Bifurcation Generated Mechanical Frequency Comb.

We demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, nonlinear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a "frequency-comb" regime in the spectral response. By considering a generic model for a 1∶3 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here makes the simple micromechanical resonator an ideal test bed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical, and biological systems.

Self-Sustained Micromechanical Oscillator with Linear Feedback.

Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motion, there needs to be an external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here, we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model for describing the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical oscillator.

Phonon softening and crystallographic orientation of strained graphene studied by Raman spectroscopy.

We present a systematic study of the Raman spectra of optical phonons in graphene monolayers under tunable uniaxial tensile stress. Both the G and 2D bands exhibit significant red shifts. The G band splits into 2 distinct subbands (G(+), G(-)) because of the strain-induced symmetry breaking. Raman scattering from the G(+) and G(-) bands shows a distinctive polarization dependence that reflects the angle between the axis of the stress and the underlying graphene crystal axes. Polarized Raman spectroscopy therefore constitutes a purely optical method for the determination of the crystallographic orientation of graphene.

Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.

Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.

Graphene mechanical oscillators with tunable frequency.

Oscillators, which produce continuous periodic signals from direct current power, are central to modern communications systems, with versatile applications including timing references and frequency modulators. However, conventional oscillators typically consist of macroscopic mechanical resonators such as quartz crystals, which require excessive off-chip space. Here, we report oscillators built on micrometre-size, atomically thin graphene nanomechanical resonators, whose frequencies can be electrostatically tuned by as much as 14%. Self-sustaining mechanical motion is generated and transduced at room temperature in these oscillators using simple electrical circuitry. The prototype graphene voltage-controlled oscillators exhibit frequency stability and a modulation bandwidth sufficient for the modulation of radiofrequency carrier signals. As a demonstration, we use a graphene oscillator as the active element for frequency-modulated signal generation and achieve efficient audio signal transmission.

Performance of monolayer graphene nanomechanical resonators with electrical readout.

The enormous stiffness and low density of graphene make it an ideal material for nanoelectromechanical applications. Here, we demonstrate the fabrication and electrical readout of monolayer graphene resonators, and test their response to changes in mass and temperature. The devices show resonances in the megahertz range, and the strong dependence of resonant frequency on applied gate voltage can be fitted to a membrane model to yield the mass density and built-in strain of the graphene. Following the removal and addition of mass, changes in both density and strain are observed, indicating that adsorbates impart tension to the graphene. On cooling, the frequency increases, and the shift rate can be used to measure the unusual negative thermal expansion coefficient of graphene. The quality factor increases with decreasing temperature, reaching approximately 1 x 10(4) at 5 K. By establishing many of the basic attributes of monolayer graphene resonators, the groundwork for applications of these devices, including high-sensitivity mass detectors, is put in place.