Inhomogeneous Resonators Research Articles

A Half-Analytical Method to Predict the Sound Absorption of Multiple Inhomogeneous Resonators Based on Sellers’ Method

A Half-Analytical Method to Predict the Sound Absorption of Multiple Inhomogeneous Resonators Based on Sellers’ Method

Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators

We investigate the destabilization mechanisms of dissipative solitons in inhomogeneous nonlinear resonators subjected to injection and to time-delayed feedback. We consider the paradigmatic Lugiato-Lefever model describing inhomogeneous driven nonlinear optical resonator. We analyze the pinning-depinning transition of dissipative solitons by introducing a potential induced by the inhomogeneity. Further, we identify conditions under which these structures are destabilized and describe different bifurcation scenarios. We show that the combined influence of inhomogeneities and delayed feedback induces an Andronov-Hopf-bifurcation that leads to oscillations of the dissipative soliton around the inhomogeneity. Finally, we show that for large values of the feedback strength, the dissipative solitons escapes from the potential well and starts to drift.

Experimental study on a compact lined circular duct for small-scale propeller noise reduction

In a recent work by the authors, an optimal sound absorber with a compact scale consisting of multiple inhomogeneous Helmholtz resonators with extended necks (HRENs) was designed and demonstrated for effective sound absorption in a prescribed frequency range. The development of HREN-based absorber provides a promising potential for sound absorption in a compact dimension. The present study aims to line the compact optimal absorber in a circular duct for noise attenuation. A rigid duct with the same configuration is fabricated for comparison. The acoustic performances of the lined duct and the rigid duct are experimentally evaluated by using two linear microphone arrays in an anechoic chamber. Two types of noise sources are considered: a point sound source and a rotating propeller. The experimental results reveal that a significant noise reduction is achieved by the lined duct for both the point source and the propeller noise source in the target frequency range when comparing to the rigid duct.

Wideband low-frequency sound absorption by inhomogeneous multi-layer resonators with extended necks

This study develops a structure with thin thickness targeting for wideband low-frequency sound absorption, which consists of multi-layer Helmholtz resonators with extended necks (HRENs). An analytical prediction model is established based on the classic transfer matrix method to study the acoustic characteristics of the multi-layer HREN absorber. Results show that the added layer shifts the first absorption peak of the original single-layer HREN absorber to a lower frequency and induces additional absorption peak. Then, a particle swarm optimization (PSO) algorithm is coupled with the prediction model to design optimal sound absorbing structure for effective sound absorption in a prescribed wideband frequency range. For illustration, a single-layer, a double-layer and a triple-layer optimal structures composed of 9 inhomogeneous units at each layer are designed and they yield about 90% absorption in the frequency ranges of [550,700] Hz, [400,650] Hz and [300,550] Hz. The mechanism of the continuous absorption band is due to the overlapping of the absorption peaks induced by different units. The proposed structure offers an effective acoustic absorption in the target wideband frequency range while its size is in a compact scale, and thus holds great potential for noise attenuation in various realistic applications.

An ultrathin acoustic carpet cloak based on resonators with extended necks

By employing a set of resonators with extended necks, an ultrathin acoustic carpet cloak with a thickness of about 1/30th of the operation wavelength is proposed to achieve effective cloaking around a bump at 1000 Hz. The cloak is composed of a periodic array of supercells. The supercell is constructed by a solid unit and seven inhomogeneous resonators with different extended necks. The elements in the supercell are capable of achieving distinct phase shifts ranging from 0 to 2π in a phase increment of π/4. To demonstrate the effectiveness of the cloak, both normal incidence and oblique incidence (incident angle equals to 30°) plane waves impinging on a cloaked triangular bump are investigated numerically and validated experimentally. The results show that it is possible to conceal the bump by wrapping over the surface of the bump through using the proposed ultrathin carpet cloak. As a resonant-element based acoustic device, the cloak exhibits invisibility in the frequency range from 980 to 1070 Hz. The proposed acoustic metasurface offers a simple and compact solution for acoustic cloaking and may hold promise in realistic applications.

