Effect of a small cylindrical inhomogeneity on the eigenfrequency of a semicylindrical dielectric resonator featuring an axially homogeneous eigenmode

A semicylindrical dielectric resonator with a thin cylindrical inhomogeneity in the region of the field antinode of a whispering gallery eigenmode has been studied. Characteristic equations determining the complex eigenfrequencies of such resonators with axially homogeneous eigenmodes are obtained. It is shown that the presence of a dielectric or conducting inhomogeneity leads to a frequency shift and causes additional energy losses of the eigenmode.     

Q-factor measurement of quasi-optical dielectric resonators under conditions of the whispering gallery mode degeneration removal

An approach that allows one to determine the unloaded quality factor of a quasi-optical dielectric resonator (QDR) under conditions of the resonance line splitting corresponding to twofold degenerative whispering gallery (WG) mode has been proposed. The resonator is represented by an equivalent network as two oscillatory circuits with a certain coupling between them. The approach allows one to determine the Q-factor of a single oscillatory circuit using three measured parameters, namely: 1) ratio between specific amplitudes of the resonator amplitude-frequency response (or its second derivative); 2) resonant frequency; and 3) frequency splitting of the response (or its respective second derivative). The proposed technique is illustrated by the measurements in the millimeter-wave range for sapphire quasi-optical resonators with conducting and high-T/sub c/ superconducting (HTS) film endplates.     

High-Q whispering modes in empty spherical cavity resonators

This work presents the study of high-order modes in spherical cavity resonators. In general there are resonant mode families, degenerate in frequency, that "whisper" around the spherical surface. We call these whispering spherical (WS) mode sets. Each set includes the well-known whispering gallery (WG) mode, which propagates like a ray around the azimuth. Also, we identify a new mode, which we label the whispering longitudinal (WL) mode. This mode propagates as a wave front along the longitudinal direction. The rest of the degenerate set propagates like a combination of the WG and WL modes. We show that transverse electric WS modes have high geometric factors, greater than 2000, which increase linearly with frequency. This is an order of magnitude greater than that of a TM/sub 010/ cylindrical resonator. Also, Q-factors as high as 65,000 at 13.3 GHz were measured at room temperature.     

Microwave oscillators incorporating cryogenic sapphire dielectricresonators

Progress is reported on efforts to develop a commercially-viable high purity X-band signal source incorporating a cryogenic sapphire dielectric resonator. The resonator design is of the whispering gallery type to take advantage of the excellent electromagnetic field confinement offered by this geometry. Complications resulting from the high spurious mode density of this type of resonator have been eliminated by developing a very accurate and complete mode analysis program which fully incorporates the dielectric anisotropies of the sapphire ring. This program allows the design of a window in the frequency domain where no unwanted modes exist, with accurate placement of the desired mode at the center of this region. Preliminary evaluation of the phase noise properties of simple oscillators incorporating these resonators have been performed. For example, in a dual-oscillator comparison of two oscillators operating near 13 GHz phase noise values of L(f)=-55 dBc/Hz, -145 dBc/Hz and -161 dBc/Hz were obtained for offset frequencies of 1 Hz, 1 kHz and 10 kHz, respectively     

Effect of the ellipticity of a dielectric resonator on the induced whispering gallery modes

The influence of ellipticity of a dielectric resonator on the whispering gallery (WG) oscillation modes induced by a lumped radiation source was studied. Dependence of the spectral characteristics of resonators and the spatial distributions of oscillation fields on the WG mode propagation direction is experimentally determined.     

Transmission and radiation in a slab waveguide coupled to a whispering-gallery resonator: volume-integral-equation analysis

The excitation of a whispering gallery resonator by a surface wave guided in a dielectric slab is analyzed with a rigorous volume-integral-equation approach. The analysis is based on the Green's function concept and the application of the entire-domain Galerkin technique through expansion of the electric field in the resonator in terms of cylindrical wave functions. The algorithm developed yields highly accurate results for the transmission and reflection coefficients in the waveguide. The radiated far field is computed, and the effect of the excitation of a whispering gallery mode on the radiation pattern is studied.     

Sensitivity and optimization of a high-Q sapphire dielectric motion-sensing transducer

A high-Q sapphire dielectric motion sensing transducer that operates at microwave frequencies has been developed. The device uses cylindrical whispering gallery modes of quality factor greater than 10 (5) at room temperature and greater than 10(8) at 4 K. The tuning coefficient of the transducer resonance frequency with respect to displacement was measured to be of the order of a few MHz/mum. An electromagnetic model that predicts the resonant frequency and tuning coefficient has been developed and was verified by experiment. We implemented the model to determine what aspect ratio and what dielectric mode is necessary to maximize the sensitivity. We found that the optimum mode type was a TM whispering gallery mode with azimuthal mode number of about 7 for a resonator of 3 cm in diameter. Also, we determined that the tuning coefficients were maximized by choosing an aspect ratio that has a large diameter with respect to the height. By implementing a microwave pump oscillator of SSB phase noise -125 dBc/Hz at 1 kHz; offset, we have measured a sensitivity of order 10 (-16) m/ radicalHz. We show that this can be improved with existing technology to 10(-18) m/ radicalHz, and that in the near future this may be further improved to 10(-19) m/ radicalHz.     

