Membrane Resonance Research Articles

Subwavelength total acoustic absorption with degenerate resonators

We report the experimental realization of perfect sound absorption by sub-wavelength monopole and dipole resonators that exhibit degenerate resonant frequencies. This is achieved through the destructive interference of two resonators' transmission responses, while the matching of their averaged impedances to that of air implies no backscattering, thereby leading to total absorption. Two examples, both using decorated membrane resonators (DMRs) as the basic units, are presented. The first is a flat panel comprising a DMR and a pair of coupled DMRs, while the second one is a ventilated short tube containing a DMR in conjunction with a sidewall DMR backed by a cavity. In both examples, near perfect absorption, up to 99.7%, has been observed with the airborne wavelength up to 1.2 m, which is at least an order of magnitude larger than the composite absorber. Excellent agreement between theory and experiment is obtained.

Coherent perfect absorption in photonic structures

The ability to drive a system with an external input is a fundamental aspect of light-matter interaction. The coherent perfect absorption (CPA) phenomenon extends to the general multibeam interference phenomenology the well known critical coupling concepts. This interferometric control of absorption can be employed to reach full delivery of optical energy to nanoscale systems such as plasmonic nanoparticles, and multi-port interference can be used to enhance the absorption of a nanoscale device when it is embedded in a strongly scattering system, with potential applications to nanoscale sensing. Here we review the two-port CPA in reference to photonic structures which can resonantly couple to the external fields. A revised two-port theory of CPA is illustrated, which relies on the Scattering Matrix formalism and is valid for all linear two-port systems with reciprocity. Through a semiclassical approach, treating two-port critical coupling conditions in a non-perturbative regime, it is demonstrated that the strong coupling regime and the critical coupling condition can indeed coexist; in this situation, termed strong critical coupling, all the incoming energy is converted into polaritons. Experimental results are presented, which clearly display the elliptical trace of absorption as function of input unbalance in a thin metallo-dielectric metamaterial, and verify polaritonic CPA in an intersubband-polariton photonic-crystal membrane resonator. Concluding remarks discuss the future perspectives of CPA with photonic structures.

Generation of resonance-dependent oscillation by mGluR-I activation switches single spiking to bursting in mesencephalic trigeminal sensory neurons.

The primary sensory neurons supplying muscle spindles of jaw-closing muscles are unique in that they have their somata in the mesencephalic trigeminal nucleus (MTN) in the brainstem, thereby receiving various synaptic inputs. MTN neurons display bursting upon activation of glutamatergic synaptic inputs while they faithfully relay respective impulses arising from peripheral sensory organs. The persistent sodium current (IN aP ) is reported to be responsible for both the generation of bursts and the relay of impulses. We addressed how IN aP is controlled either to trigger bursts or to relay respective impulses as single spikes in MTN neurons. Protein kinase C (PKC) activation enhanced IN aP only at low voltages. Spike generation was facilitated by PKC activation at membrane potentials more depolarized than the resting potential. By injection of a ramp current pulse, a burst of spikes was triggered from a depolarized membrane potential whereas its instantaneous spike frequency remained almost constant despite the ramp increases in the current intensity beyond the threshold. A puff application of glutamate preceding the ramp pulse lowered the threshold for evoking bursts by ramp pulses while chelerythrine abolished such effects of glutamate. Dihydroxyphenylglycine, an agonist of mGluR1/5, also caused similar effects, and increased both the frequency and impedance of membrane resonance. Immunohistochemistry revealed that glutamatergic synapses are made onto the stem axons, and that mGluR1/5 and Nav1.6 are co-localized in the stem axon. Taken together, glutamatergic synaptic inputs onto the stem axon may be able to switch the relaying to the bursting mode.

Modal and transient analysis of membrane acoustic metasurfaces

Dispersive surface waves on an acoustic 2D metamaterial, a metasurface consisting of membranes on a rigid surface, have certain propagation characteristics with potential applications for resonance based sensing and subwavelength imaging. The trapped modes of the system that is responsible for the dispersive properties of these acoustic waves are analyzed through modal analysis for a small linear membrane array to obtain the mode shapes, resonant frequencies, quality factors, and wavenumbers. Transient analysis is used for larger arrays to obtain the dispersive properties of the traveling waves and is compared to the modal analysis. Equifrequency contours of the 2D metasurface illustrate interesting features of the metasurface at different frequency regimes around the membrane resonance. These features include anisotropic wave propagation, directional band gap, negative refraction, and complete band gap. Effects of membrane pitch, randomness of resonance, and aperiodic membrane spacing on dispersion, band gaps, and quality factor of the trapped modes on the metasurface are investigated as they relate to realistic implementations for different applications.