Quantitative Modeling of Superconducting Planar Resonators for Electron Spin Resonance

We present three designs for planar superconducting microwave resonators for electron spin resonance (ESR) experiments. We implement finite element simulations to calculate the resonance frequency and quality factors as well as the three-dimensional microwave magnetic field distribution of the resonators. One particular resonator design offers an increased homogeneity of the microwave magnetic field while the other two show a better confinement of the mode volume. We extend our model simulations to calculate the collective coupling rate between a spin ensemble and a microwave resonator in the presence of an inhomogeneous magnetic resonator field. Continuous-wave ESR experiments of phosphorus donors in $^\mathrm{nat}$Si demonstrate the feasibility of our resonators for magnetic resonance experiments. We extract the collective coupling rate and find a good agreement with our simulation results, corroborating our model approach. Finally, we discuss specific application cases for the different resonator designs.

A HIGH SENSITIVE MICROWAVE MEASURING DEVICE OF THE MOISTURE CONTENT IN THE NON-POLAR DIELECTRIC LIQUIDS BASED ON AN INHOMOGENEOUS STEP COAXIAL RESONATOR

Purpose. Objective is to create a moisture meter for non-polar liquid dielectrics with low volumetric moisture content of more than 10‑3 %. Methodology. Moisture measuring is based on dielcometric method. It is implemented as a resonant method of determining a capacitance measuring transducer. Measuring transducer capacitive type has a working and parasitic capacitance. It was suggested the definition of moisture on four of resonance frequencies: when the measuring transducer is turned off, one by one filled with air, «dry» and investigated liquid, to determine the parasitic capacitance of the measuring generator, and the parasitic capacitance of the measuring transducer and humidity. Measurement frequency was increased up to microwave range to increase the sensitivity. Measuring transducer with distributed parameters representing a step heterogeneous coaxial resonator is used by. This measuring transducer has a zero stray capacitance, because the potential electrode has a galvanic connection with an external coaxial electrode. Inductive ties loop is used to neglect parasitic capacitance of the measuring generator, and to increase the quality factor of the system. Measuring moisture is reduced to measuring the two frequencies of resonance frequency and «dry» and investigated liquid. Resonant characteristics transducer in a step inhomogeneous coaxial resonator have been investigated to determine the quality factor of filled with air and transformer oil, and experiments to measure the moisture content in transformer oil have been conducted. Results. Measuring transducer of distributed type is developed and researched – it is step inhomogeneous coaxial resonator. It has a smaller geometric length and larger scatter of the first and second resonant frequencies. Expression is obtained for determination of moisture on the basis of two resonant frequencies. The formula of the two frequencies to determine the moisture is correct. Resonant characteristics are obtained for measuring transducer. Its quality factor has been determined – it does not depend on what it is filled with air or oil. The moisture content in transformer oil for the amount of water to 10-3 % with an error of no more than 6.7 % has been determined. Originality. It has been proposed to use of an inhomogeneous step coaxial resonator as a measuring transducer. Original high sensitive moisture meter for the fluid at rest and flowing fluid with low values of parasitic capacitances has been developed and researched. An original method of determining the moisture by measuring the two frequencies of resonance has been proposed and implemented. Practical value. This meter may be used to determine moisture in any of the non-polar liquid with high speed and accuracy. Moisture meter can be used in electrical engineering, aeronautical engineering, in the chemical and food industries.

Measuring of the microwave materials parameters on the base of the inhomogeneous microstrip resonator method

In this paper the method for measuring the dielectric constant and dielectric loss tangent of the dielec-tric material in the microwave range of wavelengths using the inhomogeneous microstrip resonator is pre-sented. The measurement technique and the design of the measuring cell are described, the theoretical basis of the method and results of experimental studies are given. Reference 9, figures 2, tables 1.

