Resonance Frequency Spectra Research Articles

High-Q, in-plane modes of nanomechanical resonators operated in air

Nanomechanical resonators have traditionally been limited to use in vacuum due to low quality factors that come as a result of viscous damping effects in air or liquid. We have fabricated arrays of 90 nm thick trampoline-shaped resonators, studied their resonant frequency spectrum as a function of pressure, and found that some high frequency modes exhibit quality factors over 2000 at atmospheric pressure. We have excited the in-plane resonances of these devices, verified their identities both experimentally and with finite element modeling, and demonstrated their advantageous characteristics for ambient sensing. Even after deposition of a relatively thick polymer layer, the in-plane resonant modes still boast quality factors on the order of 2000. These results show promise for the use of nanomechanical resonant sensors in real-time atmospheric sensing applications.

Interferometric profiling of microcantilevers in liquid

Silicon micro cantilevers are used as highly sensitive transducers for a wide range of physical, chemical and biochemical stimuli. Vibrating the cantilevers at higher-order resonant modes can achieve extra sensitivity, but the difficulty lies in determining exactly which modes are excited in the cantilever. This problem is exacerbated for cantilever sensors operating in liquid where the computational analysis of the resonance modes is very challenging. Using strobed interferometric microscopy, we are able to image the dynamic behavior of individual (100×500×1 μm 3) cantilevers in an eight cantilever array over frequencies from 0–1 MHz. We show how some modifications to the interferometric microscope allow for the spatial visualization of 16 longitudinal modes of cantilevers working in liquid with nanometer-scale amplitudes. We also compare the shift in frequency response and reduction in quality factor for cantilevers resonating in liquid versus in air and simulations in vacuum. Because the resonant frequency spectrum is fairly complex and does not follow simple intuition, our work maps the actual behavior of cantilevers without having any specific knowledge of the sample and environment parameters and without the necessity of involved simulations and calculations.

Coupled whispering gallery mode resonators in the Terahertz frequency range

We report on coupling of two whispering gallery mode resonators in the Terahertz frequency range. Due to the long wavelength in the millimeter to submillimeter range, the resonators can be macroscopic allowing for accurate size and shape control. This is necessary to couple specific modes of two or more resonators. Sets of polyethylene (PE) and quartz disk resonators are demonstrated, with medium (loaded) quality (Q)-factors of 40-800. Both exhibit coinciding resonance frequency spectra over more than ten times the free spectral range. Loading effects of single resonators are investigated which provide strong Q-factor degradation and red-shifts of the resonances in the 0.2% range. By coupling two resonators of the same size, we observe mode splitting, in very good agreement with our numerical calculations.

Resonating modes of vibrating microcantilevers in liquid

A study of nanomechanical cantilevers vibrating at various resonating modes in liquid is presented. Resonant frequency spectrum with 16 well resolved flexural modes is obtained. The quality factor increased from 1 at mode 1 to 30 at mode 16. The theoretical estimate of eigenfrequency using the Elmer–Dreier model [F.-J. Elmer and M. Dreier, J. Appl. Phys. 81, 12 (1997)] and Sader’s extended viscous model [C. A. Van Eysden and J. E. Sader, J. Appl. Phys. 101, 044908 (2007)] matched well with the experimental data. The apparent mass of the liquid comoved by the oscillating cantilevers decreased asymptotically with mode number.

On the nature of resonance splitting in coupled multiring optical resonators

The spectrum of resonance frequencies in so-called free-standing resonators, built with coupled ring or disk resonators is analytically and numerically investigated. The composite resonator which constitutes the core of numerous photonic devices such as channel dropping filters, dispersion compensators, laser mirrors, etc., determines the salient characteristics of the device, such as its passband width and free spectral range (FSR). The spectral characteristics of the resonances are determined by the refractive indices of the waveguides, the dimensions of the resonators, and the strength of coupling between them. Novel relationships between these parameters are described that result in the invariance of the splitting ratios and as a consequence maintain the passband characteristics of the associated devices. Waveguide attenuation affecting the Q factor of the composite resonators is found to have insignificant effect on their spectral characteristics.