Micromachined Piezoelectric-on-Silicon Thickness Extensional Mode Resonators

This paper describes characterization of a thickness extensional mode in a piezoelectrically driven MEMS composite AlN-on-Si membrane resonator. The measured resonant frequency for the mode closely matches the analytical prediction for the fundamental half-wavelength thickness extensional mode through the entire thickness of the composite membrane. The mode has been measured across a variety of devices corresponding to differing membrane geometriesand boundary conditions. For co-located devices the measured frequency of the composite membrane thickness extensional mode is found to be highly reproducible, with a standard deviation of 0.5% or less in the measured frequency device to device. Finally, the mode is compared in vacuum, air, and water for one device. Only very slight damping occurs transitioning from vacuum to air, however operation in water results in the response being significantly damped.

Fabrication of nanoplate resonating structures via micro-masonry

Advantages of using nanoscale membrane and plate resonators over more common cantilever shapes include higher quality factor (Q factor) for an equivalent mass and better suitability to mass sensing applications in fluid. Unfortunately, the current fabrication methods used to obtain such membranes and plates are limited in terms of materials and thickness range, and can potentially cause stiction. This study presents a new method to fabricate nanoplate resonating structures based on micro-masonry, which is the advanced form of the transfer printing technique. Nanoplate resonators were fabricated by transfer printing 0.34 µm thick square-shaped silicon plates by means of polydimethylsiloxane microtip stamps on top of silicon oxide base structures displaying 20 µm diameter cavities, followed by a thermal annealing step to create a rigid bond. Typical resulting suspended structures display vibration characteristics, i.e. a resonance frequency of a few MHz and Q factors above 10 in air at atmospheric pressure, which are in accordance with theory. Moreover, the presented fabrication method enables the realization of multiple suspended structures in a single step and on the same single base, without mechanical crosstalk between the resonators. This work thus demonstrates the suitability and the advantages of the micro-masonry technique for the fabrication of plate resonators for mass sensing purpose.

Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption

The ability to feed energy into a system, or - equivalently - to drive that system with an external input is a fundamental aspect of light-matter interaction. The key concept in many photonic applications is the "critical coupling" condition: at criticality, all the energy fed to the system via an input channel is dissipated within the system itself. Although this idea was crucial to enhance the efficiency of many devices, it was never considered in the context of systems operating in a non-perturbative regime. In this so-called strong coupling regime, the matter and light degrees of freedom are in fact mixed into dressed states, leading to new eigenstates called polaritons. Here we demonstrate that the strong coupling regime and the critical coupling condition can indeed coexist; in this situation, which we term strong critical coupling, all the incoming energy is converted into polaritons. A semiclassical theory - equivalently applicable to acoustics or mechanics - reveals that the strong critical coupling corresponds to a special curve in the phase diagram of the coupled light-matter oscillators. In the more general case of a system radiating via two scattering ports, the phenomenology displayed is that of coherent perfect absorption (CPA), which is then naturally understood and described in the framework of critical coupling. Most importantly, we experimentally verify polaritonic CPA in a semiconductor-based intersubband-polariton photonic-crystal membrane resonator. This result opens new avenues in the exploration of polariton physics, making it possible to control the pumping efficiency of a system almost independently of its Rabi energy, i.e., of the energy exchange rate between the electromagnetic field and the material transition.

Spatially distributed dendritic resonance selectively filters synaptic input.

An important task performed by a neuron is the selection of relevant inputs from among thousands of synapses impinging on the dendritic tree. Synaptic plasticity enables this by strenghtening a subset of synapses that are, presumably, functionally relevant to the neuron. A different selection mechanism exploits the resonance of the dendritic membranes to preferentially filter synaptic inputs based on their temporal rates. A widely held view is that a neuron has one resonant frequency and thus can pass through one rate. Here we demonstrate through mathematical analyses and numerical simulations that dendritic resonance is inevitably a spatially distributed property; and therefore the resonance frequency varies along the dendrites, and thus endows neurons with a powerful spatiotemporal selection mechanism that is sensitive both to the dendritic location and the temporal structure of the incoming synaptic inputs.

