermomechanical model of the system is developed and its predictions explored to explain and predict the entrainment phenomenon. The validity of the model is demonstrated by the good agreement between the predicted and experimental results. The model equations could also be used to analyze MEMS limit-cycle oscillators designed to achieve specific performance objectives

/pdf/analysis-of-frequency-locking-in-optically-driven-mems-1eqjlpul92.pdf

Analysis of Frequency Locking in Optically Driven MEMS Resonators

In microelectromechanical systems resonators, dissipation of energy through anchor points into the substrate adds to resonator energy loss, contributing to low values of Q. A design for improving Q based on the reflection of anchor-generated surface acoustic waves is presented here. In this design, the resonator is surrounded by a trench, or a mesa, that partially reflects the wave energy back to the resonator. Depending on the distance from the resonator to the mesa, the reflected wave interferes either constructively or destructively with the resonator, increasing or decreasing Q. The proposed design is experimentally tested using a dome-shaped flexural mode resonator for a range of distances of the mesa from the resonator. Improvements in Q of up to 400% are observed. The resonator/mesa system is modeled using a commercially available finite-element code. Experiments and simulations compare well, suggesting that a finite-element-method analysis can be used in the preliminary design of mesas for the optimization of Q. The concept of using mesas to improve Q is simulated for both flexural and in-plane modes of vibration.

Manoj Pandey

Papers

Frequency entrainment for micromechanical oscillator

Frequency locking in a forced Mathieu–van der Pol–Duffing system

Perturbation analysis of entrainment in a micromechanical limit cycle oscillator

Analysis of Frequency Locking in Optically Driven MEMS Resonators

Reducing Anchor Loss in MEMS Resonators Using Mesa Isolation