Size reduction of microstrip patch antennas with left-handed transmission line loading

A procedure for designing an electrically small microstrip patch antenna (MPA) is developed, wherein the length of a side of the MPA is reduced to significantly less than a half-wavelength. The MPA is loaded with a resonant circuit equivalent to that of a left-handed transmission line to artificially increase the effective wavelength of the device, thus creating a resonance equivalent to, but at a lower frequency than the unloaded {10} mode. The field distribution in the loaded MPA remains relatively unperturbed, unlike the {0} mode case that attempts to decrease the size by introducing a shorting-post; consequently, very low cross-polarisation behaviour is observed. The theory to predict the full spectrum of resonant frequencies of the antenna is developed, with finite-difference time-domain simulations used to finalise the antenna design. Finally, an electrically small ((lambda/6)times(lambda/4)) and thin (<lambda/65) antenna is fabricated at 465 MHz using low-temperature co-fired ceramic technology and tested for key figures of merit, including the resonant frequency and radiation pattern. The shortened antenna not only shows performance comparable to a conventional unloaded MPA, but also exhibits good cross-polarisation. The loaded MPA achieved an area reduction of 83% as compared to an unloaded version

Characterization of a large volume spherical resonator for studies of acoustically induced cavitation in liquids

This paper describes a spherical acoustical resonator system used to study acoustic cavitation phenomena in liquids as part of an effort to scale up the energy density of collapse of transient cavitation. The resonator is formed by a stainless steel spherical shell 24.1 cm in diameter (OD) and either 1.27 cm or 1.90 cm thick designed for generating transient cavitation at high static pressures. An external transducer attached to the surface of the resonator was used to excite an acoustic standing wave in the liquid in order to generate a pressure maximum near the center of the liquid. We will present the results of our characterization of this device, including hydrophone measurements of the acoustic pressure generated in the liquid and vibration analysis on the surface of the resonator carried out using laser Doppler vibrometry. The resonance frequency spectrum and modal structure are compared to numerical predictions using theory developed by (Mehl, JASA 78(2), 782–788 (1985)) [Work supported by SMDC Contract No. W9113M‐07‐C‐0178.]

Multi-frequency response from a designed array of micromechanical cantilevers fabricatedusing a focused ion beam

We demonstrate arrays of cantilevers with different lengths, fabricated by focused ion beammilling. The arrays of oscillators generate a spectrum of different resonant frequencies, whereeach frequency correlates to the corresponding individual cantilever. The frequency responsefrom all the cantilevers is collected from a single measurement under the same environmentand conditions for the entire array. The mass response of the system generated the sameΔf/f0 for the cantilevers, within 0.1% accuracy. We denote the method MFSAC: multi-frequencysignal analysis from an array of cantilevers. The simultaneous detection of severalfrequencies in one spectrum has great benefits in mass sensor applications, offering thepossibility for true label-free detection.

Electrode effects on general modes in high-overtone bulk acoustic resonators

Generally, in theoretical calculations of high-overtone bulk acoustic resonators (HBAR), metal electrode effects were always ignored. However, the acoustical impedance, thickness and loss of the electrodes affect practically the performances of HBAR operating at high-frequency. For very high-frequency cases, the thickness of the metal electrode is always on the same order of that of the piezo-film and the electrode effects on modes cannot be negligible. In this paper, based on the resonance frequency spectra and Butterworth Van Dyke equivalent circuit of HBAR, the effects of the material, loss, and thickness of the electrodes on the figure of merit, effective electromechanical coupling factor, quality factor, etc. are analyzed. It is demonstrated that the performance of HBAR can also be optimized by using the electrodes with proper impedance, loss and thickness.

Electrostatic (plasmon) resonances in nanoparticles

A surface integral eigenvalue based technique for the direct calculation of resonance values of the permittivity of nanoparticles, and hence resonance frequencies, is discussed. General physical properties of electrostatic plasmon resonances are presented. Strong orthogonality properties of resonance modes, a twodimensional phenomenon of “twin” spectrum and explicit estimates of resonance frequencies in terms of geometrical characteristics of convex nanoparticles are reported. Second-order corrections for resonance values of the dielectric permittivity are derived. Tunability and optical controllability of plasmon resonances in semiconductor nanoparticles are discussed and, as a digression, a plausible plasmon resonance mechanism for nucleation and formation of ball lightning is outlined. An efficient numerical algorithm for the calculation of resonance frequencies is developed and illustrated by extensive computational results that are compared with theoretical results and available experimental data.