Using multi-objective evolutionary algorithms to predict the parameters that determine membrane resonance in a biophysical model of bursting neurons

Many neurons exhibit membrane potential resonance (MPR), a peak in the membrane impedance amplitude (|Z|) in response to oscillatory inputs at nonzero frequency (fmax) [1]. MPR arises from nonlinearity and timescales of voltage-gated currents and may set frequency of network oscillations. Pacemaker PD neurons of the crab pyloric network show MPR whose fmax is correlated with the network frequency (~ 1Hz) [2]. In contrast, the LP follower neuron shows a higher fmax of ~ 1.4 Hz. The impedance profile of biological PD and LP neurons and the model neuron was measured using a logarithmic ZAP function (fmin=0.1 Hz, fmax=4 Hz) in voltage clamp (Vlow=-60mV and Vhigh=-30mV). The fmaxin biological PD neurons increases if either Vlow or Vhigh are increased [3], whereas the LP neuron fmax is only sensitive to Vhigh. Additionally MPR in the PD neurons is sensitive to blockers of ICa and Ih. We hypothesize that: (1) many combinations of parameters can produce MPR in PD and LP neurons; (2) The MPR mechanism in LP is distinct from PD. Experimentally, ICais difficult to measureand therefore a top-down approach is adopted to elucidate the contributions of ICaand Ih to MPR in PD and LP. Because resonance depends on the kinetics of ICaand Ih, a brute-force sampling of the parameter space is computationally unfeasible and, therefore, we search for model parameters using a genetic algorithm. The biological data were used to constrain the range of leak, ICa and Ih parameters in a single-compartment model. The genetic algorithm, NSGA-II [4] was used to optimize the MPR profile and produce a population of optimal models. A sensitivity analysis of MPR attributes on model parameters was done in these models. The distributions of optimal parameters were tightly constrained for gleak, V½_Ca_act, V½_Ca_inact and τ_Ca_inact. Additionally, strong correlations were observed between τ_Ca_act and τ_Ca_inact (negative), between V½_Ca_act and V½_Ca_inact and between gCaand V½_Ca_act (negative). In models with low Ih, fmax correlated strongly with the frequency which ICa peaked, which is controlled by τ_Ca_act and τ_Ca_inact. The parameter sensitivities also support the sensitivity to ICatime constants, demonstrating potential targets for neuromodulation. The MOEA was also used to optimize the fmaxshifts with Vlow and Vhigh to produce two model groups with properties that correspond to the differences between PD and LP. These results suggest that fmaxshift is due to different activation rates of Ih and therefore these two neurons may generate MPR through different mechanisms; a result which we aim to test experimentally. Many neurons display emergent properties in response to oscillatory inputs, such as amplified responses in certain frequency bands. These properties may be important in shaping coherent network activity. The underlying nonlinearities and time scales that shape specific features of impedance profiles can be used to link sub-threshold dynamics to supra-threshold voltage responses. We have used an MOEA to understand the multiple underlying ionic mechanisms that generate resonance and explained how PD, and not LP, fmaxcan be adjusted according to different input amplitudes.

Toward broadband electroacoustic resonators through optimized feedback control strategies

This paper presents a methodology for the design of broadband electroacoustic resonators for low-frequency room equalization. An electroacoustic resonator denotes a loudspeaker used as a membrane resonator, the acoustic impedance of which can be modified through proportional feedback control, to match a target impedance. However, such impedance matching only occurs over a limited bandwidth around resonance, which can limit its use for the low-frequency equalization of rooms, requiring an effective control at least up to the Schroeder frequency. Previous experiments have shown that impedance matching can be achieved over a range of a few octaves using a simple proportional control law. But there is still a limit to the feedback gain, beyond which the feedback-controlled loudspeaker becomes non-dissipative. This paper evaluates the benefits of using PID control and phase compensation techniques to improve the overall performance of the electroacoustic resonator. More specifically, it is shown that some adverse effects due to high-order dynamics in the moving-coil transducer can be mitigated. The corresponding control settings are also identified with equivalent electroacoustic resonator parameters, allowing a straightforward design of the controller. Experimental results using PID control and phase compensation are finally compared in terms of sound absorption performances. As a conclusion the overall performances of electroacoustic resonators for damping the modal resonances inside a duct are presented, along with general discussions on practical implementation and the extension to actual room modes damping.

