K. Takiyama

On the Complex Resonant Frequency of Open Dielectric Resonators

An analytical method is presented for calculating accurately the complex resonant frequency of dielectric pillbox resonators. In this method, an approximated field of the resonator is expanded into a truncated series of solutions of the Hehnholtz equation in the spherical coordinates, and the boundary condtion on the resonator surface is treated in the least-squares sense. The resonant frequency and the intrinsic Q value due to radiation loss are obtained in the form of approximation converging to the exact values. Numericaf results are compared with previously published calculations, which show that the present method is a relatively simple and effective one.

Analytical and Experimental Investigations on Several Resonant Modes in Open Dielectric Resonators

The complex resonant frequency of open dielectic pillbox resonators is analyzed by an analytical method proposed by the present authors, which expands the field into a truncated series of solutions of the Hehnholtz equation in the spherical coordinates and treats the boundary condition in the least-squares sense. This method is applied to calculate the characteristics of several resonant modes which will be of practical use. The accuracy of the method is confirmed by investigating the convergence of solutions. Also, numerical results are compared with experimental results of several resonant modes, which are obtained for the dielectric samples with epsilon/sub r/= 38.0 and 19.5 in the X-band.

Guided-Wave Experiments with Dielectric Waveguides Having Finite Periodic Corrugation

A planar dielectric waveguide having finite periodic rectangular corrugation is investigated analytically and experimentally, in case of surface waves propagating at an angle to the corrugation. In analytical considerations, a finitely corrugated guide is regarded as consisting of many step discontinuities connected by a length of uniform slab waveguide, and its propagation characteristics in the Bragg interaction region are derived from a cascaded connection of the transmission matrix expressing a step discontinuity. Although the present method takes only surface wave modes into account and neglects the wave with continuous spectrum, the calculated results show an excellent agreement with experimental ones which are performed for art H-guide in the microwave region.

Submillimeter Guided-Wave Experiments with Dielectric Rib Waveguides

The transmission characteristics of rib waveguides are examined in the submillimeter-wave region at Lambda/sub 0/ =337 µm. A number of miniature polyethylene rib waveguides are fabricated by means of a die-cast technique. The mode launching into such a waveguide is performed by focusing a laser beam directly on the end face of the waveguide, while the transmitted power is detected at any point on a waveguide through a movable grating coupler which can couple selectively with one of propagating modes. The measured phase constants show good agreement with the theoretical ones calculated by our analytical method, while the attenuation constants, typicafly alpha lambda /sub 0/ = 4.5 X 10/sup -3/ are found to be about 1.8 times as much as theoretical ones. Finally, the good confinement of fields in the rib portion is proved by means of two simple methods.

Two-path cutoff waveguide dielectric resonator filters

The authors propose an evanescent-mode wave-guide filter consisting of two parallel cutoff waveguide paths with dielectric resonators. They introduce an accurate design method incorporating both the full-wave analytical method and the impedance inverter method. The specified overall characteristic is then synthesized with the help of a computer-aided design method. Measurements on several kinds of filters modeled at X-band show excellent agreement with the designed characteristics. >

Analytical and Experimental Considerations on the Resonant Frequency and the Quality Factor of Dielectric Resonators

A dielectric pillbox resonator placed on a dielectric substrate is analyzed by a new method, the approximate mode matching method, in which the cross section of such a resonator is subdivided into several sub-sections having a simple geometry of the boundaries, i.e., dielectric slab radial waveguides, and the continuity condition of fields between subsections is treated in the least-squares sense. The resonant frequencies and the intrinsic Q values due to the leakage loss through the dielectric substrate calculated by this method are presented together with experimental results obtained in the 50-GHz region. As a result, it is found that the experimental results for both the resonant frequencies and the Q values agree better with our calculated ones than with the results by other approximate method, and so it will be concluded that the analytical method presented here is almost enough to discuss precisely the resonant characteristics of a dielectric pillbox resonator.

Eigenvalues of a nonconfocal laser resonator with an output-coupling aperture.

A nonconfocal laser resonator that has output-coupling apertures has been analyzed using the matrix eigenvalue technique. Numerical calculations of eigenvalues and eigenfunctions are performed for the interesting resonator consisting of one plane mirror with a coupling aperture and one spherical mirror. The effects of the coupling aperture are also discussed for several kinds of modes when both the mirror and coupling- aperture Fresnel numbers vary. It is found that the power loss of the TEM(00) mode becomes nearly constant in a finite range of the mirror Fresnel number. In such a range, the major source of a resonator loss is the power coupling through an aperture, and the coupling loss can be estimated independently of the loss caused by the spillover at mirror edges.

Microwave Network Representation of Discontinuity in Open Dielectric Waveguides and its Applications to Periodic Structures

A network approach is proposed for analyzing the interaction of discontinuities in open dielectric waveguides by taking account of the continuous spectrum accurately. This approach develops an unprecedented method to investigate the effect of finite length of periodic structures on their transmission characteristics. This paper discusses this effect on the radiation patterns when a finite periodic structure is operated in the leaky wave region, while in a different regime of operation, we present a new and completely theoretical accurate procedure for the design of grating filters on a dielectric image waveguide, demonstrating successful experiments.

Mode Propagation Through a Step Discontinuity in Dielectric Planar Waveguide

This paper presents two methods for dealing with wave propagation through a dielectric step discontinuity at normal incidence. One method helps to accelerate the convergence of solutions, especially for the TM-mode problem, and the other treats efficiently the continuous mode spectrum by introducing the Legendre transform in the case of open waveguides. As for the former, the singular fields around the dielectric edges are introduced in terms of direct use of their functional forms to the boundary condition, which is fulfilled in the sense of least squares. As for the latter, the expansion in terms of the Legendre functions is performed for optimally divided ranges of a continuous spectrum. A number of numerical examples prove that the methods presented herein are quite powerful for solving the TM-mode discontinuity problems in dielectric waveguides of both closed and open types.

Two-Path Cutoff Waveguide Dielectric Resonator Filters

We propose here a new idea to design filters for achieving new levels of performance. This type of filters is made of a rectangular waveguide with a partial H-plane bifurcation. Each bifurcated section finite in length operates as a cutoff waveguide, at the central part of which low permittivity dielectric resonators are loaded. An accurate CAD program is developed which is based on a procedure that takes into account the effect of not only the dominant, but also a large number of higher order modes generated at discontinuities . Experiments for X-band trial filters designed by a new program show good agreements with the theory.