This paper presents a measurement method for determining effective conductivity of copper-clad dielectric laminate substrates in the millimeter-wave region. The conductivity is indirectly evaluated from measured resonant frequencies and unloaded Q values of a number of Whispering Gallery modes excited in a circular disk sample, which consists of a copper-clad dielectric substrate with a large diameter of 20-30 wavelengths. We can, therefore, obtain easily the frequency dependence of the effective conductivity of the sample under test in a wide range of frequency at once. Almost identical conductivity is predicted for two kinds of WG resonators (the copper-clad type and the sandwich type) with different field distribution; it is self-consistent and provides the important foundation for the method if not for the alternative method at this moment. We measure three kinds of copper foils in 55-65 GHz band, where the conductivity of electrodeposited copper foil is smaller than that of rolled copper foil and shiny-both-sides copper foil. The measured conductivity for the electrodeposited copper foil decreases with an increase in the frequency. The transmission losses measured for microstrip lines which are fabricated from these substrates are accurately predicted with the conductivity evaluated by this method.

We have derived the novel extended UTD (Uniform Geometrical Theory of Diffraction) solution and the novel modified UTD solution for the back scattering of an incident whispering gallery (WG) mode on the edge of a cylindrically curved conducting sheet. By comparing with the reference solution obtained from the integral representation of the scattered field by integrating numerically along the integration path, we have confirmed the validity and the utility of the novel asymptotic solutions proposed in the present study. It is shown that the extended UTD solution can be connected smoothly to the modified UTD solution on the geometrical boundary separating the edge-diffracted ray and the surface-diffracted ray.

When a cylindrically curved concave conducting surface is terminated abruptly at the edge, the whispering gallery (WG) mode propagating toward the edge direction is radiated into the free space from the aperture plane at the edge. In this paper, by applying the new analysis method, we shall derive a uniform geometrical theory of diffraction solution (UTD) for the electric-type WG mode radiation field applicable in the transition region near the geometrical boundaries produced by the incident modal ray on the edge of the curved surface. The UTD is represented by the summation of the solution for the geometrical ray converted from the modal ray of the WG mode and the solution for the uniform edge diffracted ray scattered at the cylindrically curved edge. By comparing with the reference solution obtained numerically from the integral representation of the radiation field, we will confirm the validity and the utility of the UTD proposed in this paper.

A millimeter wave BPF constructed from the WG mode dielectric disk resonators is presented. The design chart for the high Q WG mode resonator is obtained from Qu calculation of some WG modes. By using the design chart, high Q WG mode resonator having no influence of unwanted higher order resonances is designed. Designed resonators have different diameter and various Resonance Frequency Separation respectively. A 3 stage maximally flat BPF is constructed so that each resonator may be coupled laterally on the edge of the disk. Designed center frequency is 62.47 GHz and 3 dB bandwidth is 100 MHz. As a result, this BPF has insertion loss of 1.5 dB and some spurious responses which were existed conventional WG mode BPF are reduced considerably.

A cryogenic Whispering Gallery sapphire resonator oscillator has been investigated using a 4 K pulse-tube cryocooler. The turnover temperature of the chosen mode in the sapphire crystal was 9.17 K with an unloaded Q-factor of 7108. The prototype sapphire-loaded cavity oscillator was designed to oscillate at 9.195 GHz. A fractional frequency stability of 210-13 was measured at integration times of 10 s.

A frequency-tuning method in the microwave region, which maintains a high unloaded Q-factor, was demonstrated using a double-sapphire-loaded cavity which operates on the Whispering Gallery mode, WGH9,1,0. Two adjacent nominally identical sapphire cylinders were positioned in a copper cavity and tuned by changing their relative coupling. A frequency tuning range of 85 MHz and a maximum unloaded Q-factor of 1.3 105 was experimentally measured at room temperature. This is only 13% less than the single resonator Q-factor, which is a small compromise to pay for the increased tuning capacity.