Guided-Mode Resonances in GaN Membrane Grating

This paper proposes guided-mode resonant GaN grating that are implemented on a GaN-on-silicon wafer structure. Numerical simulations based on rigorous coupled wave analysis (RCWA) are performed to model multiple resonances in thick GaN membranes. Back wafer etching of freestanding GaN membranes is used as a tuning mechanism to manipulate the optical performance in the visible wavelength range. Angular resolved micro reflectance measurements are conducted to characterize the fabricated GaN gratings and show the dependence of guided-mode resonances on the filling factor of the gratings, the membrane thickness, and the polarization of incident beam. The experimental results agree well with numerical simulations. This paper opens the way to fabricate guided-mode resonant GaN grating for many diverse applications.

Graphene nanoelectromechanical systems as stochastic-frequency oscillators.

We measure the quality factor Q of electrically driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ∼ 1/T, where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result, Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. This model is in good agreement with experiment. Additionally, at larger drives the resonance line width is enhanced by nonlinear damping, in qualitative agreement with recent theory of damping by radiation of in-plane phonons. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large line width at the largest drives. Our results contribute toward a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.

Ultrasonic subwavelength focusing above periodic membrane arrays in immersion

Subwavelength focusing and imaging has been a long sought after goal and one that metamaterials can possibly achieve. In 2011, Lemoult et al. used time reversal techniques to focus sound to as small as λ/25 in air by using the evanescent wave field above a gird of soda cans acting as Helmholtz resonators [Lemoult et al. Phys. Rev. Lett. 107, 064301, (2011)]. This paper will demonstrate subwavelength focusing in immersion in the 11–0 MHz frequency range with capacitive micromachined ultrasonic transducer (CMUT) arrays. CMUTs are microscale (10–100 μm wide) membrane arrays, which support evanescent surface waves that derive their dispersive properties not only from the periodic structure of the array, but also from the membrane resonance. Furthermore, CMUTs have embedded electrodes for electrostatic excitation and detection of acoustic waves which allow implementation of time reversal techniques to focus the dispersive evanescent surface waves using only the CMUTs on the same substrate as sources and receivers. Using a finite boundary element method simulation, we demonstrate subwavelength focusing at points in the near-field above a 2D CMUT array in immersion.

Invited Presentation: Graphene Nanoelectromechanical Systems As Stochastic-Frequency Oscillators

We measure the quality factor Q of electrically-driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ~ 1/T , where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators, yielding good quantitative agreement to experiment. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. Additionally, at larger drives the resonator linewidth is enhanced by nonlinear damping, in qualitative agreement with a recent theory of damping by radiation of in-plane phonons[1]. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large linewidth at the largest drives. Our results contribute towards a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.1. Croy, A.; Midtvedt, D.; Isacsson, A.; Kinaret, J. M. Phys. Rev. B 2012, 86, 235435.

Viscoelastic effects on frequency tuning of a dielectric elastomer membrane resonator

As a recent application of dielectric elastomers (DEs), DE resonators have become an alternative to conventional silicon-based resonators used in MEMS and have attracted much interest from the research community. However, most existing modeling works for the DE resonators ignore the intrinsic viscoelastic effect of the material that may strongly influence their dynamic performance. Based on the finite-deformation viscoelasticity theory for dielectrics, this paper theoretically examines the in-plane oscillation of a DE membrane resonator to demonstrate how the material viscoelasticity affects the actuation and frequency tuning processes of the resonator. From the simulation results, it is concluded that not only the applied voltage can change the natural frequency of the resonator, but also the inelastic deformation contributes to frequency tuning. Due to the viscoelasticity of the material, the electrical loading rate influences the actuation process of the DE resonator, while it has little effect on the final steady frequency tuned by the prescribed voltage within the safety range. With the consideration of the typical failure modes of the resonator and the evolution process of the material, the tunable frequency range and the safe range of the applied voltage of the DE membrane resonator with different dimension parameters are determined in this work, which are found to be dependent on the electrical loading rate. This work is expected to provide a better understanding on the frequency tuning of viscoelastic DE membrane resonators and a guideline for the design of DE devices.

