Eigenmodes Of Resonator Research Articles

Diagnosis of Metal Plates with Defects Using Laser Vibrometer

The method of nonlinear laser scanning vibrometry is used for diagnostics of thin cylindrical resonators of polycrystalline aluminum alloy D16 with latent defects and residual stresses. Flexural Lamb waves are used for diagnosis. The dependence of the frequency of the resonator eigenmode on the amplitude of the flexural Lamb waves in it is detected (the effect of the fast dynamics); it indicates the presence of defects in the material of the resonator. Coordinates of defects were identified by vibromodulation technique in the resonator.

Laser resonator modeling by field tracing: a flexible approach for fully vectorial transversal eigenmode calculation

In this work we generalize the scalar Fox and Li algorithm for the dominant transversal resonator eigenmode calculation to a fully vectorial field tracing concept. Therefore we reformulate Fox and Li’s scalar integral equation to a set of coupled operator equations. The introduction of a field tracing round trip operator concept shows that, in principle, any modeling technique which can be formulated to operate for electromagnetic fields can be used to simulate light propagation through the different subdomains of the resonator. This allows a flexible, fast, and accurate simulation of the fully vectorial dominant transversal resonator eigenmode. An example is presented to demonstrate the flexibility and accuracy of the field tracing approach.

Thermoacoustic instability – a dynamical system and time domain analysis

AbstractThis study focuses on the Rijke tube problem, which includes features relevant to the modelling of thermoacoustic coupling in reactive flows: a compact acoustic source, an empirical model for the heat source and nonlinearities. This thermoacoustic system features both linear and nonlinear flow regimes with complex dynamical behaviour. In order to synthesize accurate time series, we tackle this problem from a numerical point of view, and start by proposing a dedicated solver designed for dealing with the underlying stiffness – in particular, the retarded time and the discontinuity at the location of the heat source. Stability analysis is performed on the limit of low-amplitude disturbances by using the projection method proposed by Jarlebring (PhD thesis, Technische Universität Braunschweig, 2008), which alleviates the problems arising from linearization with respect to the retarded time. The results are then compared with the analytical solution of the undamped system and with the results obtained from Galerkin projection methods commonly used in this setting. This analysis provides insight into the consequences of the various assumptions and simplifications that justify the use of Galerkin expansions based on the eigenmodes of the unheated resonator. We demonstrate that due to the presence of a discontinuity in the spatial domain, the eigenmodes in the heated case predicted by using Galerkin expansion show spurious oscillations resulting from the Gibbs phenomenon. Finally, time series in the fully nonlinear regime, where a limit cycle is established, are analysed and dominant modes are extracted. By comparing the modes of the linear regime to those of the nonlinear regime, we are able to illustrate the mean-flow modulation and frequency switching, which appear as the nonlinearities become significant and ultimately affect the form of the limit cycle. Analysis of the saturated limit cycles shows the presence of higher-frequency modes, which are linearly stable but become significant through nonlinear growth of the signal. This bimodal effect is not exhibited when the coupling between different frequencies is not accounted for. In conclusion, a dedicated solver for capturing thermoacoustic instability is proposed and methods for analysing linear and nonlinear regions of the resulting time series are introduced.

The characteristics of a cylindrical dielectric resonator calculated by means of the method of extended boundary conditions

Equations for simulation of a cylindrical dielectric resonator are obtained by means of the method of extended boundary conditions (MEBC). The convergence and stability of the numerical algorithm based on the MEBC are considered. The properties of the whispering-gallery eigenmodes of cylindrical resonators with cross section of various shapes are studied.

Nano-diamond based spheres for radio frequency electromechanical resonators

In this work, we report on the electro-mechanical studies of high-Q spherical oscillators designed to operate in radio-frequency circuits. Resonating composite spheres, consisting of a silicon core and a thick nanodiamond shell, were studied by laser vibrometry in order to obtain mechanical quality factors and identify the resonant frequencies and eigenmodes of the system. Finite element method simulations were used to analyze and confirm the experimental data. Additionally, reflection/transmission measurements were carried out on capacitively coupled spheres in order to evaluate the electrical parameters of the system. The main aim of these investigations was to evaluate the potential of diamond-based spherical resonators to be used in modern communication devices.

Radio-Wave Oscillations of Molecular-Chain Resonators

We report a new type of nanomechanical resonator system based on one-dimensional chains of only 4 to 7 weakly coupled small molecules. Experimental characterization of the truly nanoscopic resonators is achieved by means of a novel radio-frequency scanning tunneling microscopy detection technique at cryogenic temperatures. Above 20 K we observe concerted oscillations of the individual molecules in chains, reminiscent of the first and second eigenmodes of a one-dimensional harmonic resonator. Radio-frequency scanning tunneling microscopy based frequency measurement reveals a characteristic length dependence of the oscillation frequency (between 51 and 127 MHz) in reasonable agreement with one-dimensional oscillator models. Our study demonstrates a new strategy for investigating and controlling the resonance properties of nanomechanical oscillators.

