Yoshiro Tomabechi

Resonance characteristics of whispering-gallery modes in an elliptic dielectric disk resonator

This paper presents a novel calculation method for resonance characteristics of an elliptic dielectric disk resonator. In the elliptic resonator, electromagnetic energy propagates as a whispering gallery (WG) mode along the edge region of the dielectric disk. In the novel analysis, a local propagation constant of the WG mode at each point of the elliptic disk edge is represented by a propagation constant of a WG mode in a circular disk whose radius of curvature, material constants, and thickness are equal to those of the elliptic disk. Therefore, we can easily calculate the resonance characteristics of the elliptic dielectric disk resonator by applying a conventional technique for the circular dielectric disk. The calculated results of the resonant frequencies and field distribution are well confirmed by experiments.

Reflection and transmission characteristics of an uncoincidental junction on rectangular dielectric waveguides

A novel approach to the analysis of an uncoincidental junction in a rectangular dielectric waveguide is presented. The boundary condition equations on the junction plane are presented through the tangential components of guided modes and radiation modes which are excited at the discontinuity. To obtain the reflection and transmission coefficients at the discontinuity, the equations are transformed into the spectral domain by the two-dimensional Fourier transformation. In the spectral domain, the orthogonal relationship between the guided and radiation modes is used to determine the reflection and transmission coefficients approximately. The parameters corresponding to the phase constant of the radiation fields in the spectral domain are defined by using an iterative calculation. The reflection and transmission coefficients are determined exactly. These coefficients are compared with 10-GHz band experiments. The analysis shows good agreement with experimental results. >

Coupling characteristics of eccentric arranged dielectric disk and ring

An analysis is presented for a novel coupling configuration in which a circular dielectric disk and ring are arranged eccentrically. Whispering gallery (WG) mode coupling characteristics between the dielectric disk and ring are investigated. In this paper, a coupled-mode equation based on the Lorentzs reciprocity theorem is utilized. Distributed coupling coefficients and electric field distributions around the coupling region are obtained numerically through solving the coupled-mode equation. The theory described in this paper is confirmed by comparing measured electric field distributions with calculated ones. Electromagnetic powers flowed along the disk are also calculated. It is shown that coupling quantity of the eccentric configuration would be easily controlled by changing a radius of the disk or ring. The results obtained here will be used to design a WG mode coupled resonator for millimeter wave integrated circuits.

Reflection and transmission coefficients of rectangular dielectric waveguide discontinuity with an air gap

Reflection, transmission, and radiation characteristics of rectangular dielectric waveguide discontinuities with an air gap are analyzed. A transverse displacement with the air gap is also treated. The characteristics of this discontinuity have never been analyzed with a conventional slab model. In this analysis, a two-dimensional Fourier transformation and orthogonal relations between guided and radiation modes are utilized. Calculations and experimental results in X-band are compared, and good agreement is found. To discuss the numerical results, the principle of energy conservation is introduced. The discrepancy between the results and this principle is less than 0.0003. >

A novel analysis for eigenvalues of a dielectric disk resonator with a high dielectric constant

A new analysis for eigenvalues of Whispering Gallery Modes on a three-dimensional disk resonator with a high dielectric constant is presented. In this analysis, a Generalized Effective Dielectric Constant Method is applied with some modification. The disk resonator is considered to be decomposed into two-dimensional slab waveguides and a cylindrical dielectric rod resonator. A concept of an effective dielectric constant and a caustic radius are newly introduced to obtain the eigenvalues of Whispering Gallery Modes. As a result of comparison with numerical eigenvalues and experimental ones, it is found that this analytical method is useful even so the dielectric disk resonator has a high dielectric constant.

A method for evaluating a complex permittivity of dielectric material by using whispering gallery modes on a spherical resonator

We have developed a new method for evaluating a complex permittivity of a dielectric material by using whispering gallery mode on a spherical dielectric resonator. As eigenvalue equations of the spherical resonator can be derived correctly without any approximations, we can expect a precise evaluation of the complex permittivity. In our estimation, the Newton method is used. Not only numerical resonance frequencies and unloaded quality factors derived from the eigenvalue equation but also these resulted from our experiments in millimeter wave region are substituted into the Newton method formula. We have also iterated the formula to converge the complex permittivity of the dielectric materials. Comparing our complex permittivity with a conventional value, it shows good agreement each other.

An analysis for resonance characteristics of whispering gallery modes on an elliptic dielectric disk

We analyze the resonance characteristics of whispering gallery modes on an elliptic dielectric disk resonator. We assume that the elliptic disk is decomposed into a slab waveguide having the same thickness as the elliptic disk and an elliptic rod having the same cross section as the disk. On a basis of an effective dielectric constant method, an effective permittivity of the rod resonator is derived from the propagation constant of the slab waveguide. Approximated resonance frequencies of the elliptic disk are given by an eigenvalue equation of the elliptic rod resonator with the effective permittivity. We have also performed experiments to confirm the validity and usefulness of our analysis. As a result of our study, it has been found that the present analysis is very simple and useful even if the elliptic disk has a high permittivity.

Improved analysis of resonance characteristics for high permittivity dielectric elliptic disk resonator

A new analytical method for eigenvalues of Whispering Gallery Modes in a dielectric elliptic disk is developed. The analysis has an advantage that high accuracy can be realized in the eigenvalue calculation, even if the permittivity and/or ellipticity is large. The resonance frequencies and field distributions are calculated by this method. These numerical results are in good agreement with experimental ones in microwave region. The new analytical method and results will be applied to basic design of dielectric resonators and filters in millimeter wave integrated circuits.