ANALYSIS AND CALCULATION OF A HIGH-FREQUENCY FIELD DISTRIBUTION IN AN INHOMOGENEOUS RESONATOR SYSTEM OF A MAGNETRON

The experience of developing magnetrons intended for the short-wave part of millimeter (mm) wave band proves that the most advantageous characteristics are achieved by interaction between an electron beam and a lower spatial harmonic of a degenerate oscillation mode. In commercial production, some drawbacks of this mode are eliminated by including driving inhomogeneities into magnetron's resonator system. These inhomogeneities eliminate the intradoublet competition at the operating oscillation mode as well as the competition with the doublet components of the high-voltage mode, i.e. the competitor. The calculation procedures reported in the papers related to inhomogeneous resonator systems have certain restrictions, which make them inapplicable at such a decisive development stage as an analysis of the effects exerted by driving inhomogeneities on the structure of a high-frequency (HF) field of the slowing system. In this paper a new calculation method is suggested, which utilizes the field theory and allows to detect all eigen frequencies and the corresponding HF-field distributions in a slowing system of a magnetron with driving inhomogeneities. The considerations are illustrated by an example calculation of a HF-field distribution and a spatial harmonics spectrum of the slowing system of the 2-mm magnetron with the driving inhomogeneities. The allocations of the driving inhomogeneities are compared in various combinations. A novel method was developed enabling calculation of inhomogeneous resonator systems for magnetrons operating in the short-wave part of millimeter wave band.

Analytic description of cylindrical electromagnetic wave propagation in an inhomogeneous nonlinear and nondispersive medium

In a recent publication [E. Y. Petrov and A. V. Kudrin, Phys. Rev. Lett. 104, 190404 (2010)], a method for constructing exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium has been put forward. In this Brief Report, we will use the proposed method to deal with problems of wave propagation in an inhomogeneous nonlinear and nondispersive medium. The inhomogeneous factor is chosen in the form as r(β), where β is a certain constant. By solving the Maxwell equations an exact axisymmetric solution is obtained, starting from the corresponding solution of linear field equations, to describe the propagation of cylindrical electromagnetic waves in the medium. In the limit β→0, our solutions go into a nonlinear but homogeneous case, which is the same as prevenient results. We analyze the initial value problem and boundary value problem, to compare the differences between homogeneous and inhomogeneous conditions. It is found that the amplitude and frequency of the electromagnetic wave can be controlled with different β. Our results can be used for analysis of inhomogeneous ferroelectric resonators.

Spectral properties of a ring optical resonator with an arbitrary longitudinal inhomogeneity

A ring optical resonator with an arbitrary but continuous change in the permittivity of the filling medium along the resonator axis is considered. It is shown that in the case of a small deviation of the permittivity from its average value, the double degeneracy of eigenfrequencies inherent in a homogeneous resonator is removed and the corresponding modes acquire the properties of standing waves. Simple universal expressions are derived to calculate eigenfrequencies and distribution coefficients in modes. Conditions are found under which splitting in the frequency spectrum of an inhomogeneous resonator is absent. The general results obtained in the paper can be used in numerical experiments.

Design of resonators using materials with negative refractive index

By optimizing the design we show that inhomogeneous electromagnetic resonators with almost uniform field intensity and up to twice the energy density of conventional structures are possible by exploiting the properties of negative refractive index materials. We demonstrate that using negative refractive index materials it is possible to make FWHM of the transmission coefficient independent of cavity length L.

Influence of random bulk inhomogeneities on quasioptical cavity resonator spectrum

The statistical spectral theory of oscillations in a quasioptical cavity resonator filled with random inhomogeneities is suggested. It is shown that inhomogeneities in the resonator lead to intermode scattering which results in the shift and broadening of spectral lines. The shift and the broadening of each spectral line is strongly depended upon the frequency distance between the nearest-neighbor spectral lines. As this distance increases, the influence of inhomogeneities is sharply reduced. Solitary spectral lines that have quite a large distance to the nearest neighbors are slightly changed due to small inhomogeneities. Owing to such a selective influence of inhomogeneities on spectral lines the effective spectrum rarefaction arises. Both the shift and the broadening of spectral lines as well as spectrum rarefaction in the quasioptical cavity millimeter wave resonator were detected experimentally. We have found out that inhomogeneities result in the resonator spectrum stochastization. As a result, the spectrum becomes composite, i.e., it consists of both regular and random parts. The active self-excited system based on the inhomogeneous quasioptical cavity millimeter wave resonator with a Gunn diode was examined as well. The inhomogeneous quasioptical cavity millimeter wave resonator (passive and active) can serve as a model of a semiconductor quantum billiard. Based on our results we propose that such a billiard with the spectrum rarefied by random inhomogeneities be used as an active semiconductor laser system.