Experimental Research on an Active Sting Damper in a Low Speed Acoustic Wind Tunnel

Wind tunnels usually use long cantilever stings to support aerodynamic models in order to reduce support system flow interference on experimental data. However, such support systems are a potential source of vibration problems which limit the test envelope and affect data quality due to the inherently low structural damping of the systems. When exposed to tunnel flow, turbulence and model flow separation excite resonant Eigenmodes of a sting structure causing large vibrations due to low damping. This paper details the development and experimental evaluation of an active damping system using piezoelectric devices with balance signal feedback both in a lab and a low speed acoustic wind tunnel and presents the control algorithm verification tests with a simple cantilever beam. It is shown that the active damper, controlled separately by both PID and BP neural network, has effectively attenuated the vibration. For sting mode only, 95% reduction of displacement response under exciter stimulation and 98% energy elimination of sting mode frequency have been achieved.

Authors' reply

This is a reply to comments from Hu etal. regarding, of which there are three concerns. The first concern in the comments is a one-to-one mapping relationship between coupling paths in a transversal array network topology and coupling elements in a physical filter structure. In conclusion, it is not necessary to determine the order of parallel paths corresponding to physical structures, as shown. This is because resonators in parallel paths of a transversal array network topology represent eigenmode resonances appearing in coupled resonators. This physical understanding has already been presented in using an example of a direct-coupled waveguide filter. The viewpoint of the order in parallel paths may come from a conventional design method of direct-coupled resonator filters, where the one-to-one mapping relationships can be easily found because the filters are composed of physically separated resonators. On the other hand, multiple resonances of a multi-mode resonator cannot be divided into physical coupling elements. In such cases, the transversal array network topology is a powerful tool for multi-mode filter designs. Therefore, three multi-mode filters have been demonstrated as examples of applications of our proposed parameter-extraction technique. The second concern in the comments of Hu et al. is the treatment of stray couplings in the transversal array coupling network. The stray couplings such as undesired cross couplings need to be evaluated in conventional filter designs based on direct-coupled resonator filter synthesis theory in order to obtain a desired frequency response. In the transversal resonator array network, as pointed out in, such stray couplings are included into parallel paths of resonators. We think that this is one of the advantages of the transversal resonator array network since coupled-resonator filters may be designed without any decomposition of main and stray couplings. In the initial design step of a filter, a well-known design approach of coupled-resonator filters is useful for intuitive designs, but stray couplings are not taken into account in this design step. In the final design step, the introduction of a transversal coupling network may help the fine adjustments of structural parameters, because all couplings are considered in terms of eigenmodes. To verify this idea, further studies will be needed. A similar design methodology has already been provided. The third concern in the comments of Hu etal. is a reference-phase equation.

2-D Simulation and Experimental Investigation of an Axial Vircator

A method for 2-D simulation of an axial vircator with a resonance cavity is described. It uses a self-consistent solution of relativistic motion equations and Maxwell equations for scalar and vector potentials in the Coulomb gauge. The vector potential is represented as a superposition of resonator eigenmodes, where each eigenmode corresponds to a damping oscillator. Damping enables considering radiative energy losses from the open end of the resonator. Compliance of the simulation results with both published experimental studies and those performed by our team is demonstrated.

Overview of physics results from the conclusive operation of the National Spherical Torus Experiment

