The Geometry of Resonances

Disorder in a periodic Helmholtz resonators array

Effects of resonator geometry and substrate stiffness on the tunability of a deformable microwave metasurface

Finite element computation of piezoelectric transducers requires the knowledge of elastic, piezoelectric, and dielectric coefficients of ceramics. These constants are generally not available from the manufacturer, and even, variations up to 20% can be expected in the worse cases. The classical experimental method, proposed by Mason, is based on admittance measurements and a complete determination of all the materials properties requires five resonator geometries. An interesting method, based on an adjustment of first modes of ceramic rings with a finite element code, is described. It has three advantages over the Mason method. First, it does not require particular resonator geometries; second, the experimental method is summed up on a simple impedance measurement of the whole ceramics; and third, the adjustment is unaffected by local nonhomogeneity of materials. In this paper, the whole method is developed. Then experimental and numerical results are compared for several ceramics.

We have fabricated and characterized tapered unstable resonator lasers with two slightly different resonator geometries, one with a linear taper and one with a nonlinear taper, to investigate the effect of resonator geometry on the performance characteristics. Special attention has been paid to the modal behavior and its dependence on drive current. We investigate the modal behavior by monitoring the focused spot produced by an integrated focusing grating coupler. To aid in the design of the lasers and the analysis of the measurement results, we implemented numerical simulations based on the beam-propagation method and obtained good agreement between measurements and simulations. We find that the threshold current, the efficiency and the optical field stability, including filamentation threshold, are significantly improved by adjusting the shape of the current injection region to the diverging field profile in the tapered section. Improvements in threshold current and efficiency are attributed to a more efficient use of the injected carriers, while improvement in optical field stability is attributed to reduced carrier induced phase front distortion. We conclude that a relatively small modification of the resonator geometry can lead to large improvements in laser performance.

Experimental investigation was made of the kinetics of the stimulated emission of a CaF2:Dy2+ laser with a resonator formed by a plane mirror evaporated directly on the end of the fluoride crystal and an external spherical mirror. When the resonator geometry was sufficiently far from the stability limit, the pulsed emission of the laser was in the form of a transient spiking, decaying to a quasisteady-state level. The rate of decay depended strongly only on the aperture parameter of the resonator, which governed the number of the transverse modes which were excited, but was independent of the ratio of the resonator length to the radius of curvature of the spherical mirror in a fairly wide range of both these parameters. When the resonator geometry was close to the stability limit, the laser emitted random spikes. A large number of transverse modes were emitted in the continuous regime, which was characterized by a constant emission level with a slight spiking. A strong selection of the transverse modes under continuous pumping conditions resulted in the generation of regular undamped spikes.

In this work, split ring resonators based metamaterials are studied for microwave, terahertz and infrared frequency regimes. Two different geometries, circular and rectangular split ring resonators based metamaterials are investigated numerically for different frequency regimes. Our study indicates that the effect of metal conductivity and resonator geometry shows very little impact on the fundamental resonance mode. However the higher order modes go through significant frequency tuning because of the change in resonator geometry. We have further shown that the metal conductivity is an important parameter for the metamaterials employed in infrared domains.

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In this study, several performance analyses are conducted on all-dielectric absorbers composed of cylindrical-, elliptical-, square-, rectangular-, hexagonal-, and octagonal-shaped dielectric resonators. These performance analyses include the numerical investigation of the change in the resonance frequency and the absorption peak level with respect to the changes in dielectric constant and loss tangent, respectively, in the WR-284 rectangular waveguide setup. In addition, the designed structures are also analyzed in a free-space simulation setup to present the differences that come from using different boundary conditions and excitations. The analyses reveal that the absorption spectra behaviors are similar in response to changes in dielectric constants and loss tangents among the studied geometries. Absorption peak levels of the observed higher-order resonance modes are highly dependent on the resonator geometry. On the other hand, the free-space simulation results reveal that the designed structures have negligible cross-polarization components, hence they do not practically contribute to the absorption spectra. Moreover, absorption, reflection, and transmission spectra are highly affected by differences in the simulation setup and accordingly by the excitation signal for all resonator geometries. In addition, the behavior of the absorption spectra for all the dielectric resonator geometries is investigated under the oblique incident wave for TE and TM modes. It has been noticed that the absorption spectra are nearly independent of the angle at lower incident angle values. It is believed that these analyses will contribute to the sensor studies based on all-dielectric absorber designs. Cite this article as: N. Karacan, G. Turhan-Sayan and E. Ekmekçi, "Sensitivity analyses for all-dielectric absorber structures having different dielectric resonator geometries and investigation of the effect of boundary conditions on the absorption spectra," Electrica, 24(1), 163-174, 2024.

Motivated by previous work on high-energy quantum mechanics, a simple model is devised to study the internal geometry of hadron resonances. In this model we assume new basic canonical commutation relations between the (internal) coordinate and momentum operators of the hadronic quantum system. By systematically imposing Lie algebra commutation relations between these and other observables, we discuss the free and bound particle problems, identifying in each case the corresponding internal symmetries. For the bound particle problem, which models quark confinement, this symmetry turns out to be characterized by Dirac's two-oscillator representation of theO(3, 2) de Sitter group.

