Nonlinear Dynamics of Nanomechanical Resonators

Lifshitz, Ron; Cross, M. C.

doi:10.1002/9783527629374.ch8

Cited by 36 publications

(38 citation statements)

References 66 publications

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“…Figure 3d shows that the value of α 3 is proportional to the power of the tuning laser for both softening (red) and hardening (blue) situations, as expected from theoretical analysis. The rich and completely controllable optomechanical nonlinearity in cavity optomechanics, demonstrated here for the first time, can be harnessed to explore nonlinear phenomena in nanomechanical oscillators 29 , including parametric amplification 32 , synchronization 33 and stochastic dynamics 34,35 .…”

Section: Resultsmentioning

confidence: 93%

“…Cavity optomechanical devices are inherently nonlinear mechanical systems 29 because the optomechanical interaction involves the intra-cavity field, which depends nonlinearly on the mechanical elements' position. Exploiting the nonlinear dynamics in cavity optomechanical systems will be especially important to applications that need to operate the devices in the high-amplitude regime, such as optomechanical oscillators 17,18 and optomechanical memory 19 .…”

Section: Resultsmentioning

confidence: 99%

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Multichannel cavity optomechanics for all-optical amplification of radio frequency signals

Chen

Noh

et al. 2012

Nat Commun

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optomechanical phenomena in photonic devices provide a new means of light-light interaction mediated by optical force actuated mechanical motion. In cavity optomechanics, this interaction can be enhanced significantly to achieve strong interaction between optical signals in chip-scale systems, enabling all-optical signal processing without resorting to electro-optical conversion or nonlinear materials. However, current implementation of cavity optomechanics achieves both excitation and detection only in a narrow band at the cavity resonance. This bandwidth limitation would hinder the prospect of integrating cavity optomechanical devices in broadband photonic systems. Here we demonstrate a new configuration of cavity optomechanics that includes two separate optical channels and allows broadband readout of optomechanical effects. The optomechanical interaction achieved in this device can induce strong but controllable nonlinear effects, which can completely dominate the device's intrinsic mechanical properties. utilizing the device's strong optomechanical interaction and its multichannel configuration, we further demonstrate all-optical, wavelengthmultiplexed amplification of radio-frequency signals.

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Section: Resultsmentioning

confidence: 93%

Section: Resultsmentioning

confidence: 99%

Multichannel cavity optomechanics for all-optical amplification of radio frequency signals

Chen

Noh

et al. 2012

Nat Commun

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“…MEMS oscillators may be subject to nonlinear damping involving higher powers of x andẋ [12]. One of the simpler examples is air drag that imposes a quadratically nonlinear damping force, as described in [13], in which case the equation of motion is…”

Section: B Case Of Quadratic Dampingmentioning

confidence: 99%

“…It is common for microelectromechanical systems (MEMS) devices to show nonlinear behavior arising from a nonlinearly stiffening or softening spring effect, as in [2]- [12]. Such devices are often described by Duffing's equation with a cubic restoring force.…”

Section: Introductionmentioning

confidence: 99%

Measuring Quality Factor From a Nonlinear Frequency Response With Jump Discontinuities

Davis

2011

J. Microelectromech. Syst.

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The convenient half-power bandwidth formula used for measurement of quality factor Q does not apply for nonlinear systems that have jump discontinuities in their frequency responses, since one of the half-power amplitudes is not observable. This paper shows alternatives to the half-power formula that do apply to such nonlinear systems, while preserving all of the convenience of the method. Their practical use is illustrated by experimental Q measurements for a microelectromechanical systems scanning mirror.[2011-0011]

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“…The overall thickness and length of the beam are given by H = i h i and L = j l j . Variables denoted by tilde are rescaled and made nondimensional in Section II-C, [20]. The cross-sectional area is given by…”

Section: Modelmentioning

confidence: 99%

Tip Motion—Sensor Signal Relation for a Composite SPM/SPL Cantilever

Roeser

Gutschmidt

Sattel

et al. 2016

J. Microelectromech. Syst.

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Abstract-An array of microbeams is a promising approach to increase the throughput of scanning probe microscopes and lithography. This concept requires integrated sensors and actuators which enable individual measurement and control. Thus, existing models for single beams need to be reassessed in view of its applicability for arrays, which involve additional physical interactions and a varying geometry along the beam's length. This paper considers a single composite microbeam, which is excited by a thermal actuator and its displacement is measured by a piezoresistive sensor. We derive a model that incorporates the beam's composite structure, varying geometry along its length, its thermal coupling for actuation, and thermoelastic damping. Subsequently, the influence of the beam's geometry on its eigenmodes and frequencies is analyzed in far and close proximity operation to a surface. We observe parametric excitation phenomena of multiple integers of the fundamental excitation frequency, which originates from the geometrical composition of the beam. Furthermore, we observe that the so far constant assumed factor to convert the sensor signal to the beam's displacement depends on the dissipated power within the actuator, as well as on the dynamic behavior of the system, and thus is not constant.[2015-0208]

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Nonlinear Dynamics of Nanomechanical Resonators

Cited by 36 publications

References 66 publications

Multichannel cavity optomechanics for all-optical amplification of radio frequency signals

Multichannel cavity optomechanics for all-optical amplification of radio frequency signals

Measuring Quality Factor From a Nonlinear Frequency Response With Jump Discontinuities

Tip Motion—Sensor Signal Relation for a Composite SPM/SPL Cantilever

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