Distributed bragg reflector resonators with cylindrical symmetry and extremely high Q-factors

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE0qp mode cylindrical resonant cavity that constitutes a distributed Bragg reflection (DBR) resonator. The analysis considers an arbitrary number of alternating dielectric and free-space layers of cylindrical geometry enclosed by a metal cylinder. The layers may be arranged along the axial direction, the radial direction, or both. Given only the aspect ratio of the cavity, the desired frequency and the dielectric constants of the material layers, the relevant dimensions are determined from only a set of simultaneous equations, and iterative techniques are not required. The formulas were verified using rigorous method of lines (MoL) calculations and previously published experimental work. We show that the simple approximation gives dimensions close to the values of the optimum Bragg reflection condition determined by the rigorous analysis. The resulting solution is more compact with a higher Q-factor when compared to other reported cylindrical DBR structures. This is because it properly takes into account the effect of the aspect ratio on the Bragg antiresonance condition along the z-axis of the resonator. Previous analyses assumed the propagation in the z-direction was independent of the aspect ratio, and the layers of the Bragg reflector were a quarter of a wavelength thick along the z-direction. When the aspect ratio is properly taken into account, we show that the thickness of the Bragg reflectors are equivalent to the thickness of plane wave Bragg reflectors (or quarter wavelength plates). Thus it turns out that the sizes of the reflectors are related to the free-space propagation constant rather than the propagation constant in the z-direction.     

Three-Nucleon Forces and Triplet Pairing in Neutron Matter

We report an experimental study of the electrical properties of liquid helium-4 in the temperature range 1.2–3 K. The experiment is carried out in the millimeter wave range using a whispering gallery mode dielectric resonator, and the complex permittivity of liquid helium is extracted from the data using the resonant perturbation method. The results for the temperature dependence of the dielectric constant are consistent with the previous studies. In addition, we find strong enhancement of the loss tangent around the superfluid transition temperature.     

Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique

The anisotropic loss tangent has been determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. The Q-factors of quasi-TE and quasi-TM modes were measured precisely in four cylindrical sapphire resonators at room temperature, from which was determined a maximum attainable Q-factor of (2.1 +/- 0.2) x 10(5) at 9 GHz in a quasi-TM mode. Sapphire dielectric material from three different manufacturers was compared over the 270-345 K temperature range and the 5-16 GHz frequency range.     

Analysis of the rutile-ring method of frequency-temperature compensating a high-Q whispering gallery sapphire resonator

The rutile-ring method of dielectrically frequency-temperature compensating a high-Q whispering gallery (WG) sapphire resonator is presented. Two and three-dimensional finite element (FE) analysis has been implemented to design and analyze the performance of such resonators, with excellent agreement between theory and experiment. A high-Q factor of 30 million at 13 GHz, and compensation temperature of 56 K was obtained. It is shown the frequency-temperature compensation can occur either because the rutile adds a small perturbation to the sapphire resonator or because of a mode interaction with a resonant mode in the rutile. The characteristics of both of these methods are described, and it is shown that for high frequency stability, it is best to compensate perturbatively     

Computations of Unloaded Q 0-Factor and Resonant Frequency of the TE011 Mode Hakki–Coleman Dielectric Resonators with Coupling Structures Using ANSOFT HFSS

Microwave characterization of materials using dielectric resonators is based on measurements of the Q-factor of the resonator containing a sample under test and on the loss equation for the test structure. The loss equation contains geometrical factors, which are calculated assuming an ideal metallic cavity of the resonator. In this paper a rigorous analysis of cylindrical parallel plate dielectric resonators has been performed to assess the influence of the presence of coupling holes and cables on the unloaded Q-factor and resonant frequency. Calculations have been done for the TE011 mode resonators with differing cavity to dielectric diameter ratio, conductivity of the cavity material, loss tangent and relative permittivity of the dielectric rod, position of the coupling loops and size of the coupling cables. Results have shown that Qo-factors calculated for real resonators were smaller than Qo-factors for ideal resonators. Also this paper presents a brief history of analysis of dielectric resonators.     

Computations of Unloaded Q0-Factor and Resonant Frequency of the TE011 Mode Hakki–Coleman Dielectric Resonators with Coupling Structures Using ANSOFT HFSS

Microwave characterization of materials using dielectric resonators is based on measurements of the Q-factor of the resonator containing a sample under test and on the loss equation for the test structure. The loss equation contains geometrical factors, which are calculated assuming an ideal metallic cavity of the resonator. In this paper a rigorous analysis of cylindrical parallel plate dielectric resonators has been performed to assess the influence of the presence of coupling holes and cables on the unloaded Q-factor and resonant frequency. Calculations have been done for the TE011 mode resonators with differing cavity to dielectric diameter ratio, conductivity of the cavity material, loss tangent and relative permittivity of the dielectric rod, position of the coupling loops and size of the coupling cables. Results have shown that Qo-factors calculated for real resonators were smaller than Qo-factors for ideal resonators. Also this paper presents a brief history of analysis of dielectric resonators.     