Research on the National Spherical Torus Experiment, NSTX, targets physics understanding needed for extrapolation to a steady-state ST Fusion Nuclear Science Facility, pilot plant, or DEMO. The unique ST operational space is leveraged to test physics theories for next-step tokamak operation, including ITER. Present research also examines implications for the coming device upgrade, NSTX-U. An energy confinement time, τE, scaling unified for varied wall conditions exhibits a strong improvement of BTτE with decreased electron collisionality, accentuated by lithium (Li) wall conditioning. This result is consistent with nonlinear microtearing simulations that match the experimental electron diffusivity quantitatively and predict reduced electron heat transport at lower collisionality. Beam-emission spectroscopy measurements in the steep gradient region of the pedestal indicate the poloidal correlation length of turbulence of about ten ion gyroradii increases at higher electron density gradient and lower Ti gradient, consistent with turbulence caused by trapped electron instabilities. Density fluctuations in the pedestal top region indicate ion-scale microturbulence compatible with ion temperature gradient and/or kinetic ballooning mode instabilities. Plasma characteristics change nearly continuously with increasing Li evaporation and edge localized modes (ELMs) stabilize due to edge density gradient alteration. Global mode stability studies show stabilizing resonant kinetic effects are enhanced at lower collisionality, but in stark contrast have almost no dependence on collisionality when the plasma is off-resonance. Combined resistive wall mode radial and poloidal field sensor feedback was used to control n = 1 perturbations and improve stability. The disruption probability due to unstable resistive wall modes (RWMs) was surprisingly reduced at very high βN/li > 10 consistent with low frequency magnetohydrodynamic spectroscopy measurements of mode stability. Greater instability seen at intermediate βN is consistent with decreased kinetic RWM stabilization. A model-based RWM state-space controller produced long-pulse discharges exceeding βN = 6.4 and βN/li = 13. Precursor analysis shows 96.3% of disruptions can be predicted with 10 ms warning and a false positive rate of only 2.8%. Disruption halo currents rotate toroidally and can have significant toroidal asymmetry. Global kinks cause measured fast ion redistribution, with full-orbit calculations showing redistribution from the core outward and towards V∥/V = 1 where destabilizing compressional Alfvén eigenmode resonances are expected. Applied 3D fields altered global Alfvén eigenmode characteristics. High-harmonic fast-wave (HHFW) power couples to field lines across the entire width of the scrape-off layer, showing the importance of the inclusion of this phenomenon in designing future RF systems. The snowflake divertor configuration enhanced by radiative detachment showed large reductions in both steady-state and ELM heat fluxes (ELMing peak values down from 19 MW m−2 to less than 1.5 MW m−2). Toroidal asymmetry of heat deposition was observed during ELMs or by 3D fields. The heating power required for accessing H-mode decreased by 30% as the triangularity was decreased by moving the X-point to larger radius, consistent with calculations of the dependence of E × B shear in the edge region on ion heat flux and X-point radius. Co-axial helicity injection reduced the inductive start-up flux, with plasmas ramped to 1 MA requiring 35% less inductive flux. Non-inductive current fraction (NICF) up to 65% is reached experimentally with neutral beam injection at plasma current Ip = 0.7 MA and between 70–100% with HHFW application at Ip = 0.3 MA. NSTX-U scenario development calculations project 100% NICF for a large range of 0.6 < Ip(MA) < 1.35.

Fluorescent polymer coated capillaries as optofluidic refractometric sensors

A capillary microresonator platform for refractometric sensing is demonstrated by coating the interior of thick-walled silica capillaries with a sub-wavelength layer of high refractive index, dye-doped polymer. No intermediate processing, such as etching or tapering, of the capillary is required. Side illumination and detection of the polymer layer reveals a fluorescence spectrum that is periodically modulated by whispering gallery mode resonances within the layer. Using a Fourier technique to calculate the spectral resonance shifts, the fabricated capillary resonators exhibited refractometric sensitivities up to approximately 30 nm/RIU upon flowing aqueous glucose through them. These sensors could be readily integrated with existing biological and chemical separation platforms such as capillary electrophoresis and gas chromatography where such thick walled capillaries are routinely used with polymer coatings. A review of the modelling required to calculate whispering gallery eigenmodes of such inverted cylindrical resonators is also presented.

Acoustic double negativity with coupled-membrane metamaterial

Over the past decade, the emergence of acoustic metamaterials has considerably broadened the possibility of acoustic wave manipulations. Within this area, exotic effective constitutive parameters (mass density and bulk modulus) are a most hotly pursued topic, at the core of which is the realization of acoustic double negativity. Here, we show with experiments, simulations and homogenization that a single resonant structure can achieve acoustic double negativity. The metamaterial is comprised of two decorated elastic membranes, which are connected together by a rigid ring. Impedance measurement reveals that the system’s transport behavior is governed by the three eigenmode resonances in the sub-kHz regime, which are separately tunable via system parameters. Measured displacement profiles at the sample surfaces using laser vibrometer show that the system’s eigenmodes are, respectively, dipolar or monopolar in their nature. The simplicity of the metamaterial also enables us to retrieve its effective mass density and effective bulk modulus by performing homogenization. The results help explaining the physics behind the transport properties, and confirm that a double-negative passband is realized in a frequency range (around 500–800 Hz). Excellent agreement between experiments, simulations, and theory is achieved.