Characterization of vaccinia virus particles using microscale silicon cantilever resonators and atomic force microscopy

Rapid means of characterizing and detecting virus particles are very important for a wide variety of applications. We have used vaccinia virus, a member of the Poxviridae virus family and the basis of the smallpox vaccine, as the test case and characterized these particles using atomic force microscopy and micron-scale cantilever beams, with the long-term goal of developing devices for the direct rapid detection of air-borne virus particles. The cantilever beams, driven by thermal noise and a PZT piezoelectric ceramic, served as resonating sensors to measure the mass of these virus particles. Two different size cantilevers were used, with dimensions of 21μm×9μm and 6μm×4μm. All cantilevers measured approximately 200nm in thickness. The resonant frequency spectra of the cantilevers were measured using a microscope scanning laser Doppler vibrometer before and after the addition of virus particles, and scanning electron micrographs were taken in order to quantify the number of virus particles attached to the cantilevers. The change in resonant frequency as a function of the number of adsorbed virus particles was the basis of the mass detection scheme. We have measured the average mass of a single vaccinia virus particle to be 12.4±1.3fg and 7.9±4.6fg, obtained from the larger and smaller cantilever beams, respectively, which is in the expected range of 5–10fg. The measurable mass sensitivity of cantilevers driven by the piezoelectric ceramic is found to be an order of magnitude greater than the sensitivity of cantilevers driven by thermal noise. These cantilever structures can be integral parts of biosensors for the detection of airborne virus particles.

Waves on fluid-loaded shells and their resonance frequency spectrum

Technical requirements for elastic (metal) cylindrical shells include the knowledge of their natural frequency spectrum. These shells may be empty and fluid-immersed, or fluid-filled in an ambient medium of air, or doubly fluid-loaded inside and out. They may support circumferential waves, or axially propagating waves both in the shell material, and in the fluid loading. Previous results by Bao et al. (J. Acoust. Soc. Am. 105 (1999) 2704) were obtained for the circumferential-wave dispersion curves on doubly loaded aluminum shells; the present study extends this to fluid-filled shells in air. For practical applications, steel shells are most important and we have here obtained corresponding results for these. To find the natural frequencies of cylindrical shells, one may invoke the principle of phase matching where resonating standing waves are formed around the circumference, or in the axial direction if the cylindrical shell is terminated at both ends. In this way, we obtain (circumferential and axial wave) eigenfrequency spectra for water filled aluminum and steel shells, and also for brass shells (axial-wave resonances only).

Analysis of Excitations for a Groove Guide Resonator at 10 GHz by means of the FDTD Method

Various excitations of a new groove guide resonator working in the X-band (8 GHz – 12 GHz) are investigated by means of numerical simulations. For the numerical simulations the Finite-Difference Time-Domain method is used. The groove guide resonator, modelled both with and without excitation structures, is discretised in space. The results in the time domain are then transformed into the frequency domain in order to obtain the resonance frequency spectrum. Comparison between simulations with and without excitations shows the effect of the excitations on the resonance frequency spectrum. The results are compared with those of previous analytical methods.

Resonant Interaction of a Beam and an Elastic Foundation During the Motion of a Periodic System of Concentrated Loads

The vibrations of a beam on an elastic foundation under the action of a periodic system of moving concentrated forces are analyzed against different spatial periods and different velocity ranges separated by three critical values. It is established that for velocities ranging from zero to the minimum critical value, resonance does not occur and the beam deflection weakly depends on the force velocity. For velocities exceeding the minimum critical value, a dense spectrum of resonant frequencies is observed

Robust design of quartz crystal microbalance using finite element and Taguchi method

This article presents an efficient method for the design of quartz crystal microbalance (QCM). The effects of QCM’s resonant frequency influenced by the variation of the deposited mass are studied by using the finite element analysis (FEA) software. The advantages of the demonstrated concept are the flexibility of the program structure and the reduction of the cost. Moreover, the well-known Taguchi method (TM) is applied to obtain the high Q-factor of QCM for robust design. The simulation results including resonant frequency, thickness-shear mode (TSM) and frequency spectrum are agreed well with the theoretical values and experimental studies.

