Circular Cylindrical Resonator Research Articles

Design of resonator cavity for liquid material characterization

Dielectric characterization is very essential before the material can be utilized in designing microwave networks. Circular cylindrical resonators have been widely used for material characterization, but it is not a preferable design during the measurement of liquid samples as the sample placement requires repetitive process of opening and closing the lid of the cavity. This repetition procedure easily affects the accuracy of measurement and may lead to a measurement error. In this study, a rapid and less measurement procedure of liquid material characterization is proposed. The proposed rectangular resonator design is far more convenient and easier to handle as it does not require complex sample preparation. Considering electric field leakage, a hole is designed at the top of the cavity to ease the inserting process of sample. A 5-GHz prototype of a rectangular resonator is designed and fabricated to measure a liquid sample. Complex scattering parameters are measured using a vector network analyzer before the dielectric properties are estimated using an inverse technique. The dielectric properties of distilled water are measured to demonstrate the practicality of the proposed measurement technique. As a result, the measured dielectric properties of distilled water show a reasonable agreement with the values from other literature

Complex WGM frequencies of gyroelectric cylindrical resonators

Asymptotic closed-form expressions for calculating complex transverse electric (TE)/transverse magnetic (TM) whispering gallery mode (WGM) frequencies in homogeneous gyroelectric circular cylindrical resonators of infinite length are derived. In addition, a volume integral equation (VIE)-cylindrical Dini series expansion method is extended to support the prediction of complex WGMs for continuously varying highly inhomogeneous gyroelectric circular cylindrical resonators. To this end, the entire domain orthogonal vectorial basis of VIE is extended to support very large indices of the involved Dini-type cylindrical vector wave functions via asymptotic closed-form expressions. This way, the eigenbasis required to solve the VIE becomes free of numerical instabilities arising when very large orders of the involved Bessel functions are employed. The complex frequencies obtained by the asymptotic closed-form expressions for the case of the homogeneous gyroelectric resonator, as well as those obtained by the VIE when the multilayered gyroelectric resonator is reduced to one layer, are validated by comparisons with the complex roots extracted by numerically solving the TE/TM characteristic equations obtained from the separation of variables method, using complex root finding techniques. We demonstrate the calculation of very high-order WGM frequencies for cylindrical resonators composed of homogeneous and highly inhomogeneous permittivity profiles. This asymptotic theory constitutes a rigorous tool that may serve for verifying method of analytical regularisation–based numerical solutions for other non-circular inhomogeneous cylinders, and for interpreting experimental data for applications such as WGM lasing, refractometric sensing, and magneto-optic coupling.

Computing resonant modes of circular cylindrical resonators by vertical mode expansions.

Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background. The resonant modes are complex-frequency outgoing solutions of the Maxwell's equations with no sources or incident waves. The method uses field expansions in one-dimensional (1D) "vertical" modes to reduce the original three-dimensional eigenvalue problem to 1D problems and uses Chebyshev pseudospectral method to compute the 1D modes and set up the discretized eigenvalue problem. In addition, a new iterative scheme is developed so that the 1D nonlinear eigenvalue problems can be reliably solved. For metallic cylinders, the resonant modes are calculated based on analytic models for the dielectric functions of metals. The method is validated by comparisons with existing numerical results, and it is also used to explore subwavelength dielectric cylinders with high-Q resonances and analyze gold nanocylinders.

Size-Independent Cylindrical Resonator Half-Filled With DNG Metamaterial and Excited by a Line Source

A circular cylindrical resonator with metallic (PEC) walls is half-filled with double-negative (DNG) metamaterial that is anti-isorefractive to the double-positive (DPS) material filling the remaining volume of the resonator. The resonance condition of the structure is studied, and it is shown that the resonator may perform independently of diameter size. The problem of an electric line source parallel to the axis and located anywhere inside the DPS region is solved exactly. Numerical results are presented and discussed .

Cylindrical Resonator Sectorally Filled With DNG Metamaterial and Excited by a Line Source

A circular cylindrical resonator with metallic walls is analyzed in the phasor domain. The resonator contains a wedge of double-negative (DNG) metamaterial that is anti-isorefractive to the double-positive (DPS) material filling the remaining volume of the resonator, and whose edge is located on the resonator axis. The resonance conditions are established. The problem of an electric line source parallel to the axis and located anywhere inside the DPS region is solved exactly. Numerical results are presented and discussed.

A Field Theoretic Foundation for the Representation of Quality Factor in Terms of Reactance-Slope Parameters for Electrically Large Three-Dimensional Arbitrarily Shaped Resonators

The use of reactance-slope parameters for the design of RF and microwave filters was drawn from lumped-element circuit representations. This paper provides a field-theoretic foundation for reactance-slope parameters based upon the treatment of arbitrarily shaped electrically large resonators comprised of electric and magnetic conducting enclosures. Traditional representations for these parameters in terms of the reactance for series-connected network elements and susceptance for parallel-connected network elements are related to electromagnetic fields. The resulting generalized expressions for reactance-slope parameters with utility for evaluating quality (Q) factor are developed for both electric and magnetic conducting resonators using strictly surface electromagnetic fields and sources. The generalized expressions are used to evaluate the unloaded Q for TE/sub 101/-mode rectangular resonators comprised of silver, copper, aluminum, and brass based upon two different standard rectangular waveguides with enclosed ends. Q results are also presented for TM/sub 011/-mode circular cylindrical resonators comprised of the same conducting materials. Results from the method here are compared to well-established results published in the literature. These expressions are useful for either analytically or numerically evaluating the reactance-slope parameter and Q factor.

Improved locally distorted CPFDTD algorithmwith provable stability

The contour path finite difference time domain (CPFDTD) method has been shown to give accurate results for curved metal structures. However, the numerical stability of this scheme is not guaranteed and significant skill is required to generate an appropriate grid. The authors present a modification to the two-dimensional CPFDTD method which ensures stability and which permits simple generation of the locally distorted grid. The accuracy of the scheme is demonstrated through calculation of the resonant frequencies of circular cylindrical resonators.

Weakly Coupled Dielectric Resonators

The resonant modes of a pair of coupled resonators of high epsilon/sub r/ are considered in the limit of large spacings D between resonators. Attention is focused on the lowest magnetic-moment mode, where the coupling effect leads to a split of the original mode into an even and an odd part. Formulas are obtained for the coupling coefficient, the resonant frequencies and Q of the modes. They are strikingly similar to those for weakly-coupled R-L-C circuits. The accuracy of the formulas is verified by comparing their predictions with direct numerical data, available for coupled circular cylindrical resonators.

Analysis of a Microwave Void Fraction Meter

The eigenvalue problem of an open-ended, dielectric loaded, circular cylindrical resonator is investigated by the boundary value and numerical techniques to compute the volumetric void fraction of gas bubbles in organic oil coolants used in some modern nuclear reactors. The resonator sensing section geometry is such that an organic coolant (or similar material) is transported through circular pipes acting as waveguides on both sides of the resonator section whose diameter is enlarged by a dielectric ring. The results are shown to be in excellent agreement with experimental data for the special case when the dielectric in the enlargement is the same the special case when the dielectric in the enlargement is the same as the transported material.