Dissipation in ultrahigh quality factor SiN membrane resonators.

We study the mechanical properties of stoichiometric SiN resonators through a combination of spectroscopic and interferometric imaging techniques. At room temperature, we demonstrate ultrahigh quality factors of 5×107 and a f×Q product of 1×1014 Hz. To our knowledge, these correspond to the largest values yet reported for mesoscopic flexural resonators. Through a comprehensive study of the limiting dissipation mechanisms as a function of resonator and substrate geometry, we identify radiation loss through the supporting substrate as the dominant loss process. In addition to pointing the way towards higher quality factors through optimized substrate designs, our work realizes an enabling platform for the observation and control of quantum behavior in a macroscopic mechanical system.

Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics

Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane's silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane's frame so that it assumes the form of a cm-sized bridge featuring a 1-dimensional periodic pattern, whose phononic density of states is tailored to exhibit one, or several, full band gaps around the membrane's high-Q modes in the MHz-range. We quantify the effectiveness of this phononic bandgap shield by optical interferometry measuring both the suppressed transmission of vibrations, as well as the influence of frame clamping conditions on the membrane modes. We find suppressions up to 40 dB and, for three different realized phononic structures, consistently observe significant suppression of the dependence of the membrane's modes on sample clamping-if the mode's frequency lies in the bandgap. As a result, we achieve membrane mode quality factors of 5 × 10(6) with samples that are tightly bolted to the 8 K-cold finger of a cryostat. Q × f -products of 6 × 10(12) Hz at 300 K and 14 × 10(12) Hz at 8 K are observed, satisfying one of the main requirements for optical cooling of mechanical vibrations to their quantum ground-state.

Capacitive micromachined ultrasonic transducer arrays as tunable acoustic metamaterials.

Capacitive Micromachined Ultrasonic Transducers (CMUTs) operating in immersion support dispersive evanescent waves due to the subwavelength periodic structure of electrostatically actuated membranes in the array. Evanescent wave characteristics also depend on the membrane resonance which is modified by the externally applied bias voltage, offering a mechanism to tune the CMUT array as an acoustic metamaterial. The dispersion and tunability characteristics are examined using a computationally efficient, mutual radiation impedance based approach to model a finite-size array and realistic parameters of variation. The simulations are verified, and tunability is demonstrated by experiments on a linear CMUT array operating in 2-12 MHz range.

Resonance properties of GABAergic interneurons in immature GAD67-GFP mouse neocortex

Subthreshold resonance is a characteristic membrane property of different neuronal classes, is critically involved in the generation of network oscillations, and tunes the integration of synaptic inputs to particular frequency ranges. In order to investigate whether neocortical GABAergic interneurons show resonant behavior already during early postnatal development, we performed whole-cell patch-clamp recordings from visually identified interneurons in supragranular layers of parietal regions in coronal neocortical slices from postnatal day (P) P6–P13 GAD67-GFP knock-in mice. Subthreshold resonance was analyzed by injection of sinusoidal current with varying frequency. About 50% of the investigated GABAergic interneurons showed subthreshold resonance with an average frequency of 2.0±0.2Hz (n=38). Membrane hyperpolarization to –86mV attenuated the frequency and strength of subthreshold resonance. In the presence of 1mM Ni2+ subthreshold resonance was virtually abolished, suggesting that T-type Ca2+ currents are critically involved in the generation of resonance. In contrast, subthreshold resonance was not affected by ZD7288, a blocker of HCN channels. Application of TTX suppressed subthreshold resonance at depolarized, but not hyperpolarized membrane potential, suggesting that persistent Na+ current contribute to the amplification of membrane resonance. In summary, these results demonstrate that GABAergic interneurons express subthreshold resonance at low frequencies, with T-type Ca2+ and persistent Na+ currents underlying the generation of membrane resonance. The membrane resonance of immature interneurons may contribute to the generation of slow oscillatory activity pattern in the immature neocortex and enhance the temporal precision of synaptic integration in developing cortical neurons.

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents

Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g(L) - g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.