Field quantization for open optical cavities

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\epsilon({\bf r})$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system--and--bath Hamiltonian of quantum optics. The field dynamics is investigated using the input--output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

Multisection frequency filter consisting of a series of cylindrical resonators loaded with ring gratings

AbstractThe problem of diffraction of cylindrical TEon‐wave on an axial‐symmetric series of N identical inhomogeneous resonators and sections of uniform waveguide is solved by the methods of theory of circuits and matrix functions. The resonator's internal region contains three magnetodielectric layers and a dense grating of conducting rings. The frequency and interference dependencies of the scattered field amplitudes and their dynamics are determined in the cases of strong and weak coupling between the resonators, single‐mode and multi‐mode bands, and high power density at the peripheric region. A correlation between the frequency dependence of the investigated filter and the pass bands of its infinite analogue's eigenwaves are established. The mechanism of exciting super‐high‐Q resonance oscillations absolutely transparent with loss‐free systems is analyzed. A model of the frequency filter with non‐mechanical control is proposed. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 87–90, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10524

Resonant frequency calculation for inhomogeneous dielectric resonators using volume integral equations and face‐centered node points

AbstractThe face‐centered node‐point technique, developed earlier for scattering applications, is applied to the calculation of resonance frequencies of inhomogeneous dielectric resonators. The described method leads to a well‐conditioned matrix system suitable for numerical solution, which is not the case when the permittivity is high and conventional solution techniques (e.g., pulse functions with cell‐centered point matching) are employed. In this work, we concentrate on resonators having the shape of a parallelepiped, for which there are relatively few computational results in the literature, although the method can accommodate arbitrarily shaped structures. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 356–359, 2002.

A combined efficient approach for analysis of nonradiative dielectric (NRD) waveguide components

An efficient approach is introduced for the analysis of three-dimensional nonradiative dielectric (NRD) waveguide components including inhomogeneous dielectric and housing grooves. This technique combines effectively the method of lines with the mode-matching method based on the theoretical principle similar to that of the space-spectral domain approach (SSDA). It can be applied to determine characteristics of various waveguide components and microwave integrated circuits such as resonant frequencies and scattering parameters. The framework of this technique is demonstrated in this paper through its applications to resonator problems. Absorbing boundary conditions (ABC) with two types of difference schemes were used to simulate unbounded space. It is found that numerical results of resonant frequency for the first two fundamental modes (quasi-LSM and quasi-LSE) are in good agreement with our experiments. Numerical results are presented for both homogeneous and inhomogeneous dielectric resonators as functions of different geometric parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption

A method is presented for calculating the quality factors (Q's) and the effective-average gain and loss coefficients for the modes of a dielectric sphere which has a spatial perturbation of the imaginary part of the refractive index. The method is applicable to gain calculations in spherical lasers, to spatial hole burning and to stimulated Raman scattering in spheres. A time-independent perturbation method is also used to compute the Q's of the resonances. Results computed using both methods are compared with analytical results for layered spheres. The methods are used to compute the near-resonance backscattering by a sphere having an intensity-dependent (two-photon absorption) loss.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Field rate equation and linewidth of semiconductor laser with inhomogeneous resonator medium

The spontaneous emission noise of an axially inhomogeneous laser structure is evaluated by Green functions. Explicit analytical expressions are given for the field rate equation and linewidth in the case of soft variations of the complex effective index of refraction and are applied to a gain-lever laser.

Modal analysis of inhomogeneous optical resonators

In this paper, we present a calculation which demonstrates that the lower-order modes of an optical resonator with an inhomogeneous gain distribution can potentially be obtained by employing the Fox-Li or beam propagation methods. While our calculation is performed on a highly simplified model of a typical laser’s refractive-index distribution, our results could eventually be incorporated into existing self-consistent laser models based on the beam propagation method to yield a complete picture of a laser mode structure.