Resonant spectrum method to characterize piezoelectric films in composite resonators.

In this paper, we present a direct method to characterize a piezoelectric film that is sandwiched with two electrodes and deposited on a substrate to form a four-layer thickness extension mode composite resonator (also known as over-moded resonator). Based on the parallel and series resonant frequency spectra of a composite resonator, the electromechanical coupling factor, the density and the elastic constant of the piezoelectric film can be evaluated directly. Experimental results on samples consisting of ZnO films on fused quartz substrates with different thickness are presented. They show good agreement with theoretical prediction. The mechanical effect of the electrode on the method is investigated, and numerical simulation shows that the effect of the electrodes can be properly corrected by the modified formulae presented in this paper. The effect of mechanical loss in piezoelectric film and in substrate on this method also has been investigated. It is proven that the method is insensitive to the losses.

Numerical simulation of magnetic susceptibility effects in nuclear magnetic resonance spectroscopy

A numerical algorithm is proposed which is suitable to calculate the magnetic field distribution as well as the corresponding nuclear magnetic resonance time signals and frequency spectra induced by susceptibility effects. It accounts for a wide variety of system parameters such as various sample geometries, free and hindered self-diffusion, inhomogeneous susceptibility, and variable spin concentration. It is suitable to cover multiple experimental conditions such as single pulses, echoes, sample spinning at any tilt angle, and field gradient experiments. Typical results are shown that demonstrate the separate and combined influences of self-diffusion and sample spinning on spectral line shapes. Calculated frequency shifts are compared with known analytical expressions and with experimental data on dispersions of magnetic nanoparticles.

Measuring the dielectric permittivity of sapphire at temperatures 93-343 K

We consider a method for measuring the elements of the dielectric-permittivity tensor of a slightly lossy uniaxial anisotropic dielectric using the spectrum of resonance frequencies of a metal-dielectric resonator in the form of an axially anisotropic cylindrical specimen with endface metal mirrors. Measurements of both elements of the dielectric-permittivity tensor of sapphire at temperatures 93–343 K are performed using the spectrum of symmetric E modes. To avoid the influence of the residual gaps between the specimen and the mirrors, the endface surfaces of the specimen are metallized. We performed independent measurements of the axial and transverse elements of the permittivity tensor at room temperature from the spectra of azimuthal E modes and symmetric H modes. The values of the axial and transverse elements of the dielectric-permittivity tensor of sapphire in the range 93–343 K are presented with a spacing of 10 K.

Remotely interrogated temperature sensors based on magnetic materials

A family of remotely interrogated passive temperature sensors is presented. These sensors are comprised of several layers of magnetic materials having either a resonant frequency or harmonic spectrum which varies with temperature. By incorporating a magnetic bias layer and a magnetically permeable layer, it is possible to create sensors which respond to a temperature threshold (reversibly or nonreversibly) or produce a signal which continuously and monotonically varies with temperature. In this paper, a 30%/70% Ni-Fe layer was used in conjunction with amorphous alloy strips to produce three distinct types of wireless temperature sensors operating over the range 20/spl deg/-70/spl deg/C.

Characterization of electromechanical coupling coefficients of piezoelectric films using composite resonators

By analyzing the resonance frequency spectrum of a composite resonator consisting of a piezoelectric ceramic film deposited on a substrate plate, the thickness extensional mode electromechanical coupling coefficient of the film, k(t)(2), can be directly calculated from the effective coupling factor values, k(eff )(2), for two special modes of the resonator. The effects of the mechanical loss in the piezoelectric films on the measurement are investigated by numerical simulation, and some guidelines for improving the accuracy of the k(t)(2) measurement are reported.