Band gaps in the low-frequency range based on the two-dimensional phononic crystal plates composed of rubber matrix with periodic steel stubs

In this paper, the numerical investigation of elastic wave propagation in two-dimensional phononic crystals composed of an array of steel stepped resonators on a thin rubber slab is presented. For the first time the rubber material is used as the matrix of the PCs. With the finite-element method, the dispersion relations of this novel PCs structure and some factors of the band structure are studied. Results show that, with the rubber material as matrix, the PC structures exhibit extremely low-frequency band gaps, in the frequency range of hundreds of Hz or even tens of Hz; the geometrical parameters and the material parameters can modulate the band gaps to different extents. Furthermore, to understand the low-frequency band gaps caused by this new structure, some resonance eigenmodes of the structure are calculated. Results show that the vibration of the unit cell of the structure can be seen as several mass–spring systems, in which the vibration of the steel stepped resonator decides the lower boundary of the first band gap and the vibration of the rubber that is not in contact with the resonator decides the upper boundary.

Resonant Modes of Single Silicon Nanocavities Excited by Electron Irradiation

High-index dielectric or semiconductor nanoparticles support strong Mie-like geometrical resonances in the visible spectral range. We use 30 keV angle-resolved cathodoluminescence imaging spectroscopy to excite and detect these resonant modes in single silicon nanocylinders with diameters ranging from 60 to 350 nm. Resonances are observed with wavelengths in the range of 400-700 nm, with quality factors in the range Q = 9-77, and show a strong red shift with increasing cylinder diameter. The photonic wave function of all modes is determined at deep-subwavelength resolution and shows good correspondence with numerical simulations. An analytical model is developed that describes the resonant Mie-like optical eigenmodes in the silicon cylinders using an effective index of a slab waveguide mode. It shows good overall agreement with the experimental results and enables qualification of all resonances with azimuthal (m = 0-4) and radial (q = 1-4) quantum numbers. The single resonant Si nanocylinders show characteristic angular radiation distributions in agreement with the modal symmetry.

Generalizing higher-order Bessel-Gauss beams: analytical description and demonstration

We report on a novel class of higher-order Bessel-Gauss beams in which the well-known Bessel-Gauss beam is the fundamental mode and the azimuthally symmetric Laguerre-Gaussian beams are special cases. We find these higher-order Bessel-Gauss beams by superimposing decentered Hermite-Gaussian beams. We show analytically and experimentally that these higher-order Bessel-Gauss beams resemble higher-order eigenmodes of optical resonators consisting of aspheric mirrors. This work is relevant for the many applications of Bessel-Gauss beams in particular the more recently proposed high-intensity Bessel-Gauss enhancement cavities for strong-field physics applications.

Parametric oscillation of a moving mirror driven by radiation pressure in a superconducting Fabry–Perot resonator system

A moving pellicle superconducting mirror, which is driven by radiation pressure on its one side and the Coulomb force on its other side, can become a parametric oscillator that can generate microwaves when placed within a high-Q superconducting Fabry–Perot resonator system. A paraxial-wave analysis shows that the fundamental resonator eigenmode needed for parametric oscillation is the TM011 mode. A double Fabry–Perot structure is introduced to resonate the pump and idler modes, but reject the parasitic anti-Stokes mode. The threshold for oscillation is estimated based on the radiation–pressure coupling of the pump to the signal and idler modes and indicates that the experiment is feasible to perform.

Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates

We report on the theoretical analysis of the enlargement of locally resonant acoustic band gap in two-dimensional sonic crystals based on a double-side stubbed plate. A significant enlargement of the relative bandwidth by a factor of 2 compared to the classical one-side stubbed plates is obtained and discussed. Based on an efficient finite element method, we show that this band gap enlargement is due to the coupling between the same nature of the resonant eigenmodes (in-plane or out-of-plane) of the stubs located in each plate side, producing a strong interaction with the plate’s Lamb modes. Acoustic displacement fields are computed to illustrate such mechanism and to discuss the physics behind it.

Optical switching of terahertz radiation from meta-atom-loaded photoconductive antennas

Optical switching of the spectrum and polarization of terahertz radiation from split-ring resonator-loaded photoconductive antennas has been demonstrated. The switching is based on the sensitivity of the resonance of a split-ring resonator on a photoconductive substrate to a change in the capacitance induced by optical pulse irradiation. The spectral and polarization characteristics of the split-ring resonator-loaded photoconductive antennas are discussed in terms of the coupling between the electric dipole induced by the pump laser and the eigenmodes of the split-ring resonators.

Calculation of open resonators with the help of a modified method of extended boundary conditions

The problem on the eigenmodes of a 2D open resonator is solved with the help of the method of extended boundary conditions. A modification of this method that makes it possible to substantially enhance the accuracy of computation is proposed. The results obtained by means of approximate techniques are compared to the solution obtained with the use of the singular integral equation method.

Application of asymptotic methods in the theory of open resonators

The problem of the eigenmodes of a 2D open resonator is solved. Two polarizations are considered. Eigenmodes in resonators with various mirror shapes are investigated. The results of a rigorous approach are compared to the results obtained with the help of various approximate asymptotic techniques.