The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation

The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the autocorrelation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers.Comment: Submitted to Nanotechnology April 26, 200

Array atomic force microscopy for real-time multiparametric analysis.

Nanoscale multipoint structure-function analysis is essential for deciphering the complexity of multiscale biological and physical systems. Atomic force microscopy (AFM) allows nanoscale structure-function imaging in various operating environments and can be integrated seamlessly with disparate probe-based sensing and manipulation technologies. Conventional AFMs only permit sequential single-point analysis; widespread adoption of array AFMs for simultaneous multipoint study is challenging owing to the intrinsic limitations of existing technological approaches. Here, we describe a prototype dispersive optics-based array AFM capable of simultaneously monitoring multiple probe-sample interactions. A single supercontinuum laser beam is utilized to spatially and spectrally map multiple cantilevers, to isolate and record beam deflection from individual cantilevers using distinct wavelength selection. This design provides a remarkably simplified yet effective solution to overcome the optical cross-talk while maintaining subnanometer sensitivity and compatibility with probe-based sensors. We demonstrate the versatility and robustness of our system on parallel multiparametric imaging at multiscale levels ranging from surface morphology to hydrophobicity and electric potential mapping in both air and liquid, mechanical wave propagation in polymeric films, and the dynamics of living cells. This multiparametric, multiscale approach provides opportunities for studying the emergent properties of atomic-scale mechanical and physicochemical interactions in a wide range of physical and biological networks

Electromechanically Tunable Metasurface Transmission Waveplate at Terahertz Frequencies

Dynamic polarization control of light is essential for numerous applications ranging from enhanced imaging to materials characterization and identification. We present a reconfigurable terahertz metasurface quarter-waveplate consisting of electromechanically actuated micro-cantilever arrays. Our anisotropic metasurface enables tunable polarization conversion cantilever actuation. Specifically, voltage-based actuation provides mode selective control of the resonance frequency, enabling real-time tuning of the polarization state of the transmitted light. The polarization tunable metasurface has been fabricated using surface micromachining and characterized using terahertz time domain spectroscopy. We observe a ~230 GHz cantilever actuated frequency shift of the resonance mode, sufficient to modulate the transmitted wave from pure circular polarization to linear polarization. Our CMOS-compatible tunable quarter-waveplate enriches the library of terahertz optical components, thereby facilitating practical applications of terahertz technologies

Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices

Both bright and dark traveling, locked, intrinsic localized modes (ILMs) have been generated with a spatially uniform driver at a frequency in the acoustic spectrum of a nonlinear micromechanical cantilever array. Complementary numerical simulations show that a minimum density of modes, hence array size, is required for the formation of such locked smoothly running excitations. Additional simulations on a small 1-D antiferromagnetic spin system are used to illustrate that such uniformly driven running ILMs should be a generic feature of a nanoscale atomic lattice.Comment: Physical Review Letters, accepte

Arbitrary distribution and nonlinear modal interaction in coupled nanomechanical resonators

We propose a general one-dimensional {\em continuous} formulation to analyze the vibrational modes of antenna-like nanomechanical resonators consisting of two symmetric arrays of cantilevers affixed to a central nano-beam. The cantilever arrays can have arbitrary density and length profile along the beam. We obtain the secular equation that allows for the determination of their frequency spectrum and illustrate the results on the particular examples of structures with constant or alternating cantilever length profiles. We show that our analytical results capture the vibration spectrum of such resonators and elucidate key relationships that could prove advantageous for experimental device performance. Furthermore, using a perturbative approach to treat the nonlinear and dissipative dynamics of driven structures, we analyze the anharmonic coupling between two specific widely spaced modes of the coupled-element device, with direct application to experiments.Comment: 8 pages, 5 figures, additional info can be found at http://nano.bu.ed

Magnetic resonance spectroscopy of perpendicularly magnetized permalloy multilayer disks

Using a Magnetic Resonance Force Microscope, we compare the ferromagnetic resonance spectra of individual micron-size disks with identical diameter, 1 $m$m, but different layer structures. For a disk composed of a single 43.3 nm thick permalloy (Py) layer, the lowest energy mode in the perpendicular configuration is the uniform precession. The higher energy modes are standing spin-waves confined along the diameter of the disk. For a Cu(30)/Py(100)/Cu(30) nm multilayer structure, it has been interpreted that the lowest energy mode becomes a precession localized at the Cu/Py interfaces. When the multilayer is changed to Py(100)/Cu(10)/Py(10) nm, this localized mode of the thick layer is coupled to the precession of the thin layer