We calculated linear and nonlinear responses of a Kerr nonlinear microsphere sandwiched by two prisms using the excitation of whispering gallery modes due to near-field coupling. As numerical calculations, the finite-difference time-domain method that takes into account the Kerr nonlinear effect was used. We dealt with two types of spheres, i.e., the Kerr-material sphere and the dielectric sphere coated by the Kerr material. It was found that the optical switching phenomena are induced in such spheres. The switching results from the fact that the variations of the refractive index of the nonlinear spheres affect the excitation condition of the whispering gallery modes.

Using a point matching method, we have numerically analyzed resonance frequencies and unloaded Q factor of whispering gallery modes in a millimeter wave region that are well known as an intrinsic mode of a dielectric disk resonator. We express field distributions of the resonance modes by a summation of spherical waves. Tangential electromagnetic fields inside the disk are matched to those outside the disk at appropriate matching points on a boundary. As the result, a 4N 4N (N; number of matching points) determinant is derived as an eigenvalue equation of the disk resonator. Since elements of the determinant are complex numbers, a complex angular frequency is introduced to make a value of the determinant zero. For a location of the matching points, we also introduce a new technique which is derived from a field expression of the whispering gallery modes. Since an azimuthal angle dependence of the field distributions with a resonance mode number m is presented by the associated Legendre function Pnm(cos θ), we define abscissas θi of the matching points as solutions of Pm+2N-1m (cos θ) = 0. Considering the field symmetry, we also modify the eigenvalue equation to a new eigenvalue equation which is expressed (4N - 2) (4N - 2) determinant. From the results of our numerical analysis, we can find that the resonance frequencies and unloaded Q factor well converge for number of matching points N. A comparison of numerical results and experimental ones, in a millimeter wave band (50 - 100 GHz), shows a good agreement with each other. It is found that our analysis is effective for practical use in the same wave band.

The millimeter wave filter using two whispering-gallery mode dielectric disk resonators is presented in this paper. The coupling coefficients of dual disk resonators and the external Q values of the single resonator excited by a dielectric waveguide are investigated theoretically and experimentally. A 2-stage bandpass filter which is designed at the center frequency of 69.85 GHz with a bandwidth of 500 MHz shows a low-loss property of 1.8 dB insertion loss.

Resonance characteristics of a coupled dielectric resonator which consists of a Whispering Gallery mode dielectric disk resonator and a ring resonator located eccentrically are analyzed. New analytical results of resonance characteristic based on the distributed coupling phenomena between the disk and the ring are obtained. The resonance performances have also been verified experimentally on X band model. We have found that Free Spectral Range of the coupled resonator is several times larger than that of the single disk resonator and the single ring resonator, respectively. As a result, the eccentric coupled resonator discussed in this paper can be used as a frequency selective element in millimeter wave integrated circuits.

To evaluate the radial eigenmode field distributions and the resonance wavelengths of axially symmetric pillbox resonator, a numerical method is described which is based on the FE-BPM expression in cylindrical coordinates. Under the weakly guiding approximation, we solve Fresnel equation and can get a fairly accurate result. By using effective index method, 3-D pillbox guiding structure is reduced to 2-D one which is then used for the analysis. One advantage of this method is that it is applicable for the axially symmetric optical waveguides with arbitrary index distribution. The validity of this method is checked by comparing the results of this method with those of the analytical ones. This method is applied for the evaluation of the coupling properties of a coupled structure consisting of a pillbox resonator and a curved waveguide placed outside the pillbox. This coupled structure has a good prospect to be used as optical wavelength filter. By varying the separation distance between the pillbox and the outer curved waveguide, the power transfer due to coupling is determined near the resonance wavelength 0.9 µm.

A three-dimensional analysis of Whispering-Gallery modes (W. G. modes) in a coaxial dielectric resonator is proposed and presented. The coaxial dielectric resonator is constructed from a lossy dielectric disk and ring which have diameters of several tens times as large as wavelength. Eigenvalue equations of the W. G. modes are derived rigorously from field expressions and boundary conditions. The resonant frequencies, unloaded Q values and field distributions are calculated numerically from the eigenvalue equations. These calculated results are in good agreement with experimental ones for an X band model. As a result, it is shown that a considerable quantity of modal energy can be confined in a loss-less gap between the disk and ring, and then the unloaded Q value is higher than that of a conventional dielectric disk and ring resonator.