The objective of this work is the design and the application of various adaptive control concepts to manipulate shear-flows under varying flow conditions, i.e. Reynolds-numbers. A combination of a self-tuning PI-controller, based on an online-estimation of the plant dynamics, and the extremumseeking controller is introduced as an effective control strategy to reduce and/or to increase the reattachment length of a backward-facing step flow. Four loudspeakers are used as actuators driven by a zero-phase sinusoidal voltage signal. The amplitude of the loudspeaker input is calculated by the PI-controller achieving that the measured reattachment length permanently follows its set point. The optimal forcing frequency essentially depending on the Reynolds-number is determined by the extremum-seeking controller. In this work a new adaptive I-controller is introduced as an appropriate approach to control plants, which are characterised by an output saturation. An offline-identification confirms that this flow possesses such a non-linear behaviour. The adaptation law exploits this behaviour guaranteeing a desired tracking dynamics of the closed-loop over a wide range of operating points. A wind tunnel experiment exemplarily demonstrates the use of this controller under moderate variations of the Reynolds-number. For a second flow configuration, the flow within a diffusor, the extremum-seeking controller is employed to adjust the geometry of an acoustic resonator located upstream of the diffusor. The slot width of the resonator and the height of the resonator volume are tuned by the controller. It is shown by experiments that the controller find the optimal geometry of the resonator for several initial values of the sloth width and height. Consequently, the pressure recovery is maximised by the use of the controller. To improve the performance of the closed-loop dynamics an adaptation of the seeking radius and, for fast changes of the Reynolds-number, an adaptation of the controller gain k is necessary. The extremum-seeking controller can also be used to reduce the radiated sound of a turbomachinery. Air injection by valves generates a destructive secondary sound field which is out of phase with the primary sound field caused by a rotor-stator-interaction. The injected air mass is determined by the controller to minimise the overall sound-pressure-level measured downstream of the stator. This work exemplarily shows that the employed adaptive controller and especially the extremumseeking controller are suitable approaches for flow control. Furthermore it is shown that the extremum-seeking controller can be successfully transferred to other flow configurations.

A novel electrically small composite right/left-handed transmission line (CRLH TL) cell based on the Minkowski-shaped geometry of a complementary single split ring resonator is proposed and analysed by the S parameters extraction method. EM simulation results have confirmed the roughly tri-band response of the proposed CRLH TL cell attributed to the fractal multiband nature. A tri-band bandpass filter (BPF) centred at 1.1, 2 and 2.74 GHz with minimum insertion loss 0.4, 1.1 and 1.45 dB was synthesised and fabricated by employing an additional two Hilbert-shaped quarter-wave open-circuit stubs which provided transmission zeros located between passbands to obtain high selectivity. This simple design concept was verified by measurement as well as simulation results.

This paper investigates the resonant modes of Fabry-Perot interferometers with end reflectors embedded in linear, homogeneous, uniaxially anisotropic media. It is shown that for almost all practical cases the resonant modes consist of transverse electric (TE) modes and transverse magnetic (TM) modes relative to the direction of the optic axis in the medium. Two distinct integral equations are derived which together with Maxwell's equations are sufficient to perform a detailed analysis of these modes. However, since the results of the analysis of Fabry-Perot resonators in isotropic regions are available and well understood, the approach of the paper is to reduce a given "anisotropic resonator" to two corresponding equivalent "isotropic resonators": one for determining the TE modes and the other for determining the TM modes. The equivalent isotropic resonator for the TE modes has the same geometry as the actual resonator in the anisotropic medium. The geometry of the equivalent isotropic resonator for the TM modes is derivable in a very simple manner from the geometry of the actual resonator in the anisotropic medium and from the specified orientation of the direction of the optic axis in the medium. The well-known results for resonators embedded in isotropic media may henceforth be applied to determine the resonant modes of the anisotropic resonator.

This paper describes the use of microfluidic microwave sensors for measuring the length, volume, speed and dielectric properties of different liquids in a segmented flow. The sensor is a variant of the split ring resonator, operating around 4 GHz, realized in a microstrip implementation. Changes of the resonant frequency and quality factor are performed when a segment enters the sensing region, in this case the gap regions. Two different geometries of resonators were used for the sensors, each with two gaps to accommodate a planar microfluidic channel. The segments consisted of mineral oil and water. Sensor simulations were performed using COMSOL Software, which compare favorably with the experimental measurements.

In recent years study acoustic metamaterials have found great attention due to its enormous ability to guide and manipulate elastic wave in a medium. Frequency bandgap is a great feature that can be achieved by acoustic metamaterials. The bandgap is the frequency range at which the elastic wave doesn't propagate through the medium. In another word, the frequency band gap offers wave isolation ability for a structure. An acoustic metamaterial usually consists of resonators and a host media. The frequency bandgap is mainly the result of brag scattering in the structure. The orientation and geometry of resonators in a unit cell possess a great influence on brag scattering. This study is dedicated to understanding the influence of resonators volume percentage in the frequency bandgap. Several resonator geometries of two different combinations are studied. Finally, comparing the outcome from both the combinations, a claim is made regarding the effect of volume fraction on frequency band gaps.

Acoustic resonators based on antiferromagnetic crystals of "easy plane" type, like α -Fe2O3 or FeBO3, are of interest for applications in magnetoacoustic sensors of electrical and mechanical values because of high sensitivity of their resonance frequency to variations of external magnetic field or mechanical stress. One of the requirements for magnetic control of resonators is a single-value dependence of resonance frequency on magnetic field strength. This requirement is violated when the geometry of resonator allows for crossover of acoustic modes in the range of magnetic field variation. Designing of resonators with frequency control in a wide range requires knowledge of field-dependent acoustic parameters of the crystals and appropriate method for calculation of the resonator eigenfrequencies. In this letter, we present the complete set of acoustic parameters deduced for α -Fe2O3 single crystal that are used for simulation of acoustic mode structures and spectra of vibrations in disk resonator. The results of simulation using COMSOL Multiphysics software are compared with experimental measurements carried out on two resonators of different ratios of sizes that illustrating continuous and discontinuous dependence of the resonance frequency on the magnetic field. Prevention of discontinuity by correction of the resonator geometry is demonstrated.