Plasmonic whispering gallery cavities as optical nanoantennas

We study the resonant modes of surface plasmon whispering gallery cavities based on a circular groove in a Au surface. We use spatially, angle-, and polarization-resolved cathodoluminescence spectroscopy to measure the resonant plasmonic local field distribution at deep-subwavelength resolution and determine the far-field radiation distribution for each plasmonic mode. We show mode-selective excitation of the plasmonic modes and resolve the modal angular radiation pattern. The results show that plasmonic whispering gallery resonators can be used as versatile antennas both in receiving and transmitting mode.     

Effect of a ring layer filled with various substances on the eigenfrequency and Q-factor of a cylindrical quasi-optical dielectric resonator

The influence of a ring layer filled with various substances on the eigenfrequency and Q-factor of a cylindrical quasi-optical dielectric (Teflon) resonator has been investigated. The spectral and energy characteristics of an axially homogeneous whispering gallery eigenmode of this resonator are analyzed for the first time as dependent on the radius and thickness of the ring layer. It is established that the eigenfrequency behaves differently when the ring layer is filled with liquids characterized by large and small losses.     

The analog of the Kanazawa-Gordon formula for cylindrical resonators

In this paper, a formula relating the shift in the resonant frequency of a shear piezoceramic cylindrical resonator to the viscosity of a Newtonian liquid that loads the resonator surface was established. This formula is analogous to the classical Kanazawa-Gordon formula that describes the change in the resonant frequency of a shear planar resonator loaded with a Newtonian liquid. To this end, the author applied the perturbation method to analyze the behavior of the piezoceramic cylindrical resonators vibrating in a shear mode and loaded with a viscous liquid. The shift in resonant frequency obtained using the perturbation method (mechanical model) was compared to an exact value of the shift in resonant frequency obtained from the complete electromechanical model (admittance diagrams) that describes shear vibrations of a piezoceramic cylindrical resonator loaded with a viscous liquid. Good conformity between the two types of results obtained can prove the correctness of the analytical formulas established in this paper. The results of this work can be applied for the design and construction of viscosity sensors.     

Thermal control of a dual mode parametric sapphire transducer

We propose a method to control the thermal stability of a sapphire dielectric transducer made with 2 dielectric disks separated by a thin gap and resonating in the whispering gallery (WG) modes of the electromagnetic field. The simultaneous measurement of the frequencies of both a WGH mode and a WGE mode allows one to discriminate the frequency shifts due to gap variations from those due to temperature instability. A simple model, valid in quasi-equilibrium conditions, describes the frequency shift of the 2 modes in terms of 4 tuning parameters. A procedure for their direct measurement is presented.     

Whispering gallery modes induced in a partly shielded hemispherical dielectric resonator

Whispering gallery modes induced in a partly shielded hemispherical dielectric resonator by lumped radiation sources were experimentally studied for the symmetric and asymmetric arrangement of the hemisphere relative to the cylindrical metal shield. The oscillation mode characteristics are presented for the shielded hemispherical resonator and an analogous open dielectric resonator. The proposed resonator is a promising device for the creation of highly stable solid-state millimetric wave oscillators.     

Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities

We show that the artificial resonances of dielectric optical cavities can be used to enhance the detection sensitivity of evanescent-wave optical fluorescence biosensors to the binding of a labeled analyte with a biospecific monolayer. Resonant coupling of power into the optical cavity allows for efficient use of the long photon lifetimes (or equivalently, the high internal power) of the high-Q whispering gallery modes to increase the probability of photon absorption into the fluorophore, thereby enhancing fluorescence emission. A method to compare the intrinsic sensitivity between resonant cavity and waveguide formats is also developed. Using realistic estimates for dielectric cylindrical cavities in both bulk and integrated configurations, we can expect sensitivity enhancement by at least an order of magnitude over standard waveguide evanescent sensors of equivalent sensing geometries. In addition, the required sample volume can be reduced significantly. The cylindrical cavity format is compatible with a large variety of sensing modalities such as immunoassay and molecular diagnostic assay.     

High performance distributed Bragg reflector microwave resonator

A new resonator device structure is described that achieves Q-factors well above those currently realizable for conventional room temperature microwave structures. The new structure consists of a microwave cavity, for which the enclosure walls consist of distributed Bragg reflectors (DBR) made of low-loss sapphire. For this configuration, most of the resonant field resides in empty space, with small field strengths in the thin layers of sapphire which comprise the DBR structure. The physical structure takes the form of interpenetrating concentric rings and plates of low-loss sapphire contained in a cylindrical metal enclosure. The theoretical analysis of the DBR resonant structure allows the positions and dimensions of the component rings and plates to be precisely determined for a specified resonant frequency. The resonator Q can be accurately calculated, and plots of the resonant fields clearly show the physical mechanism leading to the observed efficiency of this resonator structure. Experimental results are given for resonators designed at 9.0 and 13.2 GHz. The measured unloaded Q's at room temperature are over 650000